Archaeological Stratigraphy as a formal language for virtual reconstruction. Theory

and practice.

Emanuel Demetrescu

CNR-ITABC

Istituto per le Tecnologie Applicate ai Beni Culturali

Via Salaria, km 29.3 - 00015 Monterotondo, Roma

Abstract

In recent years there has been a growing interest in 3D acquisition techniques in the field of cultural heritage, yet, at thesame time, only a small percentage of case studies have been conducted on the virtual reconstruction of archaeologicalsites that are no longer in existence. Such reconstructions are, at times, considered “artistic” or “aesthetic” endeavors, asthe complete list of sources used is not necessarily provided as a reference along with the 3D representation. One of thereasons for this is likely the lack of a shared language in which to store and communicate the steps in the reconstructionprocess. This paper proposes the use of a formal language with which to keep track of the entire virtual reconstructionprocess. The proposal is based on the stratigraphic reading approach and aims to create a common framework connectingarchaeological documentation and virtual reconstruction in the earliest stages of the survey. To this end, some of thetools and standards used in archaeological research have been “extended” to taxonomically annotate both the validationof the hypothesis and the sources involved.

Keywords: 3D virtual reconstruction, archaeological stratigraphy, 3D reconstruction methodology, 3D modelling inarchaeology, Virtual Stratigraphic Unit, Extended Matrix

1. Introduction1

The goal of this paper is to propose a theoretical and2

practical framework with which to keep track of, manage,3

and publish the steps in the archaeological reconstruction4

process. The primary approach (see infra sec. 3) is based5

on the same formal language already in use to create ar-6

chaeological stratigraphic records during excavation and7

survey1, and makes use of its consistency and standard-8

ization. The stratigraphic method is based on the laws9

of the geological stratification (see infra par. 3.1) and is10

characterized by a taxonomic approach and data consis-11

tency (see Barker 2003, Carandini 1981, Giuliani 1976,12

Medri 1988, Medri 2003). There are several examples of13

institutionally defined standards (see ADS - Archaeolog-14

ical Data Service “http://archaeologydataservice.ac.uk/”15

and Parise Badoni and Ruggeri 1988.).16

In order to fulfill this statement, a subset of the “classic”17

archaeological record-keeping concepts and tools – such as18

Email address: emanuel.demetrescu@itabc.cnr.it (EmanuelDemetrescu)

1In this paper, with the term survey, I mean not only the ac-quisition of the shape (laser scanner, drawings, photogrammetry) ofextant buildings, objects and other archaeological contexts but alsothe examination and data recording of its stratigraphy (phases ofconstruction). It results in a ”4D survey” with data collection aboutgeometries and chronological sequence (see infra sec. 5).

the Stratigraphic Unit (or Context)2, the Activity, and the 1

Matrix of Harris – have been “extended” (see infra sec. 2

4) to include and define not only re-constructive elements 3

(like “lost” columns, friezes, capitals, etc.), but the sources 4

on which they are based as well. The primary tools used 5

are (1) the Virtual Stratigraphic Unit (or USV) organized 6

into a diagram; and (b) the Extended Matrix (EM)3. 7

Archaeological stratigraphy, intendend as the study of 8

the actions’ sequence made in the past, provides a robust 9

methodology to acquire and manage data (segmentation 10

and annotation of the context in small parts) that can 11

be applyed to archaeological excavations, extant buildings, 12

objects and other contexts where it is possible to distin- 13

guish di↵erent phases of construction (4D data). 14

The objective of this paper is not to propose solutions 15

for the visualization of the 3D model’s degree of reliability 16

(such as, gradient colors), but is rather to formalize the 17

2Despite the fact that nowadays the stratigraphic method is themost common approach used in archaeological excavation, some dis-crepancies still exist in the naming of its basic unit: in Englishspeaking countries it is called “Context”, in Italy ”Unita Strati-grafica” (US), in some excavations (i.e. Villa Magna, see www.villa-magna.org) “Stratigraphic Unit” (SU), in still other instances “lo-cus”, and so on and so forth. For the purposes of this paper, theabbreviation “SU” has been arbitrarily chosen so as to remain con-sistent with the ”USV” abbreviation of the proposed Virtual Strati-graphic Unit.

3See infra sec. 4.1

Preprint submitted to Journal of Archaeological Science January 30, 2015

steps involved in each reliability evaluation and visualiza-1

tion: which sources have been chosen and how they have2

been used in the virtual reconstruction.3

Virtual reconstruction, sometimes confused with post-4

processing of digital acquisition (mesh reconstruction, like5

in Kazhdan et al. 2006), is a series of steps which in-6

cludes the documenting, interpretation, and visualization7

of “lost” archaeological contexts (for a critical approach to8

the terminology see Golvin 2003, Golvin 2005 and Seville9

Principles, p. 3, “definitions”). Despite the fact that this10

application’s potential for use by the scientific community11

has been widely recognized (Ryan 2001, Ryan et al. 2002,12

Hermon et al. 2005, Hermon and Nikodem 2007, p. 1, Her-13

mon 2008, Niccolucci 2012 and Cerato and Pescarin 2013),14

only a small percentage of case studies regarding recon-15

struction exist in scientific literature, and furthermore its16

contributions to the integration of 3D modeling in archae-17

ological research methods are fairly uncommon. Accord-18

ing to Munster 2013, p. 198 and Munster and Kohler (in19

print) in recent years only 20% of papers written about20

the use of 3D technology in archaeology focus on the 3D21

reconstruction of lost contexts. A recent survey (Cerato22

and Pescarin 2013, p. 290), based on 686 publications,23

reports that only 1% of contributors propose methods to24

be used in the validation of models. 3D reconstruction25

is most often used in communications (Internet, museum26

installations, etc.).27

As a result, virtual reconstruction, as a field of archaeo-28

logical research, is an as yet undefined discipline, one that29

is still largely fragmented when it comes to methodology,30

both in terms of data transparency and common standards31

(for a critical review with bibliography on the lack of scien-32

tific accuracy and methodological consistency in the prac-33

tice of virtual reconstruction see Beacham et al. 2006, sec.34

4 and, recently, Denard 2012, p. 57, footnote 2).35

In recent years several initiatives within the community,36

like the London Charter4 and the Sevilla Principles5, have37

highlighted the principles of scientific visualization and the38

need for the formalization of re-constructive processes, but39

they are intended as guidelines and not as norms or stan-40

dard solutions. This is primarily due to the complexity41

and variety of technologies involved in virtual reconstruc-42

tion: digital acquisition, spatial-enabled databases, meta-43

data enrichment, and 3D modeling. The scientific aspects,44

like archaeological record fragmentation and context diver-45

sity, are, however, the hardest to deal with (on the need46

for a multidisciplinary approach see Bakker et al. 2003, for47

ontological aspects, see Doerr 2003, p. 79..48

Indeed, a major problem with the current methodology49

is the di�culty of representing and dealing with uncer-50

tainty. This issue, however, is not only related to digital-51

based reconstruction, but is, first of all, a “classic” core52

topic (Gros 1985, p. 185 and Medri 2003, pp.186-192) of53

4See “www.londoncharter.org”.

5See “www.arqueologiavirtual.com/carta/”.

archaeological record management and interpretation, as 1

the practice of archaeological reconstruction began long 2

before the advancement of computers (Manacorda 2007, 3

p. 102). 4

It is for this reason that this paper takes an “archaeo- 5

logical approach”, aiming to define: a) a formal language 6

based on existing archaeological standards; and b) an an- 7

notation system with which to document reconstruction 8

processes that is capable of linking them to both the survey 9

and interpretation procedures within the same framework 10

(see infra sec. 3, 4). 11

A review of related works is outlined in section 2. Sec- 12

tions 3 and 4 explore the theoretical aspects of the pro- 13

posed approach and the definition of the tools involved. 14

The paper ends with an examination of ”applicability and 15

definition of uses ”(see infra sec. 5) and conclusions (see 16

infra sec. 6). 17

2. Related works 18

2.1. Current connections between 3D survey and 3D re- 19

construction 20

The awareness that the creation of a 3D model for sci- 21

entific purposes requires a solid semantic enrichment, has 22

led, in recent decades, to the search for formal solutions 23

with which to link the model to its sources. Thus, what 24

is needed is an arrangement of tools and standards that 25

is able to manage complex datasets and that is based 26

on shared ontologies like the CIDOC-CRM (Doerr 2003, 27

Binding et al. 2008) or, more recently, CHARM (Gonzalez- 28

Perez and Parcero-Oubina 2011 and Gonzalez-Perez et al. 29

2012). 30

Over the past few years, more and more projects in this 31

field of research have focused on a “visual approach” to se- 32

mantic enrichment, with a data-granularity more similar 33

to that of the archaeological stratigraphic record (Fiorini 34

and Archetti 2011, Drap et al. 2012, Micoli et al. 2013, 35

p. 245-246, Cappellini et al. 2012, Stefani et al. 2011). In 36

some cases 3D technology is used as a tool in the manage- 37

ment and tracking of processed data at the stratigraphic 38

level (Apollonio et al. 2012, p. 1273) while, in other cases, 39

complex monuments are represented with acyclic graphs 40

(Gaiani et al. 2011, p. 59 fig. 17, Apollonio et al. 2012, p. 41

1277 and p. 1283 fig. 12 and Apollonio et al. 2013). 42

In the 1980s, the stratigraphic approach, initially used 43

exclusively in archaeological excavation, began to be ap- 44

plied to architecture as well, as a tool for identifying 45

phases of construction through stratigraphic readings of 46

the masonry (Parenti 1985, Parenti 1988, Hoggett 2000 47

and Bianchi et al. 2004). In just a short time this approach 48

became a common standard in documentation methods. 49

At present, however, a major topic in the visual ap- 50

proach is the segmentation of the 3D model, in which 51

the solutions span from a real-time, interactive approach 52

2

(Serna et al. 2012, p. 37) to a pre-calculated, fully geo-1

metric segmentation of the model based either on the ar-2

chaeological record or on the typology of the architectonic3

elements (Apollonio et al. 2012).4

These approaches are used exclusively for the creation5

of 3D models of monuments as they appear in the present6

day, based on a survey of the existing remains (“reality-7

based” models). In recent years, the use of the term8

“reality-based model” (Remondino and Rizzi 2010) has be-9

come fairly common in geomatics applications to indicate10

3D models obtained from a survey, as opposed to those11

created through a computer graphics approach, which is12

intended to be hypothetical. In archaeological theory, re-13

construction is based on sources that have been reorga-14

nized according to hypotheses and characterized by vary-15

ing degrees of certainty. As a result, a possible term for16

scientifically accurate 3D models could be “source-based17

models” (models obtained from “source-blending” during18

the reconstruction process).19

In recent years the survey activities of many archaeolog-20

ical excavation projects have expanded with the introduc-21

tion of “digital born” (De Felice et al. 2008b, p. 278)22

documentation created directly in 3D (De Felice et al.23

2008a, Katsianis et al. 2008, Fiorini 2008, Fiorini and24

Archetti 2011, Forte et al. 2012, Dellepiane et al. 2013).25

The introduction of precise and/or low-cost 3D acquisi-26

tion techniques (Remondino 2011) in the archaeological27

field has not only challenged and improved the e�ciency of28

some of the standards used in the record-keeping process29

(D’Andrea 2006, Bianchini 2008, De Felice et al. 2008a,30

De Felice et al. 2008b and Fiorini 2008), but has also led to31

the implementation of modeling methods used for virtual32

reconstruction purposes that are directly related to the 3D33

survey (Balletti et al. 2007 and Dell’Unto et al. 2013). In34

this way the reality-based model is used as a “spatial refer-35

ence” in modeling, and the 3D reconstruction metrics are36

consistent with the archaeological remains, thus “inherit-37

ing” their geometrical accuracy.38

2.2. An in-depth look at 3D reconstruction: current limi-39

tations in virtual reconstruction granularity40

In archaeological research, the 3D model is often consid-41

ered a tool with which to synthesize and convey di↵erent42

elements, each with varying degrees of reliability. As a43

result, the process behind the reconstruction is unread-44

able. To avoid this “black box” e↵ect, a wide range of45

tactics for managing and visualizing reliability and uncer-46

tainty have been implemented in an e↵ort to establish a47

“model validation” process. Some methods are proposed48

to represent uncertainty in reconstructions (Kensek 2007),49

chronological uncertainty (Zuk et al. 2005 and Pang et al.50

1997), typological details of the image sources (Dudek51

and Blaise 2004 and Blaise and Dudek 2009), uncertainty52

charts representing ambiguity in virtual reconstructions53

(Pollini et al. 2005) and interactive visualization solutions54

(Bakker et al. 2003, Borra 2004, Bonde et al. 2009). But 1

these tactics lack a common and agreed-upon standard. 2

However, one of the most common solutions in the man- 3

agement and visualization of reliability is what is generally 4

known as the “generative layers with query-able elements” 5

approach. This approach consists in the segmentation of 6

the model based on the typology and the supposed “de- 7

gree of certainty” of the sources used in the reconstruction 8

(usually represented with a color scale). It has been tested 9

with di↵erent solutions and terminologies, but has not re- 10

sulted in the creation of a common standard. In some 11

cases the validation of the model passes through “gradi- 12

ents of consistency” and is based on documentary sources 13

(see Borra 2004, Vico Lopez 2012, p. 117). In other cases 14

such sources may be grouped according to “levels” and 15

“classes” (see Viscogliosi 2006, pag. 213) or simply ac- 16

cording to “typologies” (see Dell’Unto et al. 2013). 17

In these approaches the data granularity relies on the 18

sources and not on the stratigraphy. In other words, 19

the segmentation adheres to the typology of the sources 20

used for the reconstruction (i.e. ancient drawings, liter- 21

ary sources, etc.), while the processes used to create the 22

3D model from its sources are known only to the archae- 23

ologists (cfr. Figure 1). In fact, there is a discrepancy 24

between the archaeological record and the visual represen- 25

tation of the reliability. 26

This problem has been partially dealt with in a few 27

case studies (Hermon et al. 2006, Hermon and Nikodem 28

2007) based on quantitative methods (fuzzy logic, etc.), 29

such as the Roman Theater of Paphos (Georgiou and Her- 30

mon 2011), in which the validation of the model is calcu- 31

lated numerically as an “Index of Reliability” (IR). In this 32

approach, based on the “Level of Existence” (LOE) and 33

on the “Level of Geometrical Reality” (LOGR), the gran- 34

ularity of the 3D model’s semantic annotation is object- 35

based and not source-based. Nonetheless, the indexes are 36

assigned only upon individual approval by the archaeolo- 37

gists: there is no explicit link to the archaeological data (as 38

stratigraphic record), nor to the available sources which 39

are the basis for the index assignments. At the same time, 40

no annotation tool for the reconstruction process is pro- 41

vided for. Other case studies show a connection between 42

the archaeological sources and the detail of the 3D model, 43

but only in terms of elements like the architecture’s static 44

aspects (Vico Lopez 2012), and without any specific con- 45

nection to the stratigraphic record. Meanwhile, others fo- 46

cus on an “experimental approach” in which 3D recon- 47

struction modeling is used to verify a hypothesis and re- 48

sults in a cyclical validation process (Viscogliosi 2006, pp. 49

214-217, Lulof et al. 2013). Finally, still others highlight 50

the importance of workflow standardization (Baldwin and 51

Flaten 2011), but do not propose tools capable of formal- 52

izing the reconstruction processes. 53

A qualitative di↵erent approach is followed by Cyber 54

Archaeology, with the aim to go beyond the reconstruc- 55

tion processes and focus in a wider, systemic simulation 56

3

(a)Survey.

analogies

evidences

evidences

analogies +evidences +general rules

evidences +analogies +general rules

formalized andpublished

rest in the mind ofthe archaeologist

(b) Actual granularity.

USV 101

USV/S 100

SU 2

SU 1

(c) Proposedgranularity.

SU 1

SU 2

USV 50

USV 51

(d) ExtendedMatrix.

Figure 1: Current limitations in virtual reconstruction granularity: (a) the model obtained from the survey, or “reality-based model”, (b)the “source-granularity approach”: the model is divided according to a single source typology (square brackets), but each segment is actuallybased on di↵erent sources blended together (curly brackets). In this approach, the process used to obtain the the stratigraphic unit from itssources is known only to the archaeologists. (c) The proposed “SU-granularity approach”: it is possible to provide the source details for eachSU. (d) The Extended Matrix regarding the previous Figure c (for details see sec. 4).

of the past (Forte 2014). The authenticity of the recon-1

struction is rightly considered as a “false dilemma” since2

the reconstruction is always an approximation of the past:3

the real core-topic is to make transparent the full process4

of model creation. To achieve this goal a primary tool is5

represented by the collaborative environment possibilities.6

The importance of making transparent the reconstruction7

processes and the wider systemic approach results in an8

acceleration and simplification of the interpretative pro-9

cesses through collaborative environments. Even though10

no shared standards or technical solutions have been pro-11

posed to formalize and make the reconstruction processes12

part of the archaeological modeling language (Harris Ma-13

trix) and documentation (stratification description) as it14

is used by archaeologists.15

Despite the progress made in recent years in the annota-16

tion and semantics of 3D surveys, since the analysis of the17

London Charter, the situation in the virtual reconstruction18

field of research has not changed dramatically.19

3. Main approach and theoretical aspects20

As discussed in the previous paragraphs, the virtual re-21

construction field currently lacks: 1) a methodology that22

is consistent with archaeological records in terms of data23

granularity; and 2) a tool with which to document the24

re-constructive process. How can such an approach be es-25

tablished? What are the necessary elements involved ?26

3.1. Nicolas Steno and stratigraphical gaps: a starting27

point for archaeological reconstruction28

The need for a virtual reconstruction arises when, in an29

archaeological context, certain gaps appear (due to dam-30

age or transformation). Nicolas Steno’s categorization of31

gaps and laws of stratigraphy make it possible to extract32

information useful in the archaeological reconstruction di- 1

rectly from the gaps themselves. When Nicolas Steno the- 2

orized the principles of stratigraphy in the 17th century 3

(Ascani et al. 2002), he defined the historical language (as 4

opposed to the mathematical language) of the “Book of 5

Nature”. This approach led to the distinction between 6

so-called “readable pages” (those objects visible to the ob- 7

server) and “unreadable pages” (contexts and objects from 8

the past which have been lost). 9

Steno based his theory primarily on the fundamental im- 10

portance of the “gap” in the reconstruction of the sequence 11

of events6 (Hansen 2002). An important characteristic of 12

gaps in nature is that, paradoxically, they provide asser- 13

tions which would otherwise not appear in non-lacunous 14

systems. Due to the physical absence of existing struc- 15

tures, gaps create discontinuous systems, such as a bite 16

taken from an apple. This broken structure allows us to 17

make two assumptions: 1) the bite from the apple is more 18

recent than the creation of the apple, because it is dis- 19

continuous in relation to the apple; and 2) the bite is an 20

external influence on the apple. It follows that one can say 21

much more about the bitten apple than about the whole 22

one. An example of this property of lacunous systems can 23

be observed in the Meta Sudans in the Colosseum val- 24

ley in Rome. One can make assumptions about the Meta 25

Sudans’ Augustan stage (see Figure 2) only because of 26

the subsequent destruction of the Flavian stage over the 27

course of centuries, and especially at the beginning of the 28

twentieth century (see Panella 2001). In the following sec- 29

tions we will examine the theoretical implications of gaps 30

in archaeological reconstructions and how to semantically 31

6This methodological awareness, however, did not bring about theexpected results until the 19th century, mainly because Descartes’reductionist paradigm triumphed (as demonstrated by the famousquarrel between Descartes and Steno).

4

Figure 2: The Flavian Meta Sudans (dotted line), built over theprevious one (solid line). The gaps produced over the years make itpossible to “read” the complete stratigraphy.

annotate these assumptions by taking advantage of their1

“known” degree of certainty (see sec. 4.1.1).2

3.1.1. Structural gap/non-structural gap3

According to Steno, history is full of structural gaps4

which provide us with assertions that can be inferred from5

the logic of natural history. At the same time, history6

is also full of non-structural gaps, the existence of which7

we are only indirectly aware of due to analogous conclu-8

sions, and the meaning of which can only be understood9

intuitively or extrapolated indirectly from the logic of nat-10

ural history and mathematics. It is important therefore to11

di↵erentiate between:12

1. specific data (certain): structural gaps allow us to ob-13

tain this information from that which has been pre-14

served;15

2. general data (uncertain): preserved remains can pro-16

vide information about that which has been lost or17

destroyed, through analogous conclusions and calcu-18

lations.19

How is this taxonomy related to archaeological recon-20

structions? The field of 3D architectural survey is usually21

focused on that which has been preserved and considers22

gaps to be “lost data”. Despite the fact that the “lack23

of information” concept itself is not explicitly defined in24

standard archaeological documentation, the stratigraphic25

approach places particular emphasis on the causes of dam-26

age (anthropic or natural such as cuts, spoliations, smooth-27

ing, etc.) and formalizes them as a “negative stratigraphic28

unit”7 or “-SU” (the process of subtracting material from29

7The concept of removed stratigraphy (or negative stratigraphicunit) is not a common standard used worldwide despite the fact that

SU

USV/S

-SU

Figure 3: Example of a structural gap: remains of a wall. Thewall (SU) has experienced a cut (-SU) that testifies to a structuralgap filled in by a reconstruction hypothesis (USV/S). For technicalterminology see sec. 4.

the stratification, see Carandini 1981). 1

This information is represented as an interface which 2

a↵ects other, positive SUs. It is the “evidence of an ab- 3

sence”, a surface which indicates a missing volume, a detail 4

of a surviving object, and, as a result, substantiating ev- 5

idence for a reconstruction hypothesis (see Figure 3 and 6

Figure 4). 7

-SUSU

(a)

SU USV/S

(b)

Figure 4: (a) The model resulting from the survey or the “reality-based model”, (b) the “source-based model”. The remains of thecapital (SU) have undergone a cut (-SU) that can be filled in bya reconstruction hypothesis (USVs). For technical terminology see

sec. 4.

It follows that the negative stratigraphic unit testifies 8

to the existence of a structural gap (see Steno’s definition 9

above) and is a reliable starting point for archaeological 10

reconstruction. 11

Practical aspects and methods for the extraction of 12

“gap-based” data for virtual reconstruction will be exam- 13

ined in sec. 4.1. 14

has been theorized from the beginnigs of the stratigraphic approach(see infra sec. 3.1). Examples of use of -SU can be found in theItalian archaeological school.

5

3.2. The reconstruction process as part of the archaeolog-1

ical survey and excavation2

For archaeologists, the survey and the excavation are3

both records of measurements and exercises in interpre-4

tation. It is nearly impossible to look at a fragment and5

understand what it is without mentally reconstructing the6

shape of the complete original object (see Manacorda 2004,7

p. 7). Furthermore, the documentation of the negative8

stratigraphic unit as a testimony of lost elements facili-9

tates re-constructive processes as data is obtained. There-10

fore, one could say that the first step in virtual reconstruc-11

tion actually occurs during archaeological documentation12

(especially in terms of the “involuntary” reintegration of13

structural gaps).14

According to Steno’s terminology (see infra sec. 3.1.1),15

such re-constructive processes can be divided into two16

types:17

1. Reintegration of the structural gap represented by the18

negative stratigraphic unit (-SU) at the time of survey19

documentation: the absence of an object is recorded20

and it is possible to make a series of assumptions re-21

garding its position, material, geometry, shape, and22

size with a high degree of certainty. There is a direct23

relationship with the documentation process.24

2. Reconstruction of non-structural gap: the reinte-25

grated element has no physical continuity with the26

remains, therefore the archaeological documentation27

becomes an indirect source alongside other external28

sources (like paintings, historical maps, photos, etc.).29

There is an indirect relationship with the documenta-30

tion process.31

3.3. A synoptic and synchronic representation of virtual32

reconstruction33

The division of the reconstruction processes into groups34

is only the first step. It is then necessary to create a visual-35

ization of the structured information. In “classic” archae-36

ological research, the representation of the stratigraphy is37

performed through the so-called Matrix of Harris (Har-38

ris 1979), technically an acyclic, oriented graph in which39

the nodes represent stratigraphic units or “actions”8 and40

the arcs represent the chronological relationships between41

them (upper is newer, lower is older). This graph is a42

“holistic” description of the archaeological context: each43

element is considered individually (the node) and in rela-44

tion to the others (the relative position of the node in the45

graph). The elements are identified and organized by ar-46

chaeologists during the documentation phase and the laws47

of stratigraphy provide reliable reference points in terms48

of chronological order (i.e. the cut to the wall is always49

more recent than the wall itself).50

The Matrix of Harris presents all of the archaeological51

elements in a single document and in a two-dimensional52

8The SU, in stratigraphic terms, is also called an “action”, refer-ring to an action that happened in the past.

space. Consequently, its representation is synoptic (all of 1

the elements and their relationships to one another are 2

included in the same document “under the eye of the ob- 3

server”) and synchronic (all of the archaeological phases 4

are a part of the same, unique sequence) with reliable 5

benefits in terms of human-readability and data manage- 6

ment/overview. The visualization of the 3D reconstruc- 7

tion, on the other hand, lacks both synoptic and syn- 8

chronic representations of virtual reconstructions: 9

• No synoptic representation. It is not possible to vi- 10

sualize all of the aspects of a monument in a single 11

image unless one performs complex operations in or- 12

der to create an exploded view of the model (Kensek 13

2007). This is necessary because the reconstructed 14

model usually obstructs the view of the original re- 15

mains, as these are volumetrically smaller (see Figure 16

5 at page 7). As a result, it is not possible to un- 17

ambiguously and simultaneously represent the pres- 18

ence of archaeological remains and their proposed re- 19

construction, nor the relationship between them. An 20

interactive approach is usually used in this type of 21

situation, giving the observer the ability to explore 22

the model three-dimensionally (3D GIS). In this way, 23

however, the advantages of the synoptic representa- 24

tion are lost. 25

• No synchronic representation. A reality-based model 26

is the representation of an archaeological context as 27

it appears at the exact moment of the 3D survey, and 28

requires a stratigraphic segmentation in order to un- 29

cover previous phases. Such a model may be con- 30

sidered a palimpsest of all of the changes made over 31

the centuries (raised walls, new windows, porticoes 32

that have been filled in or replaced, etc.). Conse- 33

quently, every reality-based model theoretically re- 34

sults in as many di↵erent 3D reconstructions as time- 35

periods identified in the stratigraphy (see Medri 1988 36

and Figure 6 at page 7). Unfortunately it is not pos- 37

sible to synchronously represent all of a monument’s 38

various phases with a 3D visualization unless one uses 39

hard-to-read methods, like transparent surfaces and 40

materials. 41

Computer-based 3D visualization is not necessary the 42

most appropriate means of addressing all communication 43

aims in Cultural Heritage research (see London Charter, 44

principle 2.1, p.6.). It is for this reason that the following 45

paragraph (sec. 4.2) introduces a modified version of the 46

Matrix of Harris, the “Extended Matrix” (EM), as a tool 47

with which to annotate and complete the 3D modeling 48

processes. 49

4. Definition of norms, tools and practical aspects 50

(ver. 1.0) 51

As mentioned earlier, both the typology of the gap and 52

the stratigraphic granularity are fundamental to a coherent 53

6

a)

b)

Figure 5: Limits of 3D visualization and exploded views of the model.Without this device, the source-based model (b) would obstruct thevisibility of the corresponding reality-based one (a).

Source-based model1150 A.D.

Source-based model1100 A.D.

Tangible-based model2014 A.D.a)

b)

c)

Figure 6: A reality-based model (a) is equivalent to n source-basedmodels from n time-periods (i.e. b, c). Note how the di↵erent solu-tions are not alternatives, but rather consecutive versions.

and taxonomic annotation of the reconstruction process. 1

In practice, these concepts require norms and symbols for 2

the visualization and management of data that are as sim- 3

ilar as possible to the common modeling language in use 4

by archaeologists, particularly the SU (Stratigraphic Unit) 5

and the Matrix of Harris. The aim of the following terms 6

is to propose definitions for these “working tools”. 7

4.1. Proposal for the Virtual Stratigraphic Unit (USV) 8

The virtual stratigraphic unit (USV) is a re-constructive 9

hypothesis regarding a specific SU that is no longer in ex- 10

istence due to the occurrence of a gap at some point in the 11

history of the archaeological context (i.e. the destruction 12

of a building’s roof). The hypothetical presence of a col- 13

umn atop the remains of a temple’s podium is an example 14

of a virtual stratigraphic unit relating to a specific SU (the 15

column) which is no longer in existence. The term “vir- 16

tual” is here considered a synonym for “potential” (from 17

the Latin term virtus), and expresses the likelihood of a 18

specific SU having existed in the past. 19

4.1.1. USV typology 20

USV typology can be determined according to the gap 21

from which it is derived9: 22

• structural gap based USV (USV/S): the USV/S is di- 23

rectly related to a tangible SU that proves “the pres- 24

ence of an absence”. An example is an interface of 25

destruction -SU (negative Stratigraphic Unit) which 26

a↵ects an SU wall (see Figure 3) and testifies to the 27

missing upper part of the wall (the USV/S). There 28

is evidence supporting the stratigraphic connection 29

between the -SU and the USV/S and, according to 30

Steno’s definition, at least some of the information 31

is certain. Some of the properties of the SU a↵ected 32

by the -SU can indeed be passed on to the USV/S 33

(directly inheritable properties): in the example at 34

Figure 8, a marble fragment of a frieze automatically 35

indicates that the same material was used in the cor- 36

responding USV/S - uncut frieze. At the same time, 37

properties like size, shape, and position must be com- 38

bined with other data in order to be identified (Figure 39

8): i.e. a fragment of a frieze (SU) must be combined 40

with a general rule10 in order to transmit the total 41

height to the corresponding USV/S - uncut column 42

(non-directly inheritable properties). The symbol to 43

represent the USV/S is a parallelogram (see Figure 44

7(b)). 45

Sometimes the USV/S can be based on variations of 46

the -SU, like footprints. In this case there is physical 47

proof of an absence as well. An example of this is the 48

9For details see Steno’s gap classification (infra sec. 3.1.1) andthe derived reconstruction processes (infra sec. 3.2).

10By “general rule” I here mean an assumption made about arecognizable “trend” or typology in a given time-span (i.e. the pro-portions of the column vary according to the expected total height).

7

SU 9

(a) (b) (c)

SF 1

(d) (e)

USV

(f)

(g) (h) (i) (j)

Figure 7: Examples of symbols used in the Extended Matrix: (a) Stratigraphic Unit or “SU”; (b) Virtual Stratigraphic Unit or “USV/S”,related to a structural gap (see sec. 4.1); (c) USV/N related to a non structural gap (see sec. 4.1); (d) SF (Special Find) not in situ (see sec.4.4); (e) USV serving as a representation of an SF not in situ (see sec. 4.4); (f) Seriation node (see sec. 4.5.1); (g) Extractor node, capableof extracting specific information from the sources and transforming them into properties of the USV (see sec. 4.3.2); (h) Combination node,useful in combining two or more extractor nodes (see sec. 4.3.4); (i) Property node, validates the USV it is connected to (see 4.3.3); and (j)source useful for the reconstruction (text, image, etc., see sec. 4.3.1)..

SU USV/S

material materialpartial dimensions

totaldimensions

othersources

propertiesof the extantremains

propertiesinheriting

propertiesof the USV

Figure 8: Example of a directly inheritable property and a non-directly inheritable property.

central square of Trajan’s Forum, where the signs left1

in the mortar of the floor provide an accurate idea of2

the missing marble slabs (see Figure 9).3

• non structural gap based USV (USV/N): the USV/N4

is primarily connected to another USV (USV/S or5

USV/N), but the stratigraphic connection is uncer-6

tain and based only on sources. The symbol used to7

represent a USV/N is a hexagon (see fig. 7(c)).8

This typology has significant repercussions in the way9

multiple USV/Ss can be connected with one another in the10

Extended Matrix, as well as in the way that their “valida-11

tion” is defined.12

Figure 9: The floor of the central square of Trajan’s Forum in Rome.The footprints in the mortar are proof of USV/S lost marble slabs(Virtual Stratigraphic Unit based on a structural gap).

4.2. Integration of the USV in the Matrix of Harris: the 1

Extended Matrix 2

The Matrix of Harris helps archaeologists to navigate 3

their way through complex systems like that of stratifi- 4

cation, where hundreds of units must be managed at the 5

same time. Furthermore, elements with di↵erent purposes 6

(lints, columns, etc.) and from di↵erent time periods (Ro- 7

man, Medieval etc.) can be meaningfully connected to one 8

another, with the entire “graph” serving as a “mind map” 9

(see Figure 20) of relative chronology. In fact, the Matrix 10

of Harris can also be considered a semantic annotation of 11

the archaeologist’s thoughts, expressed as a time-line rep- 12

resenting a sequence of SUs (or actions which happened 13

in the past). 14

The USV can be represented as part of the tangible 15

SU (archaeological remains), in a modified version of the 16

matrix of Harris: the “Extended Matrix”. Here the USV 17

can have a stratigraphical relationship to: a) one or more 18

SUs; or b) one or more USVs. The hypotheses that a lintel 19

8

existed on top of a conserved column (a USV on an SU)1

and that a wooden beam existed on top of this lintel (a2

USV on a USV) are both examples of relationships which3

are represented in the Extended Matrix (see Figure 10).4

4.2.1. General graphic notation in EM5

Every element is constructed from bottom to top. The6

black lines connecting the nodes indicate the stratigraphic7

relationship, while the dotted lines indicate chains of data8

transformation (paradata). The visual representation of9

the nodes makes use of the symbols introduced in Figure7.10

4.2.2. Hybrid aspects of the Extended Matrix11

The SU and the USV display the same behavior within12

the matrix. Nevertheless, the Matrix of Harris represents13

the documentation of tangible contexts (from the archae-14

ological survey) while the Extended Matrix also includes15

the representation of objects which are no longer in ex-16

istence, and which are modeled from other sources (see17

Figure 11 for a schematic representation of the Extended18

Matrix’s hybrid nature). This di↵erence requires the in-19

troduction of additional elements (see Figure 7), like the20

“source” node and a subset of paradata (Denard 2012, p.21

66,Baker 2012, p. 169) nodes, which are used to validate22

the USV/S (for details see sec. 4.3). These nodes can also23

be considered data metamorphosis nodes : the proposed24

paradigm is similar to the DIKW hierarchy (Data ! In-25

formation!Kwnowledge!Wisdom, see Zeleny 1987 and26

Acko↵ 1989.). Figure 12 shows an example of a validation27

workflow, from source node to USV. The information is28

collected from the source node by the extractor node and,29

subsequently, a property is passed along which is used to30

validate the USV.31

4.3. Validation nodes for the USV: sources and paradata32

4.3.1. Source node33

In the approach presented in this paper, sources are el-34

ements of the Extended Matrix and are involved in the35

USV validation process. The symbol used to represent the36

source is a “blank document”, as shown in Figure 7(j).37

Examples of sources are:38

• digital or tangible media (drawings, photos, texts, 3D39

models, etc.);40

• tangible objects (archaeological discoveries, etc.);41

• abstractions like general rules11 or archaeological ty-42

pologies.43

An SU or a USV can also be a source for another USV.44

In Figure 8 the dimensional properties of the SU act as45

a source for the dimensional properties of the USV lin-46

tel. Thus every element within the EM (Extended Matrix)47

11See footnote 10.

USV 2

SU 1

USV 3

(a)

SU 1

material

USV 2

wooden lintel could occur when lenght => n meters

the intercolumnium lenght is compatible with a wooden lintel

intercolumnium: distance from the next column in series

there is a relation between the lenght of a lintel and its materialstone < n meterswood => n meters

wood

lintel

column

(b)

Figure 10: Examples of a stratigraphic sequence of tangible andsource-based actions: (a) a wooden beam on a wooden lintel (USV3on USV2) and, again, a wooden lintel on a preserved column (USV2on SU1); (b) detail of the EM in relation to figure “a” representingthe validation of USV2 (see sec. 4.3.4).

9

10 A

.D.

10 A

.D. r

econ

str. Gap-solving through

hypothesis.Source-based modelling

Survey (laser scanner, photogrammetry, etc..)Reality-based modelling

SU 2

USV 100

USV 507

SU 1

Figure 11: The hybrid nature of the EM.

material

USV 101 wall

opuslatericium

virtualstratigr.

unit

property

extractor

source

node contentdescript.

Figure 12: Summary of the USV validation workflow, from the sourceto the USV/N (example of Du Perac’s drawing.).

Figure 13: Trajan’s Column by Etienne Du Perac, 1575 (The arrowpoints to the remains of the “library” near Trajan’s Column).

can be used as a source, which means that archaeologists 1

must identify and keep track of the important relationships 2

which they are aware of. 3

Let us now take a look at an example from a case study: 4

the goal is to reconstruct Trajan’s Forum using the per- 5

spective of the Trajan Column found in Du Perac’s draw- 6

ing (Figure 13) as a source. This image provides a lot of 7

information about the state of the buildings in the 16th 8

century. Furthermore, the right side of the drawing re- 9

veals an interesting detail, indicated with a black arrow. 10

This outline can be interpreted as the remains of the for- 11

mer wall of the east library in Trajan’s Forum (for our 12

purposes, a USV/N). To make use of this record, it is im- 13

portant to distinguish between the source and the content 14

that it provides: the source is the whole document (Du 15

Perac’s drawing) and acts as a container of information, 16

while the content (the outlined element) is the result of 17

extrapolated data (see Figure12). In the EM this action 18

is represented with the “Extractor node”. 19

4.3.2. Extractor node 20

In the Extended Matrix, the source is processed by an 21

“extractor node” that performs the following functions: 22

1. uniquely identifies the detail “captured” by archaeol- 23

ogists in the source; 24

2. transforms the detail into a property of the USV to 25

which it is connected (see sec. 4.3.3). 26

From a practical standpoint, the extractor node can be 27

an image, written text, or anything else that may be used 28

to uniquely highlight something in the source. For in- 29

stance, in Figure 12, Du Perac’s drawing (source node) is 30

connected to an extractor node that is a B/W mask high- 31

lighting the remains of the large wall in Trajan’s Forum. 32

The symbol used to represent an extractor node is shown 33

in Figure 7(g). 34

10

4.3.3. Property node (USV)1

The property node is directly related to the USV and is2

the result of one or more sources transformed by paradata3

nodes (extractor, combination, etc.). The basic qualities4

of the property node are:5

• position, placement;6

• shape, material;7

• dimensions, proportions;8

• style.9

This is not a finite list: other qualities may be added.10

The symbol for the property node is represented in Fig-11

ure 7(j).12

In the example of Du Perac’s drawing (see Figure 12),13

the extractor node transmits a material property (opus14

latericium) to the USV.15

4.3.4. Combine node16

When two or more extractor nodes feed a property, it is17

necessary to combine them. In Figure 10, USV 2 is vali-18

dated by a ”known” property: the material. This property19

comes from two sources: the placement value of SU 1 (dis-20

tance between the SU 1 column and the other columns)21

and a general rule regarding the relationship between a22

lintel’s length and its material. In other words, the recon-23

struction process is, in this case, based on the following24

statement: the intercolumnium length is compatible with25

a wooden lintel. The symbol for the combination node is26

represented in Figure 7(h).27

locationshapedimensionmaterialplacementstyle.....

imagetext3D2D....

imagetext3D2D....

PropertySource Extractor

Figure 14: Schematic of the paradata workflow nodes and their val-ues.

4.4. The anastylosis of Special Finds28

During the reconstruction process, one may also have to29

deal with objects that have been displaced from their orig-30

inal context. The position of these objects can be restored31

by establishing a reconstruction hypothesis. An example32

of this type of situation is a column found in the destroyed33

level of a temple, such as in Figure 15(a). This fragment,34

known as a special find (SF) in excavation taxonomy, can35

be restored to its position on top of SU1 (stratigraphic36

unit in its original place) in accordance with a hypothesis. 1

The information available regarding SF1 is incomplete: the 2

material, shape, style, and dimensions are known, but no 3

data is available regarding other properties like position 4

and placement. However, reviewing the steps in the vali- 5

dation process is not the purpose of this section (see sec. 6

4.3), so, for the sake of brevity, it is enough to say that 7

a validation process must be formalized, the same as for 8

a USV. The symbol used to represent a special find is a 9

white octagon (see Figure 7(d)). 10

Once an SF has been placed in the Extended Matrix, a 11

hypothesis can be created for a USV with which to rein- 12

tegrate it. In this case, however, the USV has a lower 13

degree of certainty as compared to other USV/Ss that are 14

based on “normal” SUs (see Figure 16). The symbol used 15

to represent this type of USV is a black octagon (see Fig- 16

ure 7(e)). 17

SF 1 SU 1

(a)

USV 101

USVs 100

SF 1

SU 1

(b)

SU 1

SF 1

USV 100

USV 101

(c)

Figure 15: Example of anastylosis: a) Special Find - SF1 (fragmentof a column) found in a secondary position, and a base of columnin situ; b) reconstruction proposal for the column; c) EM of theprevious figure (b).

4.5. Avoiding redundancy and improving readability in the 18

EM 19

The EM can be a very complex graph, especially when 20

dealing with hundreds of SUs and USVs. For that reason, 21

11

SU 1

SF 1 USV 50

USV 40knownproperties

only somepropertiesare known

morereliability

lessreliability

Figure 16: Comparison between SU-based and SF-based USVs

some rules can help to avoid redundancy and improve data1

readability.2

4.5.1. Seriation of the USV3

Sometimes groups of USVs can be considered as a whole.4

This is the case for a series of objects like a colonnade or5

a sequence of acroterion. In these cases the Extended Ma-6

trix provides a seriation node that acts like a proxy for the7

entire group, like the USV 2000 in Figure17. Hopefully8

the seriation node can be validated by some of the known9

SUs and USVs included within the “proxy” itself (for in-10

stance, the remains of one or two columns can contribute11

to the validation12 of an entire colonnade). The seriation12

node acts like a “whole” and simplifies the stratigraphic13

relationship with the earlier (upper) SU (i.e. a lintel USV14

connected to a lower seriation node colonnade).15

The symbol used to represent a seriation node is a black16

ellipse (see Figure 7(f)).17

4.5.2. Avoiding redundancy in SU-USV/S-USV/N triplets18

As with the Matrix of Harris, the EM is not a rep-19

resentation of the physical chain of events, but rather a20

non-redundant chronological sequence. Furthermore, each21

USV/S, both from the point of view of the stratigraphic22

relationship and as a source for other USVs, becomes a23

“proxy” for the corresponding SU/SU, and indicates the24

object as a whole (i.e. in Figure18, the USV/S 504 wall25

becomes a proxy for the USM13 30 with respect to the26

extraction node above).27

4.6. Virtual Activities (AV)28

To improve readability, it is possible to group di↵erent29

actions within Virtual Activities, as happens in the Matrix30

of Harris’ archaeological sequence. This approach is partic-31

ularly important for complex EMs and results in a tagging32

of the nodes involved (both USV, sources and paradata).33

In Figure19 the elements that make up the lintel (AV 3),34

the decoration (AV 4), and the roof (AV 5) are grouped in35

such a way as to improve readability and provide a model36

for a solution which may be reused in other contexts.37

12The “validation” process of a USV is based on the connectionsbetween one or more properties.

13USM stands for Unita Stratigrafica Muraria (masonry strati-graphic unit), see Parenti 1985.

Figure 17: Extract from the EM of the Temple (Figure20) represent-ing the temple’s USV 2000 colonnade and USV 2001 capitals.

12

Post

ant

iqui

ty2n

d B.

C.2n

d B.

C. N

S Re

cH

umus

Geo

logy

S Re

c

AV 2

USV 505

USV 506

Material

SF001

Disposition

USV 505

Dimension

VSU 2001

Style

QuantityIntercolumnium

StylePosition

Position

Position

US 1n

US 1

US 2

USM 15 USM 201

USM 21b

USM 26

US 3 US 140

A 1

USM 8 USM 14eUSM 14USM 14o

USM 14c

A 2

USM 13USM 6 USM 13s USM 141USM 7

A 3

USM 21

USM 20

US 1000

US 0

US 80

AV 1

USV 503

Material Shape

A 4

USM 31USM 30

USV 502USV 500

USV 520

USV 504

AV3

USV 508

Material

Dimension

AV 5

USV 509

USV 510 USV 511

SF003SF002

USV 700 USV 700

AV 4

USV 512

AV 0

USV 501

Style

2nd

B.C.

VSU 2000

Figure 20: Example of an Extended Matrix applied to a temple.

13

Figure 18: Extract from the EM of the Temple (Figure20) represent-ing the USM30 wall with its USV/S 504 reconstruction hypothesisand a USV/N 506 column above.

AV3

USV 508

Material

Dimension

AV 5

USV 509

USV 510 USV 511

SF003SF002

USV 700 USV 700

AV 4

USV 512

Figure 19: Extract from the EM of the Temple (Figure20) represent-ing the Virtual Activities 3 (lintel), 4 (decoration), and 5 (roof).

5. Applicability and definition of uses 1

Is it possible to use the Extended Matrix and the USV 2

in instances in which the archaeological excavation has not 3

been investigated with a stratigraphic approach? Docu- 4

ments show that there have been many surveys and ex- 5

cavations of archaeological contexts in which no informa- 6

tion about the stratigraphy has been collected. Regard- 7

less, in these cases a “posthumous” stratigraphic reading 8

may be performed, thus obtaining a Matrix of Harris of 9

the masonry sequence. Setting aside concerns regarding 10

the integrity of this archaeological record, a stratigraphic 11

reading can generally be achieved (preservation and ac- 12

cessibility of the archaeological context permitting). A 13

well-known example of this type of situation is the archae- 14

ological remains in Pompei, which were excavated without 15

documenting the SU and these days are surveyed and stud- 16

ied according to a stratigraphic approach (Apollonio et al. 17

2012). 18

The significance of this topic is immediately clear if one 19

thinks of the enormous amount of data collected before 20

the introduction of the stratigraphic reading, and an even 21

higher number of datasets were created before the recent 22

introduction of “digital born” data and 3D survey tech- 23

niques, also known as “legacy data” (for use of the terms 24

“legacy data” and “digital born data”, see De Felice et al. 25

2008b, pp. 277-278 and De Felice et al. 2008b, pp. 278-283, 26

respectively). It is very common for virtual reconstruction 27

specialists to have to deal with these kind of “lacunous” 28

datasets. Furthermore, archaeological reconstruction the- 29

ory is based on a comparative analytical approach and, for 30

that reason, the contexts must be related to one another. 31

As a result, a common approach must be used to handle 32

all of these cases, an approach which relies on a strati- 33

graphic reading and which is independent from the survey 34

techniques or digging methods. 35

6. Conclusions 36

The current version (1.0) of the Extended Matrix is able 37

to synchronously and synoptically represent: 38

• the stratigraphy of the remains, such as earth, walls, 39

etc. (positive stratigraphic units); 40

• the structural gaps in the elements (negative strati- 41

graphic units); 42

• the reconstruction hypothesis based on: 43

stratigraphy (SU, USM); 44

structural gaps (-SU); 45

related sources involved (source nodes)14; 46

hypothesis about the structural gaps (USV/S); 47

hypothesis about the non-structural gaps 48

(USV/N). 49

14For details about source management see 4.3.1.

14

6.1. Future works1

The stratigraphic approach presented in this paper has2

been tested in several archaeological contexts, but addi-3

tional case studies need to be conducted in order to refine4

the framework, especially in the solutions to represent the5

virtual stratigraphy directly on the 3D model. At the same6

time, an integration of methodologies with which to store7

the source quality in the EM (according to the scenarios8

specified in sec. 5) could be included in a future version9

(2.0). At present, the Extended Matrix is drawn with10

the free desktop edition of yED15 and linked to models11

in Blender 3D16, while the data exchange is based on xml12

format intended for graph data storage (graphml). For the13

next version of the EM, a software solution could be pro-14

vided to link USVs and 3D models with the goal to make15

easy the annotation of the 3D reconstruction processes.16

15See www.yworks.com.

16See www.blender.org.

15

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