Document Image Decoding Approach to Character Template ...

Document Image Decoding Approach to CharacterTemplate Estimation 1

Gary E. Kopec2Xerox Palo Alto Research Center

Mauricio Lomelin 3Microsoft Corp.

November 29, 1995

Abstract

This paper develops an approach to supervised training of character templates from page images and

unaligned transcriptions. The template estimation problem is formulated as one of constrained max-

imum likelihood parameter estimation within the document image decoding framework. This leads

to a two-phase iterative training algorithm consisting of transcription alignment and aligned tem-

plate estimation (ATE) steps. The maximum likelihood ATE problem is shown to be NP-complete

and thus a number of simple suboptimal solutions are developed. The training procedure is illus-

trated by its use in creating a document-specific decoder for high-accuracy transcription of a large

(400 page) text document. Depending on the language model used, the decoder character error rate

is a factor of 7–20 less than that of a commercial omni-font OCR program; the best case error rate

is 0.036%.

Index Terms: document image decoding, Markov models, template estimation, character

recognition1Submitted Nov. 1995 to IEEE Trans. Pattern Analysis and Machine Intelligence.2Correspondence: Information Sciences and Technologies Laboratory, Xerox Palo Alto Research Center, 3333Coyote Hill Rd., Palo Alto, CA 94304; e-mail: [email protected]; phone: (415)-812-4454; fax: (415)-812-4374.3Work performed while author was a student at the Massachusetts Institute of Technology.

*** Kopec and Lomelin; CTE... (DRAFT, do not distibute) *** 1

1 Introduction

Document image decoding (DID) is an approach to document recognition that is based on a commu-

nication theory view of the processes of document creation, transmission and recognition [11]. A

major issue in applying DID to a particular recognition problem is developing explicit models of the

character shapes and positioning in the documents to be recognized [10]. Unlike most approaches

to character recognition, DID emphasizes the use of document-specific bitmap templates as charac-

ter models, rather than “omni-font” feature-based models. The focus on document-specific models

is motivated by the observation that the error rate of a font-specific recognizer can be significantly

less than that of a multi-font system [1]. Thus, in many cases the cost of constructing specialized

templates will be more than offset by a reduced need for post-recognition proofreading and error

correction.

The traditional approach to creating character templates is to average and threshold a set

of aligned sample images for each character. The sample images are typically obtained by inter-

actively segmenting and labeling a set of training pages. Manual segmentation and labeling is a

simple and reliable approach to data preparation that is applicable to a wide variety of document

types. However, it can be very expensive, even with powerful interactive tools such as those de-

scribed in [7].

The success of automatic speech recognition systems based on hidden Markov models (HMMs)

has motivated recent attempts to develop HMM-based methods for printed text recognition [12, 4].

One of the main advantages of the HMM approach is that optimal estimation of character model

parameters can be carried out using whole word or text line images with unaligned transcriptions.

This eliminates the need for segmentation of the training data into individual glyph images prior

to training. However, existing HMM training algorithms are applicable to only a limited range of

character shape and positioning models. HMM text recognizers typically are based on a simple 1-

dimensional typsetting model in which a line of text can be partitioned into individual glyphs by ver-

tical cuts. Thus, although HMM training procedures such as the Baum-Welch (forward-backward)

algorithm [14] do not require segmented input, they do assume that the input is segmentable into

disjoint rectangular regions representing individual glyphs.


Complex graphical notations such as music and equations are not well described in terms of

non-overlapping rectangular components. Moreover, even for simple text, bounding box overlap

can occur in the case of italics or pairwise kerning. Thus, current HMM training methods are not

suitable for the full range of typesetting models found in contemporary documents.

This paper presents an approach to supervised maximum likelihood template estimation,

similar in spirit to current HMM methods, that is applicable to the general sidebearing model of

character shape and positioning that is widely used in digital typography [15]. The inputs to the

training procedure are images of whole pages or text lines plus the corresponding unaligned tran-

scriptions. The method does not assume that the training data can be segmented into individual

glyphs by rectangular subdivision. Rather, glyph segmentation and template estimation are per-

formed contemporaneously on a pixel-by-pixel basis.

The proposed algorithm is a two-phase iterative procedure. The first phase is transcription

alignment, in which the glyph origins are located and labeled using a current set of templates. The

second phase is aligned template estimation (ATE) in which templates are estimated using the cur-

rent labeled glyph origins. The iteration can be started in either phase, i.e., by providing either a set

of initial glyph positions or a set of initial templates.

The training procedure is applicable to a class of multilevel character shape models that gen-

eralizes the bilevel models defined in [11]. The principles underlying the method apply to a general

class of layout models based on stochastic context-free attribute grammars [5, 6]. For simplicity,

however, we will develop the method for the important specific case of Markov image sources [11].

The rest of this paper is organized as follows. Section 2 briefly reviews Markov image

sources and formulates the supervised maximum likelihood template estimation problem. Section 3

defines the multilevel source and channel models. Section 4 discusses aligned template estimation

for multilevel models. Section 5 discusses transcription alignment and the related problem of ini-

tial conditions for the iteration. Section 6 illustrates various aspects of the proposed algorithms and

demonstrates their use in high-accuracy document-specific decoding. Finally, section 7 contains a

brief summary.


2 Background and Problem Formulation

DID is based on a classical communications theory view of document-based information transmis-

sion. A stochastic message source selects a finite string M from a set of candidate strings accord-

ing to a prior probability distribution. An imager converts the message into an ideal image Q. The

message source and imager are typically modelled as a single subsystem called the image source. A

channel maps the ideal image into an observed image Z by introducing distortions due to printing

and scanning, such as skew, blur and salt-and-pepper noise. Finally, a decoder receives image Zand produces an estimate M̂ of the original message according to a maximum a posteriori (MAP)

decision criterion.

Most of the work in DID has focussed on a class of image sources called Markov sources.

A Markov image source is a directed graph consisting of a finite set of states (nodes, vertices) Nand a set of directed transitions (branches, edges) B. Two distinguished members ofN are the ini-

tial state nI and the final state nF . Each transition t connects a pair of states, Lt and Rt, that are

called, respectively, the predecessor (left) state and the successor (right) state of t. Each transition

is labeled with a 4-tuple of attributes, (Qt;mt; at; ~�t), where Qt is a bitmap template, mt is a mes-

sage string, at is the transition probability and ~�t is the vector displacement of t. The template or

message string may be null, i.e. effectively omitted.

A complete path � through a Markov source is a sequence of transitions t0; : : : ; tP�1 whereLt0 = nI , RtP�1 = nF and Rti�1 = Lti for i = 1; : : : ; P � 1.4 In general, a given transition will

occur multiple times in a complete path; we will let Nt be the number of occurances of transition t.A complete path defines a composite message, or transcription, M� = mt0 � � �mtP�1 ,

formed by concatenating the message strings of the transitions of the path. Also associated with

each path is a sequence of positions in the image plane, ~x0; : : : ; ~xP , recursively defined by ~xi+1 =~xi + ~�ti , where ~x0 is an initial position, normally ~0.5 The pairs f(~xi; ti); i = 0; : : : ; P � 1g are

called the labeled glyph positions defined by � and we will let ~x(t)1 ; : : : ; ~x(t)Nt denote the coordinates

of the glyph positions labeled with a particular transition t. By virtue of the labeled glyph positions4All complete paths through a source do not necessarily have the same length. However, for notational simplicitythe dependence of P on � will not be indicated.5We use an image coordinate system in which x increases to the right, y increases downward, and the upper leftcorner of the page is at x = y = 0.


canvas

templateorigin

x

y

W

H

(−χ, ψ)

Figure 1: Canvas parameters and template coordinate system. The lower left corner of the canvasis at (��; ) in the template coordinate system.

a path defines an alignment between the transcription and the image plane.

A complete path or a set of labeled glyph positions defines a composite ideal image Q� byQ� = P�1]i=0 Qti[~xi] (1)

whereQti[~xi] denotesQti shifted so that the origin of its local coordinate system is located at ~xi andUrepresents a template composition rule that defines how the individual templates are merged to

form Q�. In [11] the ideal and observed images are taken to be bilevel bitmaps, with pixel values

of 0 and 1 corresponding to background (normally white) and foreground (normally black), respec-

tively, andU

is the bitwise inclusive or operator.

We denote by qt(~x) the pixel value (color) ofQt at position ~x relative to the local origin of the

template.6 In principle, each template extends over the entire image plane. However, the support

of Qt (the set of locations where qt(~x) differs from the background color) is typically localized to a

small region in the vicinity of the origin. In particular, we assume that the support of each template

lies within a rectangle C of height H and width W . We call this rectangular region the canvas of

the template, illustrated in fig. 1. The template origin is assumed to lie within the canvas, so that0 � � < W and 0 � < H . The canvas parameters H , W , � and may depend on the template,6The color of a template pixel is simply it value and does not necessarily have a physical interpretationas an intensityor color in the ordinary sense (e.g. RGB coordinates).


although we will suppress this dependence. A typical choice forW is 3–5 times the character width.

A complete set of pixel values fqt(~x) j t 2 B; ~x 2 Cg defines a template parameter vector� whose elements are indexed by (t; ~x). The supervised template estimation problem is to find �given an image Z and its transcriptionM . A valid � is required to satisfy the template disjointness

constraint, which can be informally stated as the requirement that the shifted templates Qti[~xi] on

the right hand side of (1) have disjoint support [11]. The disjointness constraint is motivated by the

observation that typefaces are normally designed so that adjacent characters in a line of printed text

do not overlap.

The template disjointness constraint is formalized as follows. Given a set of labeled glyph

positions, each template pixel (t; ~x) defines a set of image locationsI(t; ~x) = n~x+ ~x(t)i ; i = 1; : : : ; Ntothat can be loosely described as the pixels ofQ� or Z that are covered by (t; ~x). Two template pix-

els (t1; ~x1) and (t2; ~x2) are said to conflict if I(t1; ~x1) \ I(t2; ~x2) 6= ;. The set of template pixels

that conflict with (t; ~x) will be denotedK(t; ~x). The template disjointness constraint prohibits pairs

of distinct foreground template pixels from conflicting.

Maximum likelihood template estimation is the problem of finding �̂ such that�̂ = arg max� Pr fZ j �;Mg (2)

and �̂ satisfies the template disjointness constraint. By expanding in terms of paths that are consis-

tent with the transcription, (2) can be written�̂ = argmax� X�jM�=M Pr fZ;� j �;Mg (3)= argmax� X�jM�=M Pr fZ j �;�;MgPr f� j �;Mg : (4)

Since � consists only of pixel color values, it clear that Pr f� j �;Mg = Pr f� jMg. Further-

more, since M is fixed it is easily shown that Pr f� jMg can be replaced by Pr f�g. Moreover,Pr fZ j �;�;Mg = Pr fZ j Q�;�g, where the subscripts on Q�;� reflect dependence on both the


path and the template parameters, and thus (4) becomes�̂ = argmax� X�jM�=M Pr fZ j Q�;�gPr f�g : (5)

As discussed in [11], it is usual to approximate the sum in (5) by its largest term, in which case�̂ = argmax� max�jM�=M Pr fZ j Q�;�gPr f�g : (6)

Finally, following [11] we note that (6) remains valid if the right hand side is divided byPr fZ j Q0g,where Q0 is the all-background image, and the logarithm is taken. If this is done we obtain�̂ = argmax� max�jM�=M [L(Z j Q�;�) + log Pr f�g] (7)

where L(Z j Q�;�) = log Pr fZ j Q�;�gPr fZ j Q0g : (8)

A straightforward approach to the joint maximization over � and � implied by (7) is to

iteratively maximize over � and � in separate parameter update steps,

step 1. �0 arg max�jM�=M [L(Z j Q�;�) + log Pr f�g] (9)

step 2. �0 argmax� L(Z j Q�;�) (10)

starting with some initial templates or glyph positions and continuing until a stopping criterion is

reached. Step 1 of the iteration finds an alignment between the transcription and the image, using

the current set of templates. Step 2 finds a set of templates given the current alignment and is called

aligned template estimation (ATE). Fig. 2 summarizes the overall structure of a supervised template

estimation algorithm based on (9) and (10).

The transcription alignment and ATE operations depend on the exact form of the likelihood

function L(Z j Q). The likelihood function, in turn, is determined by the assumed image source


Templates

Image

Labeled

Glyph Positions

Image

Transcription

Templates

AlignedTemplate

EstimationAlignment

Transcription

Figure 2: Iterative transcription alignment and aligned template estimation.

and channel models. The next section defines the multilevel source and channel models and derives

the corresponding likelihood function.

3 Multilevel Image Source and Channel Models

Previous published work in DID was based on bilevel image models in which Q and Z are binary

images and pixel values of 0 and 1 correspond to background (white) and foreground (black), re-

spectively [11]. The standard bilevel channel is the memoryless asymmetric bit-flip channel char-

acterized by two parameters, �0 = Pr fz(~x) = 0 j q(~x) = 0g and �1 = Pr fz(~x) = 1 j q(~x) = 1g.The likelihood function for the bilevel source and channel is given byL(Z j Q) = kQ ^ Zk + � kQk (11)

where kXk denotes the number of 1’s in X , ^ is the bitwise and operator and = log �0�1(1 � �0)(1 � �1) (12)� = log 1 � �1�0 : (13)

The multilevel source model generalizes the bilevel model by allowing a finite set of colors

for the pixels of Q, i.e. q(~x) 2 f0; : : : ; L� 1g. Level 0 denotes the background color and levels1; : : : ; L � 1 are foreground colors. The observed image Z is bilevel, as before. The multilevel


1

0

0

1

L−1

1α

0α1− 0α1− 1α

αL−1

1−αL−1

Figure 3: L-input symbol, 2-output symbol discrete memoryless channel model.

channel is the L-input symbol, 2-output symbol discrete memoryless channel shown in fig. 3. The

multilevel channel parameters are defined so that the case L = 2 corresponds exactly to the bilevel

model.

One motivation for the multilevel channel is the common observation that pixels in a char-

acter image are more or less “reliable”, depending on their distance from an edge. Intuitively, dif-

ferent levels might correspond to “black pixel near edge”, “black pixel away from edge”, “white

pixel near edge”, etc. While this intuition is helpful, it should be noted that our approach to pixel

color assignment is based solely on statistical criteria.

Depending on the relationship between �l and �0 one of two physical interpretations can be

attached to a foreground level. If �l > 1 � �0 then a foreground pixel is more likely than a back-

ground pixel to be observed as black. This corresponds to the common situation of black-on-white,

or “write-black”, printing. Conversely, if �l < 1 � �0 then a foreground pixel is less likely than

a background pixel to be oberved black. This corresponds, loosely, to “reverse video”, or “write-

white” printing.

A given template (or set of templates) may include both write-black and write-white levels.

In particular, we have found it useful to include a write-white level even when decoding printed

text that was physically produced by depositing black ink on white paper. In that situation, a write-

white template can be used to model “space” characters. Modeling space characters as templates

allows their parameters to be estimated in the same way as those of “printing” characters.

A related use for write-white is to explicitly model the whitespace that typically occurs in

the immediate vicinity of a black glyph (e.g. interior of ‘o’, cup of ‘u’ etc.). Templates with both


write-black and write-white levels are similar to the hit-miss transforms used for morphological

shape recognition [2]. Fig. 19 shows a set of multilevel templates for 212 characters in four fonts

of the Times family, created as described in section 6. The level parameters are �0 = :95, �1 = :999and �2 = :001. The background level is rendered as middle gray. For the “printing” characters, the

write-black (�1) and write-white (�2) levels are rendered in black and white, respectively. The four

space templates (e.g. upper left corner) have a single foreground level (�2) that is rendered in black.

The derivation of (11) presented in [11] can be generalized to multilevel models by treating

each foreground level as a separate bilevel template. If Q is a multilevel template, let ~Q(l) be the

bilevel bitmap representing the lth level set of Q, defined by~q(l)(~x) � 8><>: 1 if q(~x) = l0 otherwise.(14)

Then, it is not difficult to show thatL(Z j Q) = L�1Xl=1 h l k ~Q(l) ^ Zk + �l k ~Q(l)ki (15)= L�1Xl=1 L(Z j ~Q(l)) (16)

where l and �l are given by (12) and (13) for each level. For a write-white level, l < 0 and �l > 0.

As a result, L(Z j ~Q(l)) will be maximally positive when ~Q(l) is positioned over pure whitespace

and will decrease as more black pixels fall under ~Q(l).The significance of (16) is that the problem of multilevel ATE effectively reduces to the

bilevel case. To show this, we begin by observing that if Q1 and Q2 are multilevel templates with

disjoint support then L(Z j Q1 +Q2) = L(Z j Q1) + L(Z j Q2), where + denotes elementwise

addition. This follows from (16) and the analogous result for bilevel templates. As a result, if the

template composition operatorU

in (1) is taken to be addition we haveL(Z j Q�;�) = P�1Xi=0 L(Z j Qti;�[~xi]) (17)

which again generalizes a bilevel result. By expanding the right hand side of (15) in terms of indi-


vidual pixels, L(Z j Qti;�[~xi]) in (17) can be writtenL(Z j Qti;�[~xi]) = X~x2C L�1Xl=1 h l~q(l)ti (~x)z(~x+ ~xi) + �l~q(l)ti (~x)i : (18)

Substituting this into (17) givesL(Z j Q�;�) = P�1Xi=0 X~x2C L�1Xl=1 h l~q(l)ti (~x)z(~x+ ~xi) + �l~q(l)ti (~x)i : (19)

If the outer summation over path transitions is replaced by a summation over source model transi-

tions, (19) becomesL(Z j Q�;�) = Xt2B NtXi=1X~x2C L�1Xl=1 h l~q(l)t (~x)z(~x+ ~x(t)i ) + �l~q(l)t (~x)i (20)= Xt2BX~x2C L�1Xl=1 ~q(l)t (~x) " l NtXi=1 z(~x+ ~x(t)i ) + �lNt# : (21)

In the L = 2 case of bilevel templates, (21) reduces toL(Z j Q�;�) = Xt2BX~x2C qt(~x) " NtXi=1 z(~x+ ~x(t)i ) + �Nt# : (22)

Multilevel ATE is the problem of choosing� to maximizeL(Z j Q�;�)while satisfying the

template disjointness constraint. Comparison of (21) and (22) suggests that multilevel estimation is

equivalent to bilevel estimation of the level set bitmaps, with two minor differences. First, the level

set bitmaps must satisfy the constraint that only one value of ~q(l)t (~x) may be non-zero for a given tand ~x. However, this will happen automatically as a consequence of the template disjointness con-

straint. Second, in (22) the same values of and � are used for all templates, whereas in (21) they

depend on the level. However, this is simply a bookeeping issue that introduces no real difficulty.

Thus, the following sections focus primarily on algorithms for bilevel estimation. Except where

noted, the corresponding multilevel versions are obvious.


Figure 4: Glyph image regions for Times Roman “a”. The canvas origin is indicated by a cross.

4 Aligned Template Estimation (ATE)

Traditional character template estimation is concerned with deriving a character template from a set

of isolated images of the character. The character images are typically extracted from a page image

during a segmentation operation that preceeds template estimation. The inputs to an ATE algorithm,

by contrast, are a page image and a path in the page image (equivalently, the set of labeled glyph

positions defined by a path).

Although our ATE algorithms are not based on character image segmentation, it is instruc-

tive to consider the analog of the isolated character image in ATE. If (~xi; ti) is a labeled glyph po-

sition, the corresponding glyph image region is defined to be that portion of Z within the canvas ofQti , when the canvas origin is positioned at ~xi. Fig. 4 shows a collection of glyph image regions for

the Times-Roman character “a” drawn from a set of scanned pages [3]. As the figure illustrates, a

glyph image region typically contains glyphs and/or parts of glyphs in addition to the glyph located

at the canvas origin. Similarly, it is clear that there can be significant overlap between the glyph im-

age regions at adjacent glyph positions. As part of the estimation process, an ATE algorithm will

effectively decide which of the pixels in each glyph image region belong to the labeled glyph, and


which belong to adjacent glyphs.

If the glyphs in Z are spaced far enough apart (or the template canvasses are small enough)

that the glyph image regions do not overlap, then the template disjointness constraint is satisfied

trivially. In that case, ATE reduces to separately maximizing each term of the right hand side of

(22) and the bilevel template pixel color assignment rule becomesqt(~x) = 8><>: 1 if S(t; ~x;Z) > 00 otherwise(23)

where S(t; ~x;Z) � NtXi=1 z(~x+ ~x(t)i ) + �Nt: (24)

The reason for explicitly indicating the dependence on Z will be clear shortly. If the foreground is

write-black, the condition S(t; ~x;Z) > 0 can be written as1Nt NtXi=1 z(~x+ ~x(t)i ) > �� (25)

which has a simple interpretation. The left hand side of (25) is the fraction of pixels at ~x that are

black in the glyph image regions for Qt. The color assignment rule prescribes that the template

pixel at ~x should be black if the fraction of black pixels at ~x in the aligned glyph image regions

exceeds a threshold. Simply, the template is computed by averaging and thresholding the aligned

glyph image regions. Similar results hold for write-white foregrounds, except that the analog of

(25) has the sense of the inequality reversed.

When the glyph image regions overlap, independent application of (23) does not produce a

set of maximum likelihood templates, even if the disjointness constraint is removed. However, it is

clear that S(t; ~x;Z) > 0 is a necessary condition for (t; ~x) to be a foreground pixel in a maximum

likelihood template, i.e., (23) defines a superset of the ML foreground pixels. For this reason, (23)

is useful for generating initial sets of candidate foreground pixels in ATE algorithms.

Maximizing (22) subject to the template disjointness constraint is an NP-complete prob-


procedure (B; C; Z) do beginqt(~x) := 0 8t 2 B; ~x 2 CQ := f(t; ~x) j S(t; ~x;Z) > 0gwhile Q 6= ; do begin(s; ~w) := arg max(t;~x)2QS(t; ~x;Z)qs(~w) := 1Q := Q�K(s; ~w)� f(s; ~w)gend

end

Figure 5: A simple greedy template pixel color assignment algorithm.

lem, as shown in appendix A. Indeed, the problem remains NP-complete even if the constraint is

removed. The implied worst-case exponential complexity would not necessarily be troublesome if

ATE problems qualified as “small”. However, as an example, the foreground pixels in the templates

shown in fig. 19 were selected from a candidate set containing about 125,000 pixels. For compari-

son, we have found that exhaustive evaluation of alternative pixel assignments is feasible for up to

about 20 pixels.

The NP-completeness of ATE implies that a practical estimation algorithm cannot guarantee

that (22) will be maximized. Nevertheless, for image decoding applications it does appear possible

to construct effective templates without this guarantee. The following two simple algorithms have

been useful in practice and illustrate the main issues in template estimation. The first enforces the

disjointness constraint strictly, while the second allows templates to overlap slightly. We note that

the space of possible ATE strategies has not been extensively explored. Thus, these algorithms may

be subject to significant improvement.

A simple greedy pixel coloring algorithm is shown in fig. 5. The algorithm begins by assign-

ing all pixels to the background and constructing a set of candidate foreground pixels Q using (23).

The algorithm then iteratively selects the most promising single pixel (s; ~w) fromQ and assigns it

to the foreground. In case of a tie, one of the maximum score alternatives is selected randomly. The

selected pixel and all of its conflicts K(s; ~w) are removed from Q. The iteration continues untilQis empty.


procedure (B; C; Z) do beginQ := f(t; ~x) j S(t; ~x;Z) > 0gwhile Q 6= ; do begin(s; ~w) := arg max(t;~x)2QS(t; ~x;Z)

if qs(~w) = 1 do beginW := K(s; ~w)F := f(t; ~x) j qt(~x) = 1gV := [(t;~x)2WK(t; ~x) \ Fmake assignments to W [ V

endQ := Q� f(s; ~w)gend

end

Figure 6: A pixel color assignment refinement procedure.

The algorithm in fig. 5 produces relatively good templates, as we will see. However, it ex-

hibits a failure mode that is typical of greedy labeling algorithms that only consider one candidate

at a time. Suppose template pixel (t̂; ~̂x) maximizes S(t; ~x;Z) and that (t̂; ~̂x) conflicts with both(t1; ~x1) and (t2; ~x2). Then the algorithm will make (t̂; ~̂x) a foreground pixel and assign (t1; ~x1) and(t2; ~x2) to the background. But suppose further that (t1; ~x1) and (t2; ~x2) do not conflict with each

other and that S(t1; ~x1;Z) + S(t2; ~x2;Z) > S(t̂; ~̂x;Z). In that case, a better assignment might

be to put (t1; ~x1) and (t2; ~x2) in the foreground and move (t̂; ~̂x) to the background. However, this

possibility is not considered by the greedy algorithm.

A simple approach to eliminating the above problem is to follow the greedy algorithm with a

refinement procedure that examines perturbations to the set of identified foreground pixels. Fig. 6

shows an example of such a refinement procedure. The inputs to the algorithm include an initial

assignment that is assumed to satisfy the disjointness constraint. The algorithm attempts to improve

on the initial assignment while preserving disjointness. The basic strategy during each iteration is to

identify a small set of pixels whose assignments can be modified, as a group, without considering

pixels outside the set. The set is constructed by considering two levels of conflicts from a single

“root” pixel (s; ~w) that is in the foreground in the current assignment. The root pixels are selected


by considering the members of a candidate set Q in order of decreasing score. The set W consists

of all the pixels that conflict with the root. Since the disjointness constraint is assumed to hold,

each of the pixels inW is 0. The set V contains all of the conflicts withW that are currently in the

foreground (including the root pixel).

It is not hard to see that no set of assigments to the pixels inW[V can introduce a foreground

conflict with any pixel outside the set. Thus, the assignments toW[V may be optimized, subject to

the disjointness constraint, without regard for any other pixels. IfW[V contains fewer than about

20 members exhaustive optimization is feasible. For larger sets a useful approach is to compare

the current assignment with just one alternative, created by applying the greedy algorithm first toW and then to the pixels of V that do not conflict with the resulting foreground pixels inW . The

refinement procedure can be applied repeatedly; we have found that after three or four iterations

the change in likelihood becomes insignificant.

The greedy algorithm and refinement procedure enforce the template disjointness constraint

rigorously. If the transcription and glyph positions are accurate, doing so leads to good templates.

However, if the transcription or alignment is errorful, the disjointness constraint can cause prob-

lems. As a simple example, suppose the input consists of a very large number of glyph positions,

all of which are correct except for a single pair of adjacent glyphs whose estimated locations are

too close together. In particular, suppose that the correct templates would overlap if placed at the

two incorrect locations, but would not overlap at any of the other glyph positions. If the estimated

templates are forced to be disjoint, one or both will have missing pixels, compared with the correct

templates. This will happen regardless of the number of correct glyph positions.

Fig. 7 shows an algorithm that softens the disjointness constraint and avoids this problem.

This algorithm is structurally very similar to the greedy algorithm but is more easily explained as

a variation of independent pixel asignment. In differs from independent assignment in that (23) is

not applied independently (i.e., simultaneously) to each pixel, but rather a value of 1 is assigned

sequentially to each pixel for which S(s; ~w;Z) > 0. After each such assignment, the image Z is

modified by setting to 0 all pixels in Z that are covered by the newly-assigned template pixel, i.e.

the pixels in I(s; ~w). The effect of clearing Z is to reduce the value of S(s; ~w;Z) for conflicting

template pixels that have not yet been considered, thereby decreasing the likelihood that they will


procedure (B; C; Z) do beginqt(~x) := 0 8t 2 B; ~x 2 CQ := f(t; ~x) j S(t; ~x;Z) > 0gwhile Q 6= ; do begin(s; ~w) := arg max(t;~x)2QS(t; ~x;Z)qs(~w) := 1

for i = 1; : : : ; Ns do z(~w + ~x(s)i ) := 0Q := f(t; ~x) j S(t; ~x;Z) > 0gend

end

Figure 7: A pixel color assignment algorithm that softens the template disjointness constraint.

be set to 1.

The algorithm in fig. 7 is applicable when all foreground levels are write-black but is easily

modified for other cases. If all foreground levels are write-white, the modification simply consists

of setting the pixels of Z to 1 rather than to 0. For templates with both types of levels, separate

copies of Z are maintained for the write-black and write-white levels.

5 Transcription Alignment and Initial Conditions

Transcription alignment (9) involves finding a complete path � that maximizes L(Z j Q�;�) +log Pr f�g, subject to the constraint that M� = M , where M is the given transcription. This is a

constrained decoding problem that is analogous to the speech recognition problem of training hid-

den Markov models using sentence-level transcriptions [14]. By analogy with the speech case, con-

strained decoding can be carried out in two steps. First, the image source model and transcription

are combined into a transcription image source model. The transcription image source is defined

as a source that generates the subset of the original source images consisting of just those whose

message is M . Second, image Z is decoded using the transcription image model. The resulting

complete path defines an alignment between M and Z .

The transcription image source can be constructed using a straightforward extension to the


(1, 0)(1, 0) (1, 0)(1, 0)

Q d

"d"

d∆( , 0)

Q i

"i"

i∆( , 0)

Q d

"d"

d∆( , 0)n I n F

Figure 8: Transcription image source for simple text line and transcription string “did”.

standard algorithm for intersecting two finite-state automata [8]. This construction is applicable to

any Markov image source and transcription that can be described using regular grammars. Thus,

for example, templates for the yellow page model discussed in [11] could be trained using the two-

dimensional source models and LaTeX-like transcriptions presented therein. In practice, however,

we anticipate that applications of template estimation will primarily involve one-dimensional hor-

izontal source models, such as those described in [9], applied to images of individual text lines.

The reason is that full two-dimensional decoding is significantly more expensive computationally

than line decoding and is unnecessary if the lines can be extracted reliably through simpler means.

Moreover, for most text decoding applications it is sufficient to train using a simple text line model

in which any character may follow any other and the messages include no logical or formatting tags.

The transcription image models for such sources have the simple form illustrated in fig. 8, which

shows a line source for images of the string “did”. The model consists of a chain of transitions for

the characters of the string plus unit displacement self-transitions for horizontal spacing adjustment.

Image decoding using Markov source models with bilevel templates is described in [11].

The only change introduced by multilevel templates is in the computation of the template match

scores L(Z j Qt[~x]). However, by (16), if a multilevel template is represented by its level set

bitmaps then algorithms for the bilevel template matching operation (11) can be used to compute

the multilevel likelihood.

The iterative alignment and ATE algorithm in fig. 2 can be started with either a set of initial

templates or a set of initial glyph positions. A simple way to obtain initial templates is to excise a

sample of each required character from the training images using an interactive tool [7]. Alterna-


Figure 9: Templates for word boundary location. Baseline indicated by dash line. Left: Support ofwrite-white space character template. Right: Support of write-black printing character template.

tively, initial templates can be derived from an existing bitmap or outline font. We have found that

the training procedure is not very sensitive to the exact shapes or sizes of the initial templates. In

particular, if the templates are extracted from images it is usually sufficient to excise a single sample

of each character.

If the transcription is plain text, a set of initial glyph positions can be found by first locating

the start and end point of each transcription word in the image and then dividing the horizontal

word interval into the proper number of glyph positions. The glyph origins can be either spaced

uniformly or at intervals proportional to character set widths obtained from an existing font. We

have found that proportional spacing usually leads to better initial templates than uniform spacing

and is insensitive to the choice of font for the set widths.

The word endpoints can be found using the normal transcription alignment procedure and

templates such as those shown in fig. 9. The space template is a solid rectangle, in this case 15

pixels wide by 60 pixels high. The template for each printing character is a 15 by 15 square. The

set width of each template is taken to be 6 pixels. These dimensions and set widths are appropriate

for 12 pt fonts, although the exact values do not appear to be critical. The important dimension is

the width of the space template, which should be larger than the intercharacter gaps within a word

but smaller than the minimum interword space. When this condition is satisfied we have found that

the space templates will be reliably positioned between the words.


6 Experimental Results

We have applied the above template estimation algorithm to a variety of English documents, includ-

ing newspaper columns, 15th century books, degraded microfilm images of 19th century newspa-

pers, connected text in script-like fonts, and mathematical notation. The most extensive application

has been to create document-specific templates for decoding scanned reports in the Environmen-

tal Digital Library at the Univ. of California at Berkeley [16]. Many of these documents are rel-

atively long (100-600 pages) and contain statistical information that is useful only if accuractely

transcribed. We will use one of the Berkeley documents to illustrate the training algorithms and the

use of document-specific templates in image decoding.

Bulletin 155 (B155) [3] is a report by the California Department of Water Resources (DWR)

that summarizes the provisions of 157 state water district acts. The information about each act is

presented as a two column table that spans one to five pages. Fig. 10 shows a portion of one ta-

ble. B155 contains 375 pages of such tables (about 540,000 glyphs). B155 also contains about 20

pages of single column background material comprising a table of contents, explanations of terms,

summaries of related legislative acts, etc. The text of the tables and background pages is typeset

in 12 pt Times family fonts. The dominant style is Roman, with small amounts of Italic, Bold and

BoldItalic.

The basic scenario in document-specific decoding is to train a set of templates using a small

subset of the document pages plus their transcriptions and then use the templates to decode the re-

maining pages. In the case of B155 we trained using the 20 single column pages and then decoded

the 375 table pages. B155 was selected because of the availablility of a WordPerfect source file to

serve as ground truth in the recognition experiments and as a source of training transcriptions.7Table 1 summarizes the composition of the training data in terms of the numbers of charac-

ters and glyphs in each of the four fonts. In counting glyphs, an interword space is treated as one

instance of a space character. The training data contains a total of 212 characters, where charac-

ters in different fonts are considered to be distinct. The mean number of samples of each character

varies widely over the four fonts, from about 500 for Roman to 2 for Bold. The Bold text consists7Access to the WordPerfect source makes B155 ideal for performance evaluation but of course lessens the value ofthe resulting transcription.


Figure 10: Portion of page from DWR Bulletin 155.

Style Characters GlyphsRoman 83 42004

BoldItalic 63 1468Italic 43 316Bold 23 46

Table 1: Character and glyph counts for the training pages of Bulletin 155. Fonts are 12 pt Timesfamily.


solely of the string “District Securities Investigation Law of 1965” in which 13 characters appear

just once. As we will see, this leads to considerable difficulty in estimating the Bold templates.

The 212 training characters can be seen in fig. 19, which shows the final templates used to

decode the B155 tables, grouped by font in the order Roman, BoldItalic, Italic and Bold (i.e. in

order of decreasing training glyph count). Within each font the space character is first, followed

by the normal “printing” characters. Each row of templates is aligned with the template origins on

a horizontal baseline. Similarly, the templates in each column are aligned with their origins on a

vertical line. This template order and alignment are used in all of the figures in this section.

The templates in fig. 19 were created by 25 iterations of the algorithm in fig. 2 using the soft

constraint ATE procedure of fig. 7. Initial glyph positions were found using the word alignment

approach described in the previous section with proportional spacing of glyphs within each word.

The channel parameters were set manually to �0 = :95, �1 = :999 and �2 = :001.

Before discussing the performance of the final templates in decoding, we will illustrate var-

ious aspects of the ATE and alignment algorithms using the B155 training data. The labeled glyph

positions required by the ATE algorithms were taken from the final iteration for the templates of

fig. 19. Visual inspection revealed these positions to be relatively accurate.

6.1 Aligned Template Estimation

Fig. 11 shows a set of bilevel templates estimated by independent application of (23) to each can-

vas pixel, using the (assumed) known glyph positions. Each of the templates clearly shows the

“correct” character shape, aligned at the origin of the canvas, plus “extra” foreground pixels due

to neighboring glyphs in the glyph image regions. The number of extra pixels is relatively small

for the most common characters of the Roman font and increases as the amount of training data

decreases. Overall, the Roman templates are remarkably clean, suggesting that with a sufficiently

large and diverse training set most of the extra foreground would be eliminated as a consequence

of the averaging process in (25).

As noted previously, the supports of the independent templates are supersets of the supports

of the maximum likelihood templates. Table 2 shows the total number of template foreground pix-

els,Pt2B kQt;�k, and the training data likelihood, L(Z j Q�;�), for the various ATE algorithms.


Figure 11: Templates estimated by independent application of (23) to each canvas pixel.

AlgorithmXt2B kQt;�k L(Z j Q�;�)

independent 126833 45070greedy 79777 54943refined 80762 54967

soft 80126 55075

Table 2: Bulletin 155 foreground template pixel counts and training data likelihoods for variousATE algorithms.

Fig. 12 shows a set of templates produced using the greedy algorithm of fig. 5. Compared

with the independent templates, the greedy templates have significantly fewer extra foregound pix-

els. Table 2 confirms this and also shows that the training data likelihood is significantly greater for

the greedy templates.

The greedy algorithm selects randomly from the set of maximum score candidates during

each iteration, as discussed previously. This random selection is evident in the Italic “E” and “x”

templates in fig. 12. The training data contains one sample of each of these characters, in the word

“Explanatory”. Every allowable distribution of the foreground pixels of “Ex” between the two tem-


Figure 12: Templates estimated using the greedy algorithm.

plates has the same score and thus the maximum likelihood templates are inherently ambiguous. A

similar situation arises with BoldItalic “-K” and Bold “1965.” A partial solution to the ambiguity

problem is described below.

Several of the templates in fig. 12, most notably the BoldItalic numerals, have “holes” in

them. The BoldItalic parentheses, conversely, have extra pixels that exactly match these holes.

Each of the BoldItalic numerals except zero occurs adjacent to a parenthesis at least once in the

training data. The holes arise because the foreground pixels of the parentheses are assigned before

those of the numerals— both left and right parentheses occur more frequently than any single nu-

meral (but less frequently than all numerals combined). To satisfy the disjointness constraint, the

conflicting pixels in the numerals are then assigned to the background. This is an example of the

greedy failure mode that motivated the refinement procedure of fig. 6.

Fig. 13 shows the result of four iterations of the refinement procedure on the templates of

fig. 12. The holes are filled and all of the templates, except the Bold ones and those with inherent

ambiguities, are of fairly high visual quality. As table 2 indicates, the refinement procedure slightly

increases both the number of foreground pixels and the training data likelihood.

Fig. 14 shows results from the soft constraint algorithm of fig. 7. Visually, the soft con-


Figure 13: Templates derived from fig. 12 after four iterations of the refinement procedure.

Figure 14: Templates estimated using the soft constraint algorithm of fig. 7.


Figure 15: Templates derived from fig. 12 using the refinement procedure with a distance-based tiebreaking criterion.

straint templates are slighly better than those from the greedy algorithm, but not quite as good as the

refined greedy templates. The BoldItalic numerals have holes, but the holes in a number of other

templates are missing. Indeed, from table 2 we see that the number of foreground pixels is inter-

mediate between the greedy and refined templates. Interestingly, the soft algorithm provides the

greatest likelihood of any of the ATE procedures.

Finally, fig. 15 shows the result of a simple modification to the refinement procedure in-

tended to resolve some of the cases of template ambiguity. Rather than randomly select among

equal likelihood assignments toW [ V , an assignment was chosen with minimum total absolute

horizontal distance of the foreground pixels from the canvas origin. This has the effect of prefering

templates whose supports are localized near the origin. Comparing fig. 15 with fig. 13 shows that

the result can be a significant improvement in visual template quality.

6.2 Iterative Transcription Alignment and Template Estimation

Transcription alignment was performed on a line-by-line basis during estimation of the B155 tem-

plates, using transcription image models of the type shown in fig. 8. The line baselines were ex-


Figure 16: Templates estimated by the soft constraint algorithm from glyph positions obtained byword alignment and proportional glyph spacing within each word.

tracted by decoding the training images using a simple text page model with 12 pt Times Roman

templates generated by a PostScript font program. While the decoded text was extremely errorful,

the baseline locations were reasonably accurate.

Initial templates were created by applying the soft constraint ATE algorithm to the glyph po-

sitions estimated by the word alignment procedure described in section 5. The resulting templates,

shown in fig. 16, are inferior to those obtained using accurate glyph positions, as expected.

Fig. 17 shows the estimated templates after 20 iterations of alignment and ATE. The Roman

and BoldItalic templates are similar to those obtained using accurate glyph positions. Many of the

Italic templates are also correct but most of the Bold ones are wrong. As might be expected, many

of the individual glyph positions in all four fonts are incorrect. The relatively high quality of the

Roman and BoldItalic templates reflects the fact that there were enough accurate positions for the

averaging process to produce acceptable estimates.

Lack of tolerance to glyph position errors was cited previously as a problem with the greedy

algorithm. This is illustrated in fig. 18, which shows the templates produced after 20 iterations of

the greedy algorithm. Overall, these templates are inferior to those in fig. 17. One source of error

is illustrated clearly by the BoldItalic “D” template, which appears to have an “i” cut out of it. The


Figure 17: Templates estimates after 20 iterations using soft constraint algorithm with distance-based tie breaking criterion. Initial templates as in fig. 16.

Figure 18: Templates estimates after 20 iterations using greedy algorithm with distance-based tiebreaking criterion. Initial templates as in fig. 16.


Figure 19: Multilevel template estimates after 5 iterations of soft constraint algorithm with distance-based tie breaking criterion. Initial templates from fig. 17 with manual adjustment of canvas param-eters.

most common context for BoldItalic “D” in the training data is the word “District”. In at least one

instance, the template for the “i” was incorrectly positioned on a “D”. Because “i” is more common

than “D” in the training data, the foregound pixels of “i” were assigned before those of “D”. The

template disjointness constraint then forced the conflicting “D” pixels into the background.

Finally, fig. 19 shows the result of five iterations starting with the templates of fig. 17 after

manual adjustment of the canvas parameters. The origins and set widths of the 212 templates were

inspected and adjusted using a bitmap font editor. In addition, each template canvas was manually

trimmed to be about 10 pixels wider than the expected template support. The editing was intended

to correct gross alignment errors and thus was performed quickly and with only moderate care. Dur-

ing the final iteration, a write-white level was estimated for the printing characters, leading to the

multilevel templates shown.


Decoder Language Character ErrorsModel Substitutions Deletions Insertions Total (%)

ScanWorX word lexicon 2149 1069 1061 4279 (0.79%)DID char. unigram 430 73 80 583 (0.11%)DID char. uni+bigram� 289 72 68 429 (0.079%)DID char. bigramy 87 57 53 197 (0.036%)� bigrams for table headings, unigrams elsewherey bigrams collected from entire document

Table 3: Character recognition results on Bulletin 155 tables.

6.3 Recognition Results

The templates of fig. 19 were used to decode the 375 table pages of B155, using several simple

language models. For comparison, the pages were also transcribed using the commercial omni-

font recognition system ScanWorX.8 Results of the experiments are summarized in table 3. The

errors rates were computed in the standard way by dividing the total number of insertions, deletions

and substitutions (computed by minimum edit distance alignment of the decoded and ground truth

transcriptions) by the number of ground truth characters (543,779). The error calculation included

space characters and ignored differences in font.

The character unigram language model allows any of the 212 characters to follow any other

and exactly corresponds to the simple text column model described in [11, 9]. The unigram model

imposes no constraints on character sequencing and thus places the entire recognition burden on the

templates. As table 3 shows, the unigram error rate of 0.11% is about a factor of seven less than that

of the omni-font system. This is particular noteworthy since ScanWorX employs a large lexicon of

English words and the text of B155 is largely ordinary text.

Examination of the unigram errors revealed that a large fraction occurred in the uppercase

table headings, e.g. “COMMUNITY FACILITIES DISTRICTS” at the top of fig. 10 and many

involved uppercase to lowercase substitutions, such as “I” into “ l”. The table headings were rere-

cognized using a bigram model in which the characters allowed to follow a given character were

restricted to just those that were observed to follow the character in the training data. Thus, for ex-8Xerox Desktop Document Systems, Peabody, MA.


ample, the bigram model allowed the sequence “ IT” but not “ lT” or “ iT”. The bigram model was

derived from the entire training set and consisted of 1670 bigrams. Use of the bigram model on the

table headings reduced the overall error rate to 0.079%, a factor of ten below ScanWorX.

Finally, the tables were decoded using a bigram model derived from the ground truth for all

395 pages. This is the smallest bigram model that is capable of recognizing the data perfectly and

is included to provide an upper bound on the performance of any bigram model for this data. The

observed error rate was 0.036%, a factor of twenty below ScanWorX.

The bigram model trained on all of B155 contained 2232 bigrams, which is 652 more than

the bigram model derived from the 20 training pages alone. By considering the relative frequency

of the bigrams, it can be predicted that a decoder using the training page bigram model will mis-

recognize at least 4744 (0.87%) of the characters in the tables. Since this error rate exceeds that of

the unigram model, decoding with a pure training bigram model was not carried out.

7 Summary

A maximum likelihood approach to character template estimation using unaligned transcriptions

has been developed. The kernel of the approach is a method of aligned template estimation (ATE)

that allows the bounding boxes of adjacent glyphs to overlap. While the method was developed

specifically to support the creation of document-specific decoders in the DID framework, it is ap-

plicable to any situation in which character templates are to be derived from sample images.

8 Acknowledgements

The authors wish to thank Phil Chou for many stimulating discussions throughout the course of

this work. The B155 data was provided by the Univ. of California Environmental Digital Library

Project, headed by Robert Wilensky and supported by National Science Foundation grant IRI-9411334

as part of the NSF/NASA/ARPA Digital Library Initiative.


(1, 0) (1, 0)

Q vl1 1

rQ v Q v

l Er

Q vE

n I nF

Figure 20: Image source for independent set problem.

A NP-Completeness of Aligned Template Estimation

Aligned template estimation (ATE) is the problem of choosing � to maximizeL(Z j Q�;�) in (22)

subject to the template disjointness constraint. The theory of NP-completeness applies to decision

problems, i.e. problems whose solution is either “yes” or “no”. ATE can be transformed into a

decision problem by the standard technique of introducing a numerical parameter B and asking

whether there is a � for which L(Z j Q�;�) � B. We establish the NP-completeness of ATE

by showing that any algorithm that solves ATE exactly can be used to solve the independent set

problem, which is known to be NP-complete [13].

Let G be an undirected graph consisting of a finite set of vertices V = fv1 : : : vV g and a

finite set of edges E = f(vli; vri); i = 1 : : : Eg. An independent set of vertices is a subset V 0 � Vwith the property that no pair of vertices in V 0 are joined by an edge in E . Given a positive integerK , the independent set (IS) problem is to decide whether or not G contains an independent set of

size at least K .

Given a graph G and positive integer K , we construct an ATE decision problem whose so-

lution is equivalent to IS for G and K . This involves specifying a source model, a complete path�, an image Z and a likelihood bound B. Fig. 20 shows the source model, a simple chain of 3Ebranches that has exactly one complete path �. Each graph vertex v 2 V corresponds to a templateQv whose canvas consists of the single point at the template origin. We will view the template pix-

els as being indexed by the vertices in V . The branches of the source model occur in groups of

three, where each triple corresponds to one edge in E . The first two of the three branches represent-

ing edge (vli; vri) are labeled with templates Qvli and Qvri and have zero displacement. The third

branch has unit horizontal displacement, (1; 0).


It is not hard to see that kQ�k = E and that template pixels u and v conflict if and only if(u; v) 2 E . Thus, each independent subset V 0 � V corresponds to a set of template pixels that do

not conflict, i.e. a candidate pixel assignment � that satisfies the template disjointness constraint.

If Nv denotes the number of edges attached to vertex v it is clear that kI(v)k = Nv . Let

each templateQv be associated with a separate write-black level and let the channel parameters be

given by �0 = e1 + e (26)�v = e 1Nv1 + e: (27)

Then, ifZ is taken to be the ideal imageQ� it is easy to show from (12), (13) and (24) thatS(v;Z) =1 for each pixel v. As a result, kV 0k = L(Z j Q�;�), where � is the pixel assignment that corre-

sponds to V 0. It should be clear that the ATE decision problem with B = K is equivalent to the

given IS problem.

If the template disjointness constraint is removed, a similar construction can be used to show

that a solution to the (uncontrained) ATE problem implies a solution to the NP-complete minimum

cover [13] problem.

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