A distributed probabilistic system for adaptive regulation of image processing parameters

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS-PART B: CYBERNETICS, VOL. 26, NO. I, FEBRUARY 1996 1

A Distributed Probabilistic System for Adaptive Regulation of Image Processing Parameters

Vittorio Murino, Member, IEEE, Gian Luca Foresti, Member, IEEE, and Carlo S. Regazzoni, Member, IEEE

Abstract-A distributed optimization framework and its application to the regulation of the behavior of a network of interacting image processing algorithms are presented. The algorithm parameters used to regulate information extraction are explicitly represented as state variables associated with all network nodes. Nodes are also provided with message-passing procedures to represent dependences between parameter settings at adjacent levels. The regulation problem is defined as a joint-probability maximization of a conditional probabilistic measure evaluated over the space of possible configurations of the whole set of state variables (i.e., parameters). The global optimization problem is partitioned and solved in a distributed way, by considering local probabilistic measures for selecting and estimating the parameters related to specific algorithms used within the network. The problem representation allows a spatially varying tuning of parameters, depending on the different informative contents of the subareas of an image. An application of the proposed approach to an image processing problem is described. The processing chain chosen as an example consists of four modules. The first three algorithms correspond to network nodes. The topmost node is devoted to integrating information derived from applying different parameter settings to the algorithms of the chain. The nodes associated with data-transformation processes to be regulated are represented by an optical sensor and two filtering units (for edge-preserving and edge-extracting filterings), and a straight-segment detection module is used as an integration site. Each module is provided with knowledge concerning the parameters to regulate the related processing phase and with specific criteria to estimate data quality. Messages can be bidi- rectionally propagated among modules in order to search, in a distributed way, for the “optimum” set of parameters yielding the best solution. Experimental results obtained on indoor images are presented to show the validity of the proposed approach.

I. INTRODUCTION

MAGE understanding (IU) is one of the most challenging I research fields currently being investigated. The apparent facility with which humans perform such a task is in stark contrast to the difficulties encountered by computer vision (CV) systems to obtain comparable performances. Generally, a CV system splits an IU problem into several subproblems corresponding to different abstraction levels at which signals can be represented [l]. Each subproblem can be managed by a different processing unit, so the main issue is the design of integration strategies for a consistent cooperation between units. The simplest decomposition proposed is a hierarchically arranged set of modules which roughly reflect

19, 1995. This work was supported by the European Community under Contract no. MAST-0028-C (MOBIUS).

The authors are with the Department of Biophysical and Electronic Engi- neering, University of Genoa, 16145 Genova, Italy

Publishel Item Identifier S 1083-4419(96)00415-3.

Manuscript received August 14, 1992, revised April 24, 1994, and January

the partition of an IU problem into low, intermediate, and high levels [1]-[3]. One of the main constraint a distributed representation must satisfy is the capability to represent, in a uniform way, problems faced at different abstraction levels. The design of an efficient representation method and of an integration strategy to maintain consistency at the different abstraction levels [4] of an IU architecture are among the problems addressed in this paper. Uniformity allows a high degree of modularity and facilitates the development of a general and robust integration strategy. In particular, a general methodology for the distribution and the integration of high- level and low-level knowledge still represents an open problem to be solved.

This paper describes a fine-grain distributed framework whose processing modules are associated with separate algorithms and cooperate actively on the solution of an IU problem. Each module can receive and send messages from and to adjacent Ievels; moreover, it can infer knowledge (i.e., solutions) locally, thus allowing the achievement of solutions constrained by a-priori knowledge and available data represented at different levels [5]. Distributed representations and distributed inference allow the system to check local solutions (i.e., algorithm parameter settings) without waiting for the high-level symbolic phase to evaluate whether or not the process succeeded. A distributed reasoning mechanism for parameter selection consistent through different levels of an IU system is a peculiarity of the present framework, even though such a mechanism represents a necessity and has been considered, to some extent, for other IU systems [4], [6]-[81.

Regularization theory [9], [ 101 somehow resembles the problem considered here, in that this theory requires that a- priori knowledge be used at different levels to constrain a searched solution. The main contribution of such an approach is to provide numerical methods capable of efficiently representing a-priori constraints at the signal level [4] that control explicitly the status of the solution by means of cost func- tionals. A generalization of regularization theory to multiple levels, in a distributed way, leads to a knowledge-based (KB) approach to vision (e.g., [4], [171) that can be defined as an intensional approach [l 11. One of the characteristics of an intensional system is that the status can be linked directly to an uncertainty measure. In this sense, the measure provided by the cost functional associated with regularization theory can be regarded as an uncertainty measure.

In this paper, we propose an architecture that is based on an intensional KB control structure and that allows the progressively estimated system status to be represented and

10834419/96$05.00 0 1996 IEEE

2 IEEE TRANSACTIONS ON SYSTEMS. MAN, AND CYBERNETICS-PmT B: CYBERNETICS, VOL. 26, NO. 1, FEBRUARY 1996

DETECTION

EDGE EXTRACTION

REGULATION

SUGGESTIONS ’ ( m m e s s a g e )

DATA @U message) -

LOCAL -’ REGULATION

Fig. 1. trolled by a regulation unit.

General system architecture where each processing module is con-

evaluated in an explicit and distributed way. Normal actions are represented by data propagation along the hierarchical chain of modules, through successive adaptively regulated transformations. Backtracking actions can be performed to take modules out of inconsistent states and then to obtain the best final result. Adaptive regulation pursues the goal of reducing loss of information when input data are progressively mapped into recognition-oriented descriptive primitives. The system performs adaptive regulation of image processing parameters (Fig. 1) at each level by using both locally available a-priori information and constraints derived from solutions obtained at adjacent levels. Globally, the system is modeled as a hierarchical Bayesian Network [ll], i.e., a set of nodes associated with random variables. Each node is interpreted as a module M, of the system and is characterized by a) a parametrized transformation process T,, b) a set of random variables P, corresponding to the parameters of T,, c) the data d, produced by T,, and d) an uncertainty value Q, representing the “quality” of d, (see Fig. 2). The quality value Qz allows each module Adt to evaluate the produced data directly and to estimate the status of the system indirectly. The strategy for tuning the transformation process is based on belief revision theory (BRT) [ 111. BRT is applied to the problem of determining, in a distributed way, the optimal parameters for the set of transformations involved in an IU problem; a probabilistic measure, named belief, is derived from the global optimization criterion and locally maximized. Belief takes into account local knowledge as well as information coming from neighboring nodes. Belief is not defined as in [ l l ] , for a term representing local knowledge is introduced here, which makes it possible to search for a solution even in the absence of incoming top-down messages.

To demonstrate the feasibility of our approach, we consider, as an example, a hierarchical system made up of a chain of

four processing modules. The four modules are represented by a physical device (a camera), a noise-filtering algorithm (i.e., the Perona-Malik edge-preserving smoothing process), an edge-extraction algorithm (the Canny filtering), and a straight- line detection module (i.e., a modified Hough transformation). The first three modules need to be regulated, and the topmost module is inserted to demonstrate the usefulness of extracting information from each solution (progressively produced by the system) to generate a more complete and more reliable scene description. In particular, one of the novel aspects of the system lies in the regulation strategies used at the camera level. Commercial auto-focus and auto-iris methods can partially accomplish the regulation task but are less reliable, in that they do not allow context-dependent regulation. Such methods are not capable to make regulation strategies depend on external information sources, and adaptive parameter setting is usually applied only to specific image areas (typically, the center of an image for auto-focus). Therefore, no context-dependent and spatially varying regulation actions can be performed. Another novelty is the possibility of integrating the solutions provided by the system during the searching process. This capability has been added after noticing that parameters corresponding to the optimal quality of extracted data may spatially vary in an image. Consequently, as at some levels (e.g., the camera level) it is not physically possible to extract all necessary information by only one parameter setting, it may be useful to extract information by separate settings and then to integrate all information at higher abstraction levels, when possible. On the basis of this consideration, in the example given in the paper, straight lines are extracted starting from the set of edge images produced by the edge-extractor module. These images have been obtained by using different parameters along the processing chain and are characterized by space-varying quality values, which are used by the integration module to weight input information.

The described example represents a possible application of the proposed architecture and does not limit the general applicability of the approach. The proposed method is general as far as one deals with problems that can be solved by performing successive parametrized transformations whose outputs can be evaluated by defining specific quality criteria. However, the example presented here has its own degree of generality, as the specific modules used for it are shared (as initial processes) by many recognition systems [7], [17], and represent the basis for building up a complete IU system.

Little has been proposed in the literature to address the problem of controlling processing phases to obtain optimal performances, and no commonly accepted solutions have so far been provided. Nazife and Levine [6] proposed an expert system architecture for optimal image segmentation based on Gestalt psychology [ 121 and psychophysical vision criteria. They addressed explicitly both a quantitative and a qualitative evaluation of intermediate results, but did not impose any particular constraints on the interpretation phase. In the VISIONS framework [3], [7], [SI, [13] and in the other system versions (e.g., schema system [3]), Hanson, Riseman and others realized a KB architecture capable of performing symbolic pattern recognition and image interpretation of

MURINO et al.: DISTRIBUTED PROBABILISTIC SYSTEM FOR ADAPTIVE REGULATION 3

three-dimensional scenes by supervising low-level processing phases. These systems and our approach have several points in common, e.g., a common knowledge representation at different levels and an explicit knowledge of low-level algorithms. However, the techniques used to manage data uncertainty are related to rules rather than to the system status. Consequently, uncertainty management is not homogeneous at the various system levels, and strategies for algorithm regulation are not explicitly addressed. In [14], a paradigm for image interpretation was proposed that takes into account interactions between abstraction levels; it practically followed the approach described in [7], with the only difference of using two intermediate levels controlled by high-level symbolic reasoning. However, none of the above systems applies a theoretical intensional control scheme, which is the basis for a mutual cooperation among the modules, nor is knowledge propagated down to the lowest level (i.e., the acquisition process), as in our approach.

To sum up, the main novel aspects introduced into this paper are: 1) design of a hierarchical IU architecture where the different processing levels cooperate actively with one another to attain a final goal; 2) application of distributed probabilistic reasoning, based on belief revision theory [ 111, for parameter control within an IU system; 3) use of specific techniques for tuning the algorithms along the processing chain, starting from the image acquisition process unlike other similar systems (e.g., VISIONS); 4) use of an integration strategy for fusing the solutions obtained by different parameter settings.

The paper is organized as follows. In Section 11, a theoretical approach to the regulation problem is defined, a possible solution is proposed, and it is shown that, under suitable hypotheses, the proposed solution can be realized by using the algorithm described in the paper. In Section 111, the prototypi- cal quality-evaluation and parameter-regulation subprocesses are outlined, and, in Section IV, the functioning of each processing module is illustrated, specifying the parameters used to judge data and those used to regulate the algorithms adopted. Finally, results on sets of indoor images are reported in Section V where comparative tests are also described to demonstrate the improvement of results over those obtained by classic applications of the same algorithms.

11. PROBLEM STATEMENT

A. Bayesian Network and Belief Revision

The various processing steps to be performed for image understanding can be represented by a set of hierarchical nodes inside a singly connected network (see Fig. 2). This network processes data obtained by using redundant, often inaccurate, evidence in order to select those evidence parts that may be useful in the interpretation phase [15]. In this paper, we consider a special case involving a simple processing chain implemented as a hierarchical Bayesian network of three nodes (see Fig. 2) . According to the model by Pearl [ l l ] , which we adopt in this work, each node of the network is associated with a random variable to be estimated, and is connected with parent and son nodes through bidirectional communication channels.

level 4

level 3

level 2

level 1

level 0

d4=T4 (P4d3)

RECTILMEAR SEGMEN DETECTION MODULE

d3=T3@3,d 2)

EDGE-EXTRACT10 MODULE

PREPROCESSING MODULE

T

I MODULE 1

d0 t

real scene

Fig. 2. related top-down and bottom-up messages.

Effective system architecture modeled as a Bayesian network with

The information provided to a node is locally processed, and new messages are propagated toward the adjacent nodes.

As a general formalism, we label the problem variables by capital letters (e.g., X ) and their possible values by the corresponding lower-case letters (e.g., x), if not otherwise stated. The general problem to be solved by each node is a local estimation of the “best” value of the related variable X = IC*, on the basis of the messages coming from the adjacent nodes. To this end, it has been proved [ 111 that, under some hypotheses, each node has to compute and maximize a functional, called belief, which depends on the incoming messages. If X , is the variable to be estimated by the i-th (not terminal) node, the Belief function can be expressed as

(1) BEL(z,) = a, . X(X,) * ~ ( 2 % )

where az is a normalizing constant, the evidence X is the information coming from the lower-level nodes, and the expectation T comes from the parent nodes (see Fig. 3). According to the original theory, these two types of messages concern a- posteriori and a-priori probability distributions of the variable that is to be estimated by the i-th node, since such distributions can be evaluated by the parent and son nodes, respectively. The locally optimum xc,* value can be obtained through a maximization of BEL(x,) for all the values x, may assume. By repeating this operation in a distributed fashion, a flow of messages is activated until a stable status of the network is reached, which corresponds to optimal estimations of the problem variables.

A method based on belief revision [ I l l is used here in order to take into account the information present in the network periphery. Hence, this operation aims at identifying a compound set of propositions (one for each variable) that best explain the evidence at hand. This method seems to be very suitable for modeling IU problems and can be used as

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS-PART B: CYBERNETICS, VOL. 26, NO. 1, FEBRUARY 1996

the basis for the control mechanism of an IU system. Indeed, messages X and n- represent just evidences (i.e., observations) coming from data and expectations (e.g., models) derived from the available a-priori knowledge, respectively.

Belief revision theory (BRT) is associated with the Most Probable Explanation (MPE) criterion, which is a generalization of the Maximum A-Posteriori criterion, as it involves the estimation of a set of variables X = { X i ; i = 1, . . . , L } that are to be assigned to a set of nodes in a tree-like distributed network. In our case, the index i denotes the position of the module to be regulated in the chain (see Fig. 2). Let us suppose that the nodes at the ends (i.e., the root and the leaves) of the network contain some useful knowledge for the solution (e.g., sensor observations or a-priori expectations of an object occurrence). Such fixed knowledge can be represented as a binding of the related variables to fixed values, that is

Let us denote by X the set of all variables considered, including those in e. The MPE criterion discriminates between the possible interpretations of e by selecting from among all possible assignments X = z to the variables X (i.e., z = {zi = xi, i = 1, . . . , L } ) the configuration z* that is the most consistent with e, and satisfying the following relation

Pr(z*/e) = max X Pr(z/e). (3)

The resulting advantage is that it is possible to decompose this criterion in a distributed fashion by letting each node i compute and maximize the belief function defined as

BEL(s) = maxPr(z, ,z:/e), where x: = X - Xi. (4) x:

We assume the conditional independence of the higher-level variables X,+ = {X l : 1 > i } and of the lower-level variables X,- = {X,: k < i } of a variable 5,. As e,+ 2 xi+ and e,- C xi-, by using the Bayes rule, we can express the operation to be computed by each node i of the Bayesian network as

where p is a constant with respect to maximization variables, and

Fig. 3 shows the structure of a module in accordance with the above expression for belief, whose component terms will be described in the following.

Bel(X;) =

i-th module belief updating Fig. 3 . A generic architecture module viewed as a single node of a Bayesian network: the expectation .rr, the evidence A, and the local knowledge support y are shown.

B. MPE Criterion for Image Processing Regulation

The theory just described is well suited to the current image-processing application. A singly connected chain of three nodes is considered, where each node is associated with a processing module M, that receives input data d,-l and, by means of a transformation process T, controlled by a set of parameters P,, produces transformed output data d, (see Fig. 2). Each intermediate unit can propagate top-down (TD) and/or bottom-up (BU) messages to the adjacent modules to communicate new expectations and/or new evidences, respectively. These messages are taken into account to tune the regulation parameters of a generic module. The tuning operation is performed by considering three types of probabilistic measures integrated locally on each node: predictions coming from a higher abstraction level, evidences coming from lower-level nodes, and local supporting knowledge. The three probabilistic measures are combined by means of a belief functional [16] such that the optimal parameters for the set of given transformations can be found by performing local inferences based on the functional evaluation. This strategy differs from belief revision, as proposed in [ 111, mainly in the fact that maximization is not always possible inside the net. Therefore, sometimes it is necessary to use heuristic thresholds for the local belief measure in order to decide either to discard or to accept a new set of local parameters.

The output data provided by each module result from the input-data transformation process performed by using the set of parameters specific for the level considered. Therefore, once the real scene (do) to be considered has been fixed, the status of each module can be identified by the parameters of the related transformation, since, when do is held fixed, d,, with i # 0, can be univocally determined by using the parameters controlling the transformations at the various levels (see Fig. 2). In the case of the present belief-revision network, we denote by P the set of parameters X at all nodes of the network, and by P, a possible instantiation of these variables at the level i (for the sake of simplicity, we do not separate the


variables from their possible instantiated values). This allows us to define the propagation rules for the communication messages between modules using BRT. For an intermediate unit Mi and assuming xi = Pi in (6), we have

(7)

where

The term X is computed by the lower-level module (BU message), and indicates the conditional probability distribution for each P,-l when the conditioning factor is P,. The term 7r represents an analogous distribution (TD message) which is computed by the higher-level module and indicates the conditional probability distribution for each P,+1 when the conditioning factor is P,. As we have chosen the mutual dependence of the nodes only on adjacent ones along the hierarchical chain, the inference mechanism is a first-order (not causal) Markovian mechanism. This means that the two contributions X and T coming into a generic module M, are only related to the sets of adjacent parameters P,-l and P,+1. The term y represents the local regularizing knowledge for the optimization of the status variable P, [16]. The role of this term, which is not considered in [ll], is to allow the optimization of the local status, independently of the states of the neighboring nodes (i.e., disregarding all messages coming from the other modules). This amounts to defining local default parameter values, which are expected to yield high-quality local results.

In a space-varying case, regulation-parameter adjustments are performed to improve only particular areas, disregarding the effects of the parameter setting on the rest of an image. An image is subdivided into several windows of fixed size: the MPE criterion may be applied to each window by maximizing the associated conditional probability at each abstraction level. More precisely, some sets of parameters, Pzk, are considered both at different abstraction levels i and at different spatial locations k . P& is therefore the set of all possible values that the parameter vector P, may assume to process the window k , where i = 1,. . . , L , L being the number of levels, and IC = 1, . . . , K , K being the number of windows ( K = 16 in our case) an image has been split into (see Fig. 4). By applying the previously described maximization process to all the windows separately, the best quality data at all abstraction levels can be obtained for each window.

111. QUALITY EVALUATION AND PARAMETER REGULATION

A. Quality Evaluation Quality features q i3 ( j = 1,. . . , N;, where Ni is the number

of quality measures characterizing data at level i ) have been defined for each level. In general, a quality feature can be associated with more than one regulation parameter, so it is difficult to establish which regulation parameter most affects the type of feature considered. Quality features are computed

windowk k = I, ..., K numberofwindows Regulation Parameters Vector Pik = {p,,,,)

m = I , ..., Mi number of regulation parameters at level i

Quality Parameters Qik = (si@) j = I, ..., Ni number of quality parameters at level i

i = 0, ..., L number of levels

image at level i

Y1

Y2

Y3

Y4 U

XI x2 x3 x 4

Fig. 4. Image processed at a generic level i and divided into 16 windows. The notation indicates window positions (used in the following bar charts describing image quality). Each window k can be processed by using the regulation parameters Pik, and the related quality parameters Q i k are computed.

by applying a set of functions to a transformed datum. When all quality values have been computed, they are fused in order to extract a single quality value, Q,, that indicates the global degree of quality of the datum at level i. The fusion is performed by means of a cost function that is a weighted sum of terms, each associated with a single quality feature. These terms are arranged in such a way as to penalize a datum if the corresponding cost value is too high, i.e., far from the optimal one. Hence, a suitable criterion to achieve the best quality is to select a datum characterized by a minimum cost value Q,. All quality features can be computed for each window to obtain the related quality judgments. To sum up, the global quality value at level i can be expressed as

N ,

QZ = w,3 fiJ (sz, (9) 3=1

where fig(qZg) are the terms that penalize the quality feature values far from the optimal ones, and wtJ are the weights associated with these terms. Therefore, the higher the Qz value (also called “energy” value), the lower the quality of the datum considered. The weights represent scaling factors for reducing quality measures to a similar order of magnitude and for exploiting the meaningfulness of each quality feature in the process of global quality assessment.

The quality features selected for each module reflect the structure of the whole system and are then strictly linked to the signal partition chosen. The mechanism for determining the system levels is essentially a top-down one, i.e., the final goal of the system drives the choice of the architecture (i.e., the abstraction levels). For instance, if the target is to detect regular (man-made) objects, then, we have to extract straight segments; consequently, we need a “good” edge image, which should result from a sharply contrasted image, possibly filtered by a process not affecting the discontinuity information. Therefore, three possible abstraction levels can be defined: 1) the camera level, 2 ) the preprocessing level, and 3) the edge-extraction level.

For each local module, a set of quality features can be selected, more or less goal-dependent, depending on the type

6 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS-PART B: CYBERNETICS, VOL. 26, NO. 1, FEBRUARY 1996

Fig. 5. Scheme for the generation of evidence messages X at level i , starting from the data quality assessments at level z - 1, passing through the discretization process D;.

of signal (local task) and on its dimensionality (hence on the hierarchy level considered). As global characteristics, quality features should be computationally tractable and statistically robust. In particular, it is important to select quality features that depend on the type of signals present at the adjacent levels (lower and higher module) for the following two reasons.

1) Quality features should be capable to assess the performance of the higher module in such a way that the results of the higher module may be better as long as the quality judgment of the lower module is high. In other words, they should “meet” the desired characteristics of higher-level input data so that the related module can work under better conditions.

2) Quality features should be linked directly to the regulation parameters of the local transformation process in order to allow an intelligent regulation.

For example, the choice of the gradient feature computed by means of the Tenengrad function (see Section IV-A) at the camera level, 1) is associated with the probability of detecting a straight segment (at the higher levels) correctly, and 2) is linked directly to the focus parameter at the camera level.

To sum up, quality features should depend on the characteristics of a specific local level (i.e., type of signal) and on the characteristics of the higher level. They should be chosen such as to improve the final result of the system, and are more or less general depending on the hierarchy level considered, i.e., quality features at the highest level are more dependent on the final goal than those at the acquisition level. Therefore, quality measures at a certain level should capture the significance of the higher level, in that they should aim at improving the results produced by the higher module. In other words, if the performances of the higher module as a function of a set of measures indicating the quality of input data (coming from the lower module) are known, such measures should be used as quality features by the lower module.

B. Parameter Regulation

distribution of regulation parameters at level z as follows: The global quality value Q, is linked to the probability

* A transformation T, is applied to a datum, say dzp1, provided by a lower level by choosing the vector of parameters P, = { p , ~ , . . . , p , ~ , } (Mz being the number of regulation parameters at level z), and the local datum is obtained as d, = T, (d , - l , P,). As the lower-level datum is held fixed during local optimization (i.e., the process

Fig. 6. Profile of the expectation term T at level i when the previously used regulation parameters must be inhibited. The same holds when referred to a specific window 1.

for obtaining the best local datum), the local datum di can be expressed only in terms of local parameters, then

* Quality features qij are computed for a local datum by

(10)

0 An energy value is obtained by using (9); it depends

di Ti(Pi).

using the functions gij

qij = g i j ( d z ) = gzj(Ti(Pi)), j = 1,. . . ,Ni .

uniquely on Pi

Ni N,

j=l j=1

N,

Q i = C w i j f i j ( ~ i j ) = C w i j f i j ( g i j ( d i ) )

= c.,ijfij(gij(Ti(Pi))) = Qi(Pi). (1 1) j=1

0 The probability distribution of the regulation parameter vector at level i is expressed as

1 (12) zi

where Zi is a constant that aims at normalizing the exponential as a probability. Among all possible choices for the vector parameters at level i, the choice producing the best data at level i, say P,*, is regarded as being the most probable on the basis of the local regularizing kn2w;cuge.

* Each module can propagate a BU evaluated datum (i.e., a datum associated with its “energy”), after a local solution Pi* has been found. Hence, a X message is defined as

$Pi) = Pr{Pi} = - . exp[-Qi(Pz)]

where c = D,(Q,-I(P,-I)) is a function that maps the real energy value &,-I into the number c, by the discretization process D,. Such a number is selected from a discrete set ( e E (1,. . . , C,}) and addresses the appropriate probability distribution at level z, Uc(P,), dependent on the quality assessment at level z - 1. In our case, c E {1,2,3}, corresponding to {LOW, MEDIUM, HIGH} quality assessments (see Fig. 5). When a unit performs several tunings to raise its local quality

MURINO et al.: DISTRIBUTED PROBABILISTIC SYSTEM FOR ADAPTIVE REGULATION I

estimate new parameter values pl to be applied

I

parameters pi and thenY(Pi) h and/or x and messages parameters from X and h

A I I

A I

Fig. 7. quality evaluation and possible parameter regulation, and sending of data and messages to adjacent modules.

Flow of the operations performed by a generic module, including: reception of messages and data, application of the data transformation algorithm,

level, it propagates to the higher levels only the datum corresponding to the best local quality assessment. So far, we have not yet devised an exact form of 7r

message representation, as we have not yet linked the processing chain to a specific high-level application. So, we propagate 7r messages only to focus attention on particular subareas, or to neglect parameter values that are to be considered as improper on the basis of the local quality-evaluation process. In the bootstrap phase, no projections at all can be propagated, and 7r messages can be expressed as

1

.(Pi) = A dim{Pi}

where dim{P,} is the number of all possible different parameter settings inside the parameter space at level i. In other words, when no a-priori expectations are available from higher modules, all parameters can be assumed to be equally probable (i.e., capable of obtaining the same quality judgment). If TD suggestions are propagated, all previously used regulation parameters, say { P?}, are not suitable for higher-level quality assessments. As a consequence, their associated probabilities can be assigned to the remaining regulation parameters at level i , i.e., the parameters that have not yet been used. In this case, the maximization over all possible P,-I values has no effect, and 7r messages can be expressed as

where dim{P,#} is the number of regulation parameters previously used at level i (see Fig. 6). As a consequence, each module receives X and 7r messages and maximizes the belief function (expressed by the product of such messages by y(P,)) over all possible parameter values P,. Such maximization is performed to decrease the energy value Q, (associated with local data) down to a suitable threshold. This is a suboptimal solution to the maximization problem but has been experimentally found to be acceptable.

To summarize the overall procedure (see Fig. 7), a X message indexes one Gaussian distribution related to the probabilities of the values assumed by the application parameters in an activated module (see Fig. 8). The parameter value

Qi-I Lower level quolily jdgment

Fig. 8. Gaussian distributions at level z: they are indexed by the X message coming from the lower level i - 1. The mean value of these distributions represents the most probable value to be applied on the basis of the quality assessment Qi-1. The same holds when referred to the global image or to a specific window.

corresponding to the most probable distribution is viewed as a default value of the transformation process. Concerning the TD information flow, in the bootstrap phase, 7r messages are represented by uniform distributions (this does not alter the global profile of the BEL function). The y term can be evaluated only for sampled values corresponding to the quality of data obtained by local transformations. Therefore, first, a processing unit performs a specific transformation by using regulation-parameter values derived from X and 7r messages, and the quality Qz and the term y are computed for the datum considered; secondly, the Belief function, BEL, is evaluated and a threshold criterion is adopted to decide whether or not to accept the solution (see Fig. 9). If BEL turns out to be below the threshold, the selection of the regulation parameters to be adjusted by a module through BEL maximization is based on heuristic rules that are different at each level, depending on the knowledge associated with the local transformation process. Whenever no parameter assignment (for a specific number of times) allows the related BEL function to exceed the threshold, the best result obtained is propagated to the higher module. At the same time, a TD message is propagated to request an image improvement. This double message propagation constrains the system to work with data currently available, but does not


i A I

Fig. 9. Procedure for computing the BEL value (BEL maximization): a X message indexes a distribution, a T message inhibits a certain range of values (in the steady-state phase), and the y value, computed by using the global quality value, completes the process. The same holds when referred to the global image or to a specific window.

prevent it from improving results by requiring that the lower modules reprocess data.

In the steady-state phase (after the earliest data propagation), 7r messages are not represented by uniform distributions anymore. The way T distributions can be updated depends on the necessity to improve the quality in some image patches or in the whole image, due to a wrong selection of application parameter values. In this case, the distribution used to select the regulation parameter values aims at inhibiting the use of parameter values included in a certain range (i.e., previously used parameter settings (see Fig. 9)). As a result, a module can prevent a lower module from using parameter settings that have given unsatisfactory results.

IV. PROCESSING MODULE DESCRIPTIONS

The system consists of four independent processing modules: the Camera, preprocessing, Edge-Extraction, and Line- Detection modules (see Fig. 2). Each module is associated with a specific phase of the low-level interpretation process. This architecture has been developed starting from an expert system shell [17], by using both KB and Object-Oriented Concurrent programming approaches. It has been organized in a distributed way: there exists a single general prototype for the regulation module, whose instantiations can be spe- cialized (according to the particular task to be accomplished by the module) by specifying the related quality features and regulation parameters. This modularity enables us not only to divide the general processing into a set of subprocesses but also to make the system more portable, easily extensible, and suited to being implemented on parallel hardware [18]. The lowest module (i.e., the optical sensor) does not receive BU messages, and obtains new evidence from the environment by means of further data acquisitions. Similarly, the highest module (i.e., the line detector) does not receive TD messages,

TABLE I

EACH MODULE OF THE PROCESSING CHAIN QUALJTY AND REGULATION PARAMETERS FOR

High Hysteresis Threshold, Sz

as its task is to integrate the information coming from the lower modules and processed by using different parameter settings. In Table I, the regulation parameters and the quality features used at each system level are given. In the next subsections, the four modules are described in terms of quality criteria, regulation parameters, and functioning cycles.

A. The Camera Module

The camera module is the first of the processing chain and simulates the optical sensor’s behavior. In the early version, a set of images (acquired in an off-line phase) is provided to the system. This set is acquired without knowing the exact numerical values of the acquisition parameters but by varying tuneable parameters separately (one camera parameter at a time). In the new version, a real camera is connected to a computer, thus allowing a direct regulation of the acquisition parameters. The reasoning mechanism is not changed; it has been tested in the old system version and validated in the new one by a direct prediction of the exact parameter values

MURINO et al.: DISTRIBUTED PROBABILISTIC SYSTEM FOR ADAPTIVE REGULATION

0.0305

3.906

0.976

wfi (High Saturation)

wi6 (Mode Changes)

wi7 (Lowest Gray-Level)

TABLE I1 CRITERIA OF THE QUALITY FEATURE SELECTION AT EACH LEVEL, BASED ON THE DESIRED CHARACTERISTICS OF HIGHER-LEVEL

INPUT DATA AND ASSOCIATED WITH REGULATION PARAMETERS

0.0305

3.906

0.976

Q U A " FEAWRFS DESIRED CIiARACIEN2XlCS REGULATION OF AIGHER-LEVEL INPW DATA P-

Tenengrad High w m t F, A Flamess Proper distribution of F, A Entropy infomuon content A, BL, G LowMigh Saturation Average noise level A, BL, G LowestIHlghest Level A, BL, G Mode Changes A, BL, G

The same as for the camera High contrast NI for all level Proper distrrbution of quality

information wntent features ~

0.976

0.976

wig (Highest Gray-Level)

Wig (HG - W

1 LOW noise level Edge Number of Edges Image completeness SI, S2 for all

Extraction Number of Long Edges Primitive significance quality

0.976

0.976 Number of Connected Edges Line continuity I I Number of Edge Points I Probability of straight-line 1

TABLE I11 WEIGHTS FOR THE CAMERA ( i = 1) AND PREPROCESSING ( i = 2)

PARAMETERS USED TO COMPUTE THE GLOBAL ENERGY VALUE

to be applied. The Results section will describe two types of experiments using the two system versions, respectively.

At this level, the criteria to evaluate the image quality are based on the analysis of the histogram and on the high-frequency image content (gradient analysis) [ 191-[22]. These features comply with general visual criteria for image assessment, such as high contrast and proper distribution of information content (e.g., a suitable brightness, a specific histogram distribution, etc.), even to the detriment of adding a certain noise level. They provide a quite complete judgment of the image quality, which is useful for typical post-processing stages like edge- or region- extraction processes, and can be associated directly with a set of regulation parameters (see Table 11).

The quality features used are: Tenengrad, Flatness, En- tropy, Low/High Saturation, Lowest/Highest Level, and Mode Changes [25]. From the experiments performed, it turned out that Tenengrad, Flatness and Mode Changes are the most effective in computing the image quality, hence, they have been associated with larger weights for the calculation of the global quality.

The Tenengrad method (TN) is based on the estimation of the gradient G(z,y) at each image point (z,y) and on summing up all the magnitudes greater than a threshold value [23]. The threshold is used to make this algorithm less sensitive to spurious variations due to noise. TN is computed for each window in each image belonging to a given set, and indicates how sharp a datum is. This method assumes that a well- defined image exhibits larger intensity variations near the contours, where the gradient amplitude is assumed to be larger. Flatness ( F ) indicates the number of pixels with low gradient magnitudes and is complementary to TN, in that TN gives only an integral value indicating the gradient characteristics of the whole image, but does not discriminate between high-contrast small areas and very large areas with gradient values just above the threshold. Hence F indicates how many pixels have very low gradient magnitudes. Population entropy ( E ) is a measure of the uniformity of an image histogram. If P(1) denotes the frequency of occurrence of the grey level I , E takes on its maximum value when all P(1)'s are equal, and its minimum value when P(1) is equal to zero for all but one value of I .

QuaZity Parameters:

According to this definition, a blurred image shows a greater entropy than a sharp image, so the criterion to be followed is to minimize E [I91 in both the whole image and the image windows. The Low Saturation (LS) and High Saturation (HS) values indicate the total number of saturated pixels. An image (or a window) is of good quality if the number of saturated pixels is small as compared with the total number of image pixels. The lowest grey level (LG) and the highest grey level (HG) of an image determine its dynamics. These values, as well as HS and LS ones, depend on the camera parameters related to the brightness of a scene. The Mode Changes (MC) analysis is linked to the histogram computation. Once the histogram (of the whole image or of a window) has been computed, an approximation phase using Gaussian curves follows [24]. In this way, the histogram is approximated by a sum of normal functions, each identified by its own mean value, variance, and amplitude. Finally, the resulting modes are eliminated in two steps. First, modes with amplitude values smaller than 10 percent of the maximum amplitude are eliminated. Second, neighboring modes are fused so as to obtain an estimated histogram with some very stable modes. The number of eliminated modes provides a criterion to judge an image: the larger this number, the worse the image quality.

All quality features are computed and arranged as a linear combination in order to extract a global quality (energy) value for both the entire image and all the windows, as follows

Q1 = ~ 1 1 . TN-2 + ~ 1 2 . F2 + w13 . E2 + w14 . LS2 + ~ 1 5 . HS2 + W16. MC2 + W17 . LG2 . LS + ~ 1 8 . (255 - HG)2 . HS + w i g . [255 - (HG - LG)I2 (16)

where ~ 1 1 , . . . ,w19 are weights useful in normalizing the several contributions and in enhancing the most significant ones (see Table 111). Note that the single terms inside the summation are mainly used to ensure a monotonic behavior of the Q1 value, which decreases as the data quality increases.

The camera parameters considered are focusing distance ( F ) and aperture (A) , both related to the optical lens group, and the electronic gain (G) and black level (BL) both related to the electronic part of a camera. All these parameters affect in some way the quality of an acquired image. In particular,

Regulation Parameters and Functioning Cycle:


TABLE IV GENERAL REGULATION STRATEGY FOR THE CAMEM MODULE, I E., SET OF CANDIDATE CAMERA PARAMETERS TO BE A~JUSTED ACCORDING TO THE

QUALITY VALUES COMPUTED ON AN IMAGE k CASE 3 , THE SYMBOL A’ MEANS THAT THE APERTURE CAN RE CHANGED IF IT HAS NOT ALREADY BEEN SET BY THE FOCUSING OR THE (HIGH) BRIGHTNESS STRATEGIES

F and A affect mainly the gradient content of the image, so the Tenengrad function and Flatness are associated with these parameters. Histogram entropy, E, is affected by almost every acquisition parameter (A, G, and BL). The histogram of the grey-level frequency of occurrence of a blurred image, for instance, tends toward a uniform distribution, whereas the histogram of a sharply focused image has an impulsive intensity (e.g., bimodal, if only two different grey levels are present). Therefore, E can be affected by the degrees of image sharpness and of noise corruption. Electronic gain and black level, too, affect the histogram of an image, but their effects are mainly weighted by the quality measures related to signal dynamics and saturation. The regulations of black level, aperture, and electronic gain may sensibly affect the image brightness, hence the degree of contrast, too. Therefore, Highestnowest Gray Level, High/Low Saturation, and Mode Changes may be heavily affected by the values of BL, G, and A.

One peculiarity of our approach lies in improving data quality starting just from the acquisition level. We do not acquire data by using statistically optimal parameters and do not try to gain a higher degree of definition by means of standard restoration techniques. Instead, we try to regulate the sensor’s parameters in an active way in order to optimize its performances, which depend on environmental conditions as well as on the optical configuration. A general camera- calibration procedure does not exist, as a correct regulation procedure involves a cooperative adjustment of all parameters to obtain an acceptable tradeoff among degree of focusing, average brightness, contrast, and so on. Then, the aforesaid four regulation parameters are considered and a sort of apriori ranking is followed for the regulation process (see Table IV). Available commercial methods (e.g., autofocus, autoiris, etc.) are not flexible and efficient enough to cope with all actual situations that may occur.

In the early version, the module simulates the camera functioning by considering (in the bootstrap phase) only one image or a small set of images. Then, if required by the current processing status, other images are considered. In this case, the regulation cycle consists first in computing the image quality and then choosing the regulation parameter to be changed. Once this parameter has been chosen, another image is extracted from the set (related to that varying parameter) in order to improve the solution. On the basis of the same reasoning, the general regulation procedure is used in the new system version. It consists in changing one camera parameter at a time, acquiring an image, and computing the new quality

value. If the quality is better, the change is accepted; otherwise, the next parameter to be changed and the related value are chosen on the basis of the regulation status (i.e., using a gradient-descent-like algorithm that considers the current and the previous camera parameter values and quality judgments). An analysis of the situations that may occur during the acquisition process suggests using a heuristic strategy for the choice of the parameter to be changed. As a general strategy, the system can activate two possible regulation procedures, depending on the computed quality features. In either procedure, the camera parameter to be adjusted is chosen from a pre-specified parameter subset (see Table IV). A more detailed description of the camera regulation process can be found in [25].

As the camera module is a terminal node of the processing chain, no X term is considered. The best quality image (i.e., the image that maximizes the 7.r term) is propagated to the higher module together with the discretized qualitative judgment (i.e., HIGH or MEDIUM). This judgement is used to address a higher-level parameter distribution (represented as a Gaussian curve N ( z , a’)), which corresponds to the X message related to the preprocessing module.

B. The Preprocessing Module

The Perona-Malik filter [26] is applied to an image in order to eliminate noise, while preserving the information about the image contours. The procedure consists in an adaptive (anisotropic) filtering based on a diffusion process. The diffusion coefficient can vary spatially so as to favor smoothing operations in the image parts with no contrast.

As the result of the Perona-Malik process is a filtered image, the quality features used and the computation of the global quality value are the same as at the camera level. By using the same features, one can realize the improvement in the resulting image, as compared with the image acquired by the camera module. Therefore, these features pursue the same objectives as the camera module but are also capable to reduce the noise level possibly added by the acquisition process (see Table 11). As a result, it is possible to evaluate whether the subsequent edge extraction process can work properly or not.

Table 111 gives the weights used for the computation of the global quality.

Regulation Parameters and Functioning Cycle: The Perona-Malik filter is an iterative algorithm that explores each pixel and updates its intensity on the basis of a function dependent on the four-nearest neighbors and on a diffusion coefficient. This coefficient is computed by means of a function inversely proportional to the gradient amplitude related to the pixel considered. Therefore, points inside uniform regions are interpolated with the neighboring area (i.e., low-pass filtering [27], [28]), whereas points with large gradient amplitudes are left unaltered. As a result, we obtain an image with a reduced amount of noise and nearly the same information content. Performing several iterations of the procedure makes the image cleaner but may affect edge information, even though to a small extent (only the quality

Quality Parameters:

MURINO ef al.: DISTRIBUTED PROBABILISTIC SYSTEM FOR ADAPTIVE REGULATION 11

features related to the gradient information are affected by this processing stage). The process utilizes the number of iterations (NI) of the filtering process as the only regulation parameter. As a matter of fact, since the computation of the diffusion coefficient depends on the characteristics of the image gradient, the effects of the filtering process on an image are not the same for any number of iterations. After a certain number of iterations, the gradient image becomes so regular, with respect to the chosen diffusion coefficient, that every discontinuity is considered “informative” and is not filtered any more. This situation can be detected by comparing the quality judgments, which remain almost similar along successive iterations.

The regulation process uses incoming messages and local knowledge to achieve a good tradeoff between a high degree of regularization and information corruption. First, the filter performs the number of iterations suggested by the X message coming from the camera module; second, the produced image is evaluated by computing the corresponding local y term. This image is then propagated to the higher level only if its quality is MEDIUM or HIGH. The worse the quality of the incoming image, the larger the number of iterations. Therefore, at this level, high quality incoming images are little affected by the filtering stage, whereas low-quality images should be cleaned without affecting the informative content. Moreover, this filtering process cannot result in a notable image improvement (i.e., it cannot enhance edge information). Therefore, when an unfavorable image-quality judgment is computed and it is difficult to improve the quality by a certain number of filter iterations, the task of improving the image quality is entrusted to the camera module by propagating a T message.

C. The Edge-Extraction Module The third module includes an edge-extraction filtering

followed by an edge-following and edge-characterizing algorithm. The regulation procedure controls only the edge- extraction process. The edge-characterizing algorithm is devoted to computing, for each extracted edge, a set of attributes (i.e., a property list) to be used either as local quality parameters or as input to the next line-detection module.

Although the quality of an edge- image may include suggestions concerning a possible object to be recognized [29], we preferred to use heuristic criteria for quality evaluation linked to the final system goal. Such criteria do not consider information linked to possible model shapes, but are general and suitable for assessing the quality of any edge-image as they try to augment the probability of detecting straight lines, to weight line continuity and the relative importance of edges (i.e., a long edge is more significant than a short one), etc. (see Table 11). They consist of domain-independent methods for evaluating the primitive attributes computed by the edge-characterizing algorithm.

As an edge is a shape information source [30] (even though it may be more or less meaningful for the interpretation phase), the number of chained edges (EN) in the image is computed, as it indicates how many contours are assumed to be in a

Quality Parameters:

TABLE V WEIGHTS FOR THE EDGE-EXTRACTION ( z = 3) PARAMETERS

USED TO COMPUTE THE GLOBAL ENERGY VALUE

scene. The number of edge points (EPN) is considered, too; this value defines the datum percentage that is considered as an information source. The comparison between EPN and EN can provide a first assessment of the significance of the information in an image (e.g., the same number of edge points seems to be more useful in the interpretation phase, if associated with not too large a number of chained edges). As a description of a scene in terms of object locations is often required, the number of long edges (LEN) is computed as a further quality feature (as a matter of fact, edges defining object boundaries are usually not too short). A threshold of at least fifty points has been chosen for an edge to be considered as a “long” one. Since object contours are usually continuous and closed, the number of connected edges (CEN) is considered, too. At a glance, an edge seems to be more “informative” if connected to another edge, as it is more likely to represent an object contour. Therefore, global quality can be expressed as

Q3 = w3l. EN-^ + w32. EPN EN-^ + w ~ ~ . (1 - LEN. EN-^) + w34. (1 - CEN EN-^)

(17)

where ~ 3 1 , . . . , w34 are weights useful in normalizing the several contributions and in enhancing the most significant ones (see Table V ). At this level, global quality is assessed only to decide on the propagation of data and not to generate the X message for the higher-level module. Quality values are computed to evaluate the quality of each window; they are used by the higher-level module to weight the data-fusion process.

Edge extraction is performed by means of the Canny filter [31], which detects edges by searching for the maximum values of the image gradient in the direction of the gradient. First, a Gaussian mask with a variance value that can be set as an input parameter is convolved with the image in order to improve the signal-to-noise ratio (SNR) [27]. Then, the gradient GA(x, y) is computed for each pixel (x, y) and the points with maximum amplitudes (in the gradient direction) are selected. A hysteresis mechanism is used to extract edge points. Two thresholds, 5’1 and 5’2, are defined as input parameters: all the points (x,y) with GA(x,y) > 5’2 are regarded as edge points; if a pixel adjacent to an edge point has S1 < GA(z,y) < Sa, it is regarded as a prolongation of the edge and labeled as an edge point. In all other cases, pixels are not considered as belonging to a contour. By adjusting the thresholds, continuous edges can be obtained, even when the gradient information is not very reliable. As the task of image regularization is previously

Regulation Parameters and Functioning Cycle:


Fig. 10. Set of aerial images acquired off line by changing the focusing distance parameter (first example, see text).

(a) (b) (c) Fig. 11. upon the images to show the subdivision into windows.

Detail of the set of images acquired with different focus settings: aerial-0 in (a), aerial-2 in (b), and aerial-4 in (c). Grids are superimposed

performed by the prefiltering module, we decided not to tune the variance of the Gaussian mask the image is convolved with. Hence only 5’1 and SZ are used as regulation parameters. Moreover, small values of the mask variance are used in order not to prevent the edge-extraction module from propagating TD projections to the prefiltering module.

After the edge-extraction phase, an edge-characterizing algorithm, similar to the one described in [36], is applied. It identifies each edge by a label, and computes some attributes such as length, initial and final points, etc. The outcome of this module is a label picture with additional information about the structure of each edge. This data structure is used to

MURINO et al.: DISTRIBUTED PROBABILISTK SYSTEM FOR ADAPTIVE REGULATION

aerial-2

~

13

aerial-4 acrid-0'

lower-level regulation

,

aerial-2.perl aerial-4.per2 aerial-0.per3 ', !

I I

aerial-2'cdg2

aerial-2.linl aerial-4.lin2 aerial-0.lin3

aerial-0.edg4 aerial-4.edg3

Fig. 12. the propagated images and the related regulation phases.

Scheme of the system functioning in the first example: it describes

compute the quality features and 'then the quality judgment. The resulting image may contain different edge compositions, depending on the threshold values used, which have been set in accordance with the X message. Generally, quite high threshold values are fixed in order to extract only meaningful edges. Subsequently, once approximate object locations have been found, the filtering conditions are relaxed (i.e., lower values are chosen for the hysteresis thresholds) in order to allow a deeper inspection of the scene. It is important to stress that it is always better to extract additional information (i.e., more edges), even when it is not very significant. The presence of spurious

(c) ( 4

Fig. 13. Edge images resulting from to the application of the Canny filter (with different settings of the thresholds SI and S2) to the same images as considered in the first example. (a) edge image extracted from image aerial-0 by using SI = 10 and Sz = 30; (b) edge image extracted from image aerial-4 by using SI = 10 and 5'2 = 30; (c) edge image extracted from image aerial-0 by using SI = 30 and Sz = 50; (d) edge image extracted from image aerial-4 by using SI = 30 and S2 = 50.

--

I -- -- (a) (b) (c)

Fig. 14. two (b), and three (c) images, after edge-extraction regulation.

Results obtained by the line-detection module by fusing one (a),

edges cannot prevent a possible interpretation phase [32]; by contrast, if an object edge is not extracted, a more robust matching process may be required. According to the type of X message related to the edge-extraction module, N(30,5) and N(50,5) are set for the filter hysteresis thresholds SI and Sz, respectively, for a MEDIUM judgement, as more significant edges have to be considered, without extracting spurious edge points. The Gaussian functions N(10,5) and N(30,5) are used for a HIGH quality judgment, hence even weaker edges can be extracted without the risk of obtaining too noisy edge images.

D. The Line-Detection Module The fourth and highest module of the hierarchy is character-

ized by a somewhat different functionality, as compared with the modules so far described. It may neither propagate eval-

14 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS-PART B. CYBERNETICS, VOL 26, NO. 1, FEBRUARY 1996

AERIAL-4

Fig. 15. Weights used in applying the Hough transformation process related to the windows in images aerial-0, aerial2, and aerial-4. Window positions are indicated by yl-21, y1-22,. . . , y4-z4, from left to right and from top to bottom, as shown in Fig. 4. Weights correspond to the inverse of the quality values computed by the edge-extraction module.

uated data nor receive TD suggestions from higher modules, and it may not regulate its local processing parameters in an adaptive way. The main goal of this module is to produce the “best” scene representation in terms of straight lines extracted by the differently processed edge images obtained by the lower-level modules of the processing chain. The goal is reached by performing a data fusion [33] of all binary edge images, on the basis of quality assessments. To this end, a modified version of the Hough transform is used [34, 371. The fusion process is performed while the edges extracted from the Cartesian space are being accumulated in the Hough space. Instead of performing an integer increment of every Hough-space accumulator corresponding to an edge point, the accumulator’s value is increased by a step proportional to the quality assessment related to the window the edge point belongs to. More precisely, the Hough-transformed space accumulators are updated by considering all edge images that have been produced, as follows

Z X Y

n=l x,=1 y n = l

where: - n = 1, . . . , 2 is the number of edge images that have

been accumulated in the Hough space; - X and Y are the image width and height; - (zn, yn) is the pixel at the location (x, y) in n-th edge

image; - f ( X n , Y n ) = Q 3 0 3 1 and Q3(zn, yn) is the energy

value associated with the window (of the n-th edge image, i.e. i = 3) the pixel (zn,yn) belongs to;

Fig. 16. Images resulting from the detection of rectilinear segments by applying the classic Hough transform (i.e., without weights) to images aerial-0 (a), aerial2 (b), and aerial-4 (c) shown in Fig. 10.

- g(x,, yn, p, e ) = z . cos B + y . sin B - p, and d ( t ) is the

The probability of obtaining a straight line, after backprojection from the Hough space, depends both on the frequency at which such a line appears in every edge image (i.e., the number of images confirming the presence of a line) and on the related information content in every image (i.e., the probability of the presence of the line with respect to the quality assessment associated with each window the line belongs to in every image). In the backprojection phase, information about the spatial location of every edge in every image is available from the edge-characterizing algorithm; such information is used to update the initial and final points of every line and to avoid backprojecting several collinear edges onto the same segment. This modified version of the Hough transform seems to be a very powerful tool for an accurate fusion of differently processed edge images. It is worth pointing out that the adaptive regulation of an optical sensor’s acquisition parameters may partially affect the results obtained by the fusion process. Images acquired by using different values of the focus and aperture parameters show spatially different displacements. When using two different acquisition-parameter settings, the same point of an object may be mapped into neighboring, noncoincident points in the Hough space. This effect can be overcome by using a coarse version of the transformed space: the coarser the quantization, the larger the number of Cartesian lines mapped into a single accumulator. As a result, small differences in the location of the same edge can be eliminated, thus providing a single edge. However, it is not possible to make the Hough space too coarse, hence the image resulting from the fusion process may contain some parallel edges very close to each other.

normalized delta function.

V. EXPERIMENTAL RESULTS

Two experimental examples will be presented. For the first, the old version of the system was employed, using a set of images pre-acquired regulating the camera parameters separately. For the second, an actual camera connected to a host computer was employed. Moreover, results obtained by using nonregulated versions of the algorithms will be compared with those obtained by regulated algorithm versions. These examples aim at demonstrating how an adaptive regulation of each processing phase can result in a progressive increase in the information to be used in the subsequent interpretation phase.


In the present system, a straight-line detection module operates as an information-fusion processing unit, thus providing a more complete and reliable scene structure.

A. First Example In the bootstrap phase of the system, a set of images of the

same scene but acquired by using different parameter settings, is provided to the camera module. Fig. 10 shows a set of six images (numbered from aerial-0 to aerial5, from top to bottom and from left to right) acquired by using different focus settings. These images are representative of a larger set of images of the same scene that present a narrow depth of field; hence, different areas are focused in each image. For example, in image aerial-0 (see Fig. ll(a)), the plane on the right side (near the observer) is well focused, whereas, in image aerial-4 (see Fig. 11(c)), only the left side area is focused. A grid was superimposed upon such images to show the subdivision into windows (the windows are numbered from one to sixteen, from left to right and from top to bottom). As shown in Fig. 12, the camera module propagates the image with the best global quality, that is, it chooses image aerial-:! (see Fig. ll(b)), for which the quality judgment is MEDIUM, and propagates this image to the preprocessing module. The quality judgment associated with the propagated image indexes the distribution N ( 3 , 2 ) , representing the X term related to the default value (three iterations) of the regulation parameter of the filter. The T term is represented by a uniform distribution, as no a-priori knowledge is available at the higher levels. Therefore, the processing unit performs the filtering, computes the y values for every window and for the whole image (hence, the belief value), associates a MEDIUM global quality assessment, and detects that the quality value of patch no. 4 is very low. Therefore, a 7r message for window no. 4 is propagated to the camera module; the message requires the camera module to acquire a new image in order to improve this window (in this case, the camera module checks the other images and chooses the one where the window quality is the best). The preprocessing module propagates the filtered image (aerial2.perl) to the edge extractor, after having associated with it a MEDIUM quality value. This module produces image aerial2.edgl by using the thresholds 5’1 = 30 and Sa = 50 ( N ( 3 0 , 5 ) and N ( 5 0 , 5 ) are the Gaussian distributions related to the two thresholds, respectively, in the case of a MEDIUM quality value). The Gaussian distributions associated with the hysteresis thresholds used by the Canny algorithm are treated as independent distributions, provided that they have different mean values. Since the quality of image aerial-2.edgl is LOW, a local level regulation is performed by the edge-extractor unit. The edge-extraction process is performed again by selecting threshold values on the basis of local regularizing knowledge so that the local BEL may increase, i.e., SI = 10 and 5’2 = 30 are chosen: these values identify a local maximum for the BEL function associated with the edge-extraction level. The related quality value is MEDIUM; therefore, image aerial-2.edg2 is propagated to the line-detection module. Unfortunately, the quality of window no. 5 is very low because few edges are contained in this

area. After several local regulations have been performed, if no quality enhancement in the 5 t h window has been obtained, a 7r message is propagated to the preprocessing module in order to improve this area. At the same time, the BU message causes the line-detection module to be activated, which performs the first image transformation by extracting the rectilinear segments from the processed image (aerial-2.linl). Once all BU messages have been propagated, the bootstrap phase ends. It is important to point out that, during the bootstrap phase, the 7r expectation terms are considered as uniform distributions. As one can notice, the general criterion used is propagation of data of suboptimal quality, too, in order to waste as little time as possible, i.e., not to let the modules be inactive. This will be useful when the system is implemented on parallel hardware, and the processor associated with each module must almost always be active.

The preprocessing module is activated, which contains a 7r request to be satisfied, i.e., the improvement of the 5 t h window. After some filtering phases, the module realizes the impossibility of improving this area and a request in this sense is sent to the camera module. The camera module is activated, which propagates image aerial-4 (see Fig. l l(c)) where the 5 t h window exhibits the highest quality. The preprocessing unit performs a filtering process (N(1,2) is the parameter distribution activated by the X message) and propagates image aerial-4.per2, with a HIGH quality judgment, to the next level. Then, the edge-image is produced by applying the Canny filter with the thresholds 5’1 = 10 and S2 = 30. The line- detection module can now perform straight-line fusion of images aerial2.edg2 and aerial-4.edg3 in the Hough space by properly weighting the voting process with the quality estimates assigned to all edge-image windows.

Then, the control reaches the camera module, where a request for improving the quality of the 4-th patch has still to be met. The camera module propagates image aerial-0 (see Fig. ll(a)), where the 4-th window has the highest quality, and associates with it a HIGH quality assessment. The preprocessing module is then activated by a X evidence message of the type N(1,2); it produces image aerial-0.per3, whose quality is considered HIGH, too. Then, the edge- extraction module is activated by a X evidence message HIGH, which corresponds to N ( 1 0 , 5 ) and to N ( 3 0 , 5 ) . The quality judgment on the resulting image aerial-0.edg4 is MEDIUM, so the image is BU propagated. Finally, the line-detection module performs the third image fusion and obtains a datum that includes the information recovered from all the images (see Fig. 14(c)).

Fig. 13 shows the results of the edge-extraction process on the two images (aerial-0 and aerial-4) chosen by the system for this example. One can see different degrees of focusing in different parts of the scene (see Fig. l l (a) and (c)). Two different settings of the thresholds 5’1 and 5’2 are used for edge extraction in order to perform a comparative analysis of the use (static or dynamic) of the Canny filter. Fig. 13(a) and (b) show the edges extracted from images aerial-0 and aerial-4, respectively, by using the thresholds 5’1 = 10 and S2 = 30. Fig. 13(c) and (d) show the edges extracted from the same images by using the thresholds S1 = 30 and 5’2 = 50.


I AERtAL-4 A ERtA L-2

AE RI A t-0

Fig. 17. Energy values related to windows in (a) image aerial-0, (b) image aerial-2, and (c) image aerial-4 at the camera level (window positions are indicated by yl-21; yl -22 , . . . , y4-24, from left to right and from top to bottom, as shown in Fig. 4).

If one considers separately the two pairs of images in Fig. 13(a) and (b) or in Fig. 13(c) and (d), obtained by using the same couple of thresholds, one can notice the different scene structures extracted, due to the different degrees of focusing in the various scene areas. Instead, if one considers the pair of images in Fig. 13(a) and (c) or Fig. 13(b) and (d), obtained by applying different thresholds to the same image, one can notice significant differences and the presence of more complete and continuous edges in the higher portion of the figure, where the thresholds have been relaxed, although some spurious edges can be seen, too. The improvements in the edge images and the necessity that all the scene areas should be well focused are particularly evident, thus demonstrating that a single acquisition or the static use of a filter with fixed thresholds is not sufficient to attain a complete and reliable feature representation.

Fig. 14 shows the results of the line-detection module. They were obtained by fusing in the Hough space and backprojecting into the Cartesian space from one to three of the presented edge-images (the edges of images aerial2, aerial-4, and aerial-0). A gradual improvement in detecting rectilinear segments can be noticed, especially after the third fusion (Fig. 14(c)), which results in new meaningful segments. Unfortunately, some spurious edges appear very close to each other, due to the different focusing distances used during the acquisition of the original images; the different distances caused small displacements of the object edges. However, such edges do not cause any substantial degradation of the real scene structure, which now appears more complete and more

I AERiAL-4,3 iterations 1 1 AERIAE-4,10 iterations I

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Fig. 18. Energy values related to windows in images aerial-:! and aerial-4 at the preprocessing level. They are obtained by using different settings of the number of iterations of the Perona-Malik filter (the window positions are indicated as yl-xl; yl-22; . . . , y4-24, from left to right and from top to bottom, as shown in Fig. 4).

reliable. Fig. 15 gives the weights used for the Hough transformation process on images aerial-2, aerial-4, and aerial-0. In this picture, windows 64 x 64 pixels in size are denoted by yl-21, 91-22, . . . , y4-x4, from left to right and from top to bottom. As a comparison between the static and the adaptive application of the Hough algorithm, Fig. 16 shows the results of applying the classic Hough process to images aerial-0 in panel a, aerial2 in panel b, and aerial-4 in panel c. It is easy to notice some differences in the images, especially between image aerial-4 (Fig. 16(c)) and image aerial-0 (Fig. 16(a)) or aerial2 (Fig. 16(b)): in the left parts of the images, the rectangular shape is visible in Figs. 16a and b but is hidden in Fig. 16(c). If one compares Fig. 14 with Fig. 16, one can notice the more complete and more accurate scene structure extracted by the regulated framework, as compared with the structure extracted by the nonregulated one.

Preprocessed images are not shown, as application of the Perona-Malik filter to nearly noiseless images (like the ana- lyzed ones) results in too poor improvements to be appreciated according to a purely visual criterion. Concerning the behavior of the cost function in the image windows at the camera level, in Fig. 17(a) (aerial-4), (b) (aerial-2), and (c) (aerial-0), one can notice that this function succeeded in discriminating between well-focused and ill-focused areas in the images, thus allowing the detection of windows to be improved. This function has the lowest values in the best focused image areas (the windows are denoted by yl-xl, ~ 1 4 2 , . . . , y4-x4 , from left to right and from top to bottom). The same behavior occurs at all the other processing levels. In Fig. 18, one can notice that, though the application of the Perona-Malik filter produced


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Fig. 19. Energy values related to windows in images aerial-2 and aerial-4 at the edge-extraction level. They are obtained by using different settings of the hysteresis thresholds SI and &of the Canny filter (window positions are indicated by yl-zl, yl-z2, . . . , y4-z4, from left to right and from top to bottom, as shown in Fig. 4).

TABLE VI CAMERA PARAMETERS USED TO ACQUIRE THE IMAGES SHOWN IN FIG 20(a)-(d)

a low-pass effect on the uniform windows, it did not affect the windows with significant informative contents, so reducing the quality of the former windows and leaving the latter unaltered. Similarly, at the edge-extraction level, the cost function assumed the lowest values in the areas with more informative edges (see Fig. 19), depending on the thresholds used.

B. Second Example

As a further example of our system's functioning, we describe an experiment performed by using a real camera connected directly to the host computer. Fig. 20 shows the sequence of four images acquired in our lab by varying the aperture and focus parameters to obtain the best scene representation (the images are called real-1 to real-4, starting from (a) to (d). Table VI gives the values of the camera parameters used during the acquisition process. Due to the average degree of luminosity in the environment, the electronic parameters (gain and black level) did not need to be tuned; only a slight adjustment of the aperture was performed to make the image sufficiently contrasted. The experiment was ad hoc carried out: one object (i.e., a lamp) was placed in the

Fig. 20. Set of gray-level images acquired on line during the camera regulation process described for the second example. The images are called real-1 to real-4, starting from (a) to (d), respectively. For this example, a real camera was connected directly to a computer and the regulation was performed by predicting the camera parameters explicitly.

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Fig. 21. Energy values related to windows in the images shown in Fig. 20 (window positions are indicated by yl-21, yl-22. . . . , y4-x4, from left to right and from top to bottom, as shown in Fig. 4).

foreground, very close to the camera and far from the rest of the objects in the scene, in order to evaluate if the system was able to acquire several images where the different scene

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS-PART B: CYBERNETICS, VOL. 26, NO 1, FEBRUARY 1996

(c) (4 Fig. 22. Results of the fusion process performed by the line-detection module. Panel a refers to the first fusion (weighted straight-line detection in the edge-image extracted from the image in Fig. 20(a)), (b) refers to the second fusion (fusion of the edge images extracted from the images shown in Figs. 20(a) and (b)), (c) refers to the fusion of the edge images extracted from the images shown in Fig. 2O(a)-(d) refers to the fusion of the edge images extracted from the images in Fig. 20(a)-(d).

areas were well focused. The general strategy was to propagate all acquired images to the higher levels, even if the image qualities were not too high. In other words, we lowered the thresholds for quality acceptance, while continuing to adjust the camera parameters to improve the images. In Fig. 21, the energy values computed on the images shown in Fig. 20 are given for each window (numbered in the usual way). One can notice that the qualities of the foreground areas are good in the first images (real-1 and real_;?), whereas the background quality is quite low. An opposite situation occurred in the last images considered (real3 and red-4). Fig. 22 shows the results of the fusion process performed by the Hough algorithm. Although the scene was quite complex, a remarkable gradual improvement of the scene structure was achieved; only a small number of spurious edges are present. Fig. 23 gives the quality coefficients used to weight the fusion process (the windows are denoted by yl-lcl, ~ 1 4 2 , . . . , y4-x4 , from left to right and from top to bottom). Fig. 24 shows the segment images extracted by applying statically the Hough process to the images in Fig. 20. In this case, too, there are some differences between the images in Figs. 22 and 24. Images in Fig. 24 present very poor scene structures as compared with that in the last fused image (Fig. 22(d)).

The results presented demonstrate that all the system modules cooperate in achieving the best data quality, and that this task is made more reliable through the control of all

Fig. 23. Weights used in applying the Hough transformation process to images real-1 to real-4 (window positions are indicated by yl-zl, ylLz2,. . . , y4-s4, from left to right and from top to bottom, as shown in Fig. 4).

processing modules. The simple but efficient fusion algorithm proves that the proposed dynamic and adaptive processing can considerably improve the feature extraction process, which is basic to the interpretation phase.

VI. CONCLUSION

A KB framework for the regulation of image-processing phases has been presented, which integrates distributed probabilistic knowledge. The system is based on a set of regulation modules, each coupled to a different processing step. The general functioning of the regulation system has been described in theoretical terms by means of belief revision theory and in implementation terms by defining an inference strategy adopted in the intensional KB system. Belief revision theory has been applied to solve the regulation problem by means of a hierarchical set of message-exchanging knowledge sources. These deal with the parameters that regulate the different transformation behaviors at each level. The best transformations to be progressively applied to input data have been estimated by maximizing the joint probability of the parameters at each level, according to the MPE criterion. Each knowledge source corresponds to a regulation module and contains a-priori declarative knowledge of different types. The knowledge about the transformation to be controlled consists of a set of regulation parameters. The data obtained by each transformation have been represented as intrinsic images produced by different processing steps. Quality features allow a regulation module to access local methods for judging data in a quantitative way, by using several quality functions. Moreover,


Fig. 24. Images resulting from the detection of rectilinear segments by applying the classic Hough transform (i.e., without weights) to the images shown in Fig. 20 ((a) refers to image real-1 shown in Fig. 20(a), (b) refers to image rea l2 in Fig. 20(b), etc.).

each knowledge-source is provided with a local inference engine which activates procedural knowledge (i.e., appropriate production rules) to perform the regulation process. In this way, it is possible to use the same structure for all regulation modules by specializing each level with the knowledge related to the particular local processing to be performed. This organization allows the system to follow different local strategies to improve data quality, while maintaining a high degree of generality.

The main characteristic of the proposed system is to provide a distributed probabilistic approach to the regulation of complex tasks. Consequently, the system is well-suited for implementation on parallel architectures. Moreover, it has been shown that the Bayesian Network framework can be successfully applied to solve active vision problems [ 161, [35]. The KB approach, implemented by means of Object Oriented Programming, exhibits notable capabilities in terms of maintenance, flexibility, and expansibility. Thanks to these characteristics, the proposed framework is appropriate for many image-understanding problems, in particular, the architecture presented can be adopted at early stages in many recognition systems. Promising results on indoor scenes have been reported to confirm the validity of the approach.

ACKNOWLEDGMENT

The authors wish to thank Thomson CSF-LER (Rennes, France) for providing some of the images processed for this

work. They are also grateful to M. F. Peri, G. Razzetta and F. Brenta for their valuable assistance in the software implementation.

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Vittorio Murino ”93) was born in Lavagna (Genova, Italy) in 1964. He received the Laurea degree in electronic engineenng in 1989 and the Ph.D degree in 1993 from the Department of Biophysical and Electronic Engineering (DIBE), University of Genoa. His Ph.D. thesis involved the study of adaptive regulation techniques in the context of the distributed image recognition problems.

He is currently a Post-Doctoral Fellow, Univer- sity of Genoa, workmg in the Signal Processing

and Understanding Group of DIBE, as supervisor of research activities concerning with signal processing in underwater environment. He worked on several projects in the context of the MAST (MAnne Science and Technology) programme of the European Community, and in particular on the investigation of the underwater bottom by using visual and acoustic sensors. His main interests involve acoustical and visual underwater imaging, signal and image processing €or recognition, probabilistic techniques for signal recovery, and data fusion

Dr. Murino is member of IAPR, and AEI.

Gian Luca Foresti (M’95) was born in Savona, Italy, in 1965. He received the Laurea degree in electronic engineering in 1990, and the Ph.D. degree in telecommunications and signal processing in 1994 from the University of Genoa. Immediately after the Laurea degree, he worked with the Departe- ment of Biophysical and Electronic Engineering (DIBE), Genoa University in the area of communi- cations, signal processing and image understanding, The Ph.D. thesis dealt with distributed systems for analysis and interpretation of real image sequences.

He is currently a member of the Signal Processing and Understanding Group of D B E , and is working in the context of several projects with the participation of DIBE. His main interests involve distributed data fusion in multisensor systems, probabilistic and symbolic techniques in signal processing, and non-linear signal and image processing Techniques proposed found applications in the fields of automatic systems for surveillance of underground stations, railway lines, workmg environments, vision systems for road traffic control, and communication systems for mobile vehicles.

Dr. Foresti is author or co-author of more than 30 papers published in international journals and conferences and is member of IAPR and AEI.

Carlo S. Regazzoni (M’92) was born in Savona, Italy, on September 16, 1963 He received the Laurea degree in electronic engineering and the Ph D in telecommunications and signal processing from the Department of Biophysical and Electronic Engineering (DIBE) of the University of Genoa, in 1987 and 1992, respectively

Since 1990, he is responsible of the Industrial Signal and Image Processing (ISIP) area of the Sig- nal Processing and Understanding Group (SPUG) at DIBE In 1993, he has been Post-doctoral fellow at

the University of Toronto, with which he is still cooperating He coordinated technical activities of DIBE in several projects (e g., ESPRIT (P7809 DIMUS, P8433 PASSWORDS, P6068 ATHENA)) whose mam goal is the development of high technology support systems for the transport field (e g., distributed surveillance systems, underwater telecommunications, etc ) Currently, he is a Research Fellow in Telecommunications at DIBE His mam research interests are distributed data fusion in multisensor systems, probabilistic and symbolic techniques in signal processing, non-linear signal and image processing, non- conventional detection techniques based on higher order spectral analysis

Dr. Regazzorn is a referee of several international journal and he was a reviewer for EEC in ESPRIT Basic Research Action Proposals on High Performance Computing in 1993 He has been chairman and member of the technical committee at several conferences (IECON ’93, EUROPTO ’94, ROVA ’95) He is a member of IAPR and AIIA.

A distributed probabilistic system for adaptive regulation of image processing parameters

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