1. INTRODUCTION

In many disciplines data are not easily accessible. An

archaeologist cannot see past social dynamics,and not only

because archaeological data are hidden under the earth,but

because causes and effects were produced many years ago,

and we cannot see now and here either causes or the real

effects. In some cases,the spatial location of causal actions

or process is hidden,whereas in other cases,the temporal

location is beyond our experience. Maybe post-depositional

processes have altered the spatial location of causal actions

or process,whereas,in other cases,we have lost most data.

In fact,we cannot see what it does not exist in the present.

In circumstances when we have not all-relevant information

about a causal process,we can generate simulated data ?to

see what cannot be seen?. Better than a mere analogy with

the real world,we should imagine that the virtual model of

an archaeological entity is a projection from an

archaeological theory,that means one of the possible valid

results from this theory.

That is,we should build a virtual model from partial data

input to represent some (not necessarily all) features of the

archaeological entity we have not observed. A model is then

a knowledge structure produced by some organized

knowledge-base of higher level. We need knowledge ?to

visualise what cannot be seen?. The question is how to add

knowledge in a systematic way.

The archaeological record is always a form of simulated

reality,because we ?complete?it using virtual models. We

should take into account,that a virtual model is not

necessary a surrogate for reality,but any ?interpreted?

representation of partial inputs. As we will see,the process

of ?completion?or ?reconstruction?is analogous to

scientific explanation,and therefore,it involves induction,

deduction and analogy.

2. VISUALIZING

THE ARCHAEOLOGICAL RECORD

Observation is the process by which the human brain

transforms light intensities into mental images,which

explains perceived input. Observation is a 3-stage process:

?Perception,

?Recognition,

?Description.

Our brain receives sensory input and recognises some

information content in it using prior experience. Finally it

describes that information using a specific representation

language. That is to say,we ?see?the real world by creating

a virtual model of the reality. Sensory information comes in

form of light. Our brain processes differences among light

intensities and light sources,and it builds an explanatory

model. We do not ?see?things,but we infer the existence of

things from the spatial regularity arising from the pattern of

luminance contrasts we perceive as sensory input. Any

observation mechanism is then a translation of some

perceptual input into an explanatory model of it. This virtual

model is what we usually call image.

It does not exist anything as an artificial or virtual

observation. Nevertheless,we can use some mechanic

devices for translating perceptual inputs into a geometric

model interpreting luminance contrasts. This process of

modelling is also called ?visualisation?,which should not

be confounded with ?seeing?. We ?visualise?data when we

fit interpreted geometric elements to perceived inputs by

joining recognised points with descriptive lines,fitting

descriptive surfaces to descriptive lines,or ?solidifying?

connected surfaces (GERSHON 1994,GOLDSTEIN 1996). We

create ?geometric models?of archaeological reality in the

same way our brain translates perceptual input into mental

images.

The goal of archaeological visualisation is then to explain

spatial regularity between archaeological inputs. We are

able to ?visualise?archaeological reality,just when we

understand how differential locations and topological

relationships between archaeological entities determine

input information. That means,that the relevant properties

of any archaeological entity vary from one location to

another (either temporal location or spatial location),and

sometimes this variation has some appearance of continuity.

We perceive the spatial features of the archaeological reality

by direct interaction with reality,or using special equipment

for input acquisition:photographs,topographic equipment,

21

VIRTUAL ARCHAEOLOGY AND ARTIFICIAL INTELLIGENCE

Juan A. Barcel?

Dept. Antropolog?a Social i Prehistoria. Facultat de Lletres

Universitat Aut?noma de Barcelona,SPAIN

In this paper,it is presented a general framework for using Virtual Reality Techniques in the domain of Archaeology. It is argued that

?visualising?it is not the same as ?seeing?,but an inferential process to understand reality. Archaeological reality is most of the times

broken,incomplete or hidden. Visual models are ?interpretations?of available data,and their purpose is to ?simulate?what cannot be

seen. As scientific tools,it should be readily apparent how one gets from the perceived incomplete input to the explanatory model.

remote sensing devices,etc. Again,we are not ?seeing?

objects in the real world or in a picture or drawing,but we

perceive spatial information in form of luminance and

colour patterns. By eye inspection,picturing or remote

sensing we receive a light input and we recognise it in form

of location information,which is translated into a simple

three-dimensional representation schema:

X,Y 2D point co-ordinates:longitude,latitude

(independent variables)

Z height or depth (as dependent variables)

Numeric data refer to a surface measured at points whose

co-ordinates are known. By tracing lines,curves and

surfaces between co-ordinates,we create a geometric

model,that is a virtual explanation of location information.

The resulting model is sometimes called:shape. Shape is a

field for physical exploration:it has not only aesthetic

qualities,nor it is just a pattern of recognition. Shape also is

determining the spatial and thus the material and the

physical qualities of objects.

The key aspect of a geometric shape model is its ?spatial?

nature,and it should be considered as a visual

representation reflecting a spatial decomposition of reality

in geometric ?units?. We use this model to examine if the

characteristics in one location have anything to do with

characteristics in a neighbour location through the

definition of a general model of spatial dependence between

units. What we are looking is whether what happens in one

location (temporal or spatial) is the cause of what happens

in neighbouring locations with the idea that if we can

specify the degree of spatial regularity in a region of this

decomposed space,we can reproduce the whole system.

To represent real entities,we should ?imitate?the real

world,describing an object by more than just shape

properties. Geometric units (points,lines,areas,volumes,

etc.) express position or shape,and retinal properties

(colour,shadow,texture) enhance the marks and may also

carry additional information. We should take into account

?retinal properties?in the geometric model,because each

surface appearance should depend on the types of light

sources illuminating it,its physical properties,and its

position and orientation with respect to the light sources,

viewer and other surfaces. Variation in illumination is a

powerful cue to the 3D structure of an object because it

contributes to determination of which lines or surfaces of

the objects are visible,either from the centre of projection

or along the direction of projection.

To study variation in luminance patterns,we should

consider all the set of characteristics (based on physical

properties) assigned to a surface or volume model. We use

the term shading to describe the process of calculating the

colour of a pixel or area from surface properties and a model

of illumination sources. Texturing is a method of varying the

surface properties from point to point in order to give the

appearance of surface detail that is not actually present in

the geometry of the surface. Texture is usually defined using

six different attributes:coarseness,contrast,directionality,

line-likeness,regularity and roughness. In both cases,the

object properties are expressed as intensity values variation

of colour,light and reflectance over surface. We should

remark that the colour assigned to each pixel in a visible

surface?s projection is a function of the light reflected and

transmitted by the objects,whereas shadow algorithms

determine which surfaces can be ?seen?from the light

source. We call ?rendering?the procedures that assign to the

surfaces of an object their visual physical properties such as

colour and shadow. Rendering modes can be understood as

specialisation of an underlying transport theory model of

light propagation in a participating medium.

Nevertheless,the goal is not to obtain ?well illuminated

models?,but to explain spatial regularity using shape-

enhanced models. The goal of the visual model should not

be ?realism?alone,for the sake of imitation,but in order to

contribute to understanding of input information. By taking

into account global models of illumination for

understanding position and relative location,or including

texture information into the geometrical model,we can

understand geometrical properties which are too abstract to

be easily understood. It is the ability to view from all angles

and distances,under a variety of lighting conditions and

with as many colour controls as possible,which brings

about real information. For instance,changing illumination

and shadowing,we can get shaded relief,slope and aspect

maps,which give clues to investigate surface and

morphological differences,expressed as discontinuities in

topography,in slope and in relief. The shaded relief map is

useful to portray relief differences in hilly and mountainous

areas. Its principle is based on a model of what the terrain

might look like,as illuminated from a lighting source,

seated at any position above the horizon.

This case is just a mere 3D+1D model,where a spatial

variable (texture,colour,etc.) is draped into a 3D model of

shape. The more dependent variables the system has,the

more complete the resulting model is. We are not limited to

4 variables (x,y ,z,w),but we can in fact relate two or more

three-dimensional models (x

1

,y

1

,z

1

,w

1

),(x

2

,y

2

,z

2

,w

2

). For

instance,we can analyse the dynamics of the interaction

between content (a three-dimensional shape model) and

container (another three-dimensional shape model).

Furthermore,important semantic information necessary to

interpret an image is not represented in single pixels but in

meaningful image objects and their mutual relations. The

basic strategy is to build up a hierarchical network of image

objects,which allows the representation of the image

information content at different resolutions (scales)

simultaneously. By operating on the relations between

networked objects,it is possible to classify local context

information. Beyond the pure spectral information this

?context information?(which often is essential) can be used

together with form and texture features of image objects to

improve understanding.

3. VISUALISING WHAT CANNOT BE SEEN

Building a virtual model is a four-step procedure:data

acquisition,pre-processing,parameter estimation,and

modelling. Different surface parameters should be

estimated,taking into account the geometric relationships

of real 3D points,and how they fit to the modelled surfaces

and the specific shapes of surfaces as well. The problem is

that most of the times data are not easily accessible,because

they cannot be seen.

However,even when sensorial inputs are partial or limited,

the brain builds an image,because it uses prior-knowledge

to reconstruct partial reality. If we cannot see an entity

because it is broken or it is hidden,then the brain fill the

gaps with information that does not proceed from the data

What the brain does using prior knowledge,a computer can

22

do also. In circumstances when we have not all relevant

information about a causal process,we can generate

simulated data ?to see what cannot be seen?. I?m using here

the term ?simulation?for the process of finding the

parameters necessary to infer values at other locations in a

3D surface from the relationship embedded in the data and

in other information describing the data and their

acquisition. When we do not have enough points,we should

follow a deductive or top-down approach,that is,we create

a hypothetical model,we fit it to the incomplete input data,

and then we use the model to simulate the non-preserved

data. This is a classic syllogism:

IF b (X,Y,Z) FITS THEORY

And MODEL A IS A PROJECTION OF THEORY

THEN b (SHAPE) DERIVES FROM MODEL A

Here we are following the rule:?The most similar is taken

for the complete simulation?. The procedure is as follows:

we transform perceived data as a sequence of points,and we

try to interpret the type of shape,assuming some dependent

preference function. Once the type is decided,the closest fit

is determined using different numerical techniques.

The alternative way to completion is exactly the opposite.

Instead of selecting the more ?similar?model that fits

available data,we can deform a model we have selected

because it is a valid deduction from prior knowledge,until

it fits the known data points. Since preserved data are not

arbitrary,a generic model having a known shape is a logical

starting point for any fitting process. Pertinent features

within the data are incorporated into the basic structure of

the model. The model is then deformed to fit the unique

characteristics of each data set.

We need to build the model first,and then use it for

simulating the real object. That means,we should create a

geometric model of the interpreted reality,and then use

information deduced from the model when available data fit

the model. In most cases,we create ?theoretical?or

?simulated?geometric models. Here ?theory?means

general knowledge about the most probable ?shape?of the

object to be simulated or prior knowledge of the reality to

be simulated. The question is how to add knowledge in a

systematic way.

In general terms,we have two approaches,depending on the

nature of theory and prior knowledge. If all we know to

simulate missing data,are analogies and some other

?similar?cases,then we should build a qualitative model.

But,if we can calculate missing information from nearest

neighbour points,then completion is the task of surface

interpolation; reality is simulated as an interpolated

parametric surface fitting all known points.

3.1 USING QUALITATIVE MODELS

This is the case of ancient buildings. In most cases,

preserved remains do not shed light on the structure of

vertical walls,which therefore remain unknown.

Archaeological or art history background information is

then needed. In the Dresden Frauenkirche project (COLLINS

1993,COLLINS et al. 1993),detailed architectural drawings

and old photographs displaying the church in its original

aspect have been preserved. When existing information was

not available in the preserved input data,photographs from

contemporary churches had to be used. A similar approach

was used for the 3D reconstruction of Maltese burials.

CHALMERS and STODDART (see CHALMERS et al. 1995,

CHALMERS and STODDART 1996,CHALMERS et al. 1997) had

a complete topographic and photogrammetric survey in

which accurate watercolours of the monuments by

nineteenth-century artists were stretched to fit the real data.

In general,the reconstruction of the most archaeologically

bad preserved ancient buildings is largely based on these

types of sources:

a) Pictorial evidence from plans and photographs of the

building?s ruins.

b) Descriptive accounts by modern authors on the ruins

in both their existing condition and in their imagined

original state.

c) Evidence shown by contemporary buildings in other

neighbouring places or culturally related areas,

which gives clues as to likely construction methods

and spatial forms.

d) When old drawings and photographs are not

available,external data can be estimated from

ethnographic records.

Many other examples of integrating historical and

anthropological information to simulate archaeological data

and building ?complete?models of ancient buildings appear

also in BARCEL?et al. (2000).

The problem in all those cases is that theoretical knowledge

is not being added to the model in a systematic way. The

creator of the model is selecting additional information in a

subjective way,using what he/she wants,and not what it

really needs. For years,artists have collaborated with

archaeologists in order to ?reconstruct?all those wonderful

things not preserved in the archaeological record,and they

have provided archaeologists with artistic depictions of the

past. However,these ?illustrations?of the past are not an

explicative vision of anything. When the artist represents

what cannot be seen,then the artist uses his/her

imagination,or partial information provided by an

archaeologist,to create the images. The resulting item is not

an explanation of the past,but a personal and subjective way

of ?seeing?it.

We can use Expert Systems to integrate external knowledge

to partial input,and then simulating the missing parts of the

input (DURKIN 1994,BARCEL?1996a,FELTOVICH et al.

1997,LIEBOWITZ,1997)

Every expert system consists of two principal parts:the

knowledge base; and the reasoning,or inference,engine. In

our case,the knowledge base contains both factual and

heuristic knowledge about how to complete the model.

Factual knowledge is that knowledge extracted from

historical and anthropological sources that is widely shared,

and commonly agreed upon by those knowledgeable in the

particular field. Heuristic knowledge is the more

experiential,more judgmental knowledge of performance.

In contrast to factual knowledge,heuristic knowledge

underlies the ?art of good guessing,of good practice,good

judgement,and plausible reasoning?. That is to say,the way

we use factual knowledge in order to simulate reality.

Knowledge representation formalizes and organizes the

knowledge. One widely used representation is the

production rule,or simply rule. A rule consists of an IF part

and a THEN part (also called a condition and an action). The

IF part lists a set of conditions in some logical combination.

The piece of knowledge represented by the production rule

is relevant to the line of reasoning being developed if the IF

part of the rule is satisfied; consequently,the THEN part can

be concluded,or its problem-solving action taken. Expert

23

systems whose knowledge is represented in rule form are

called rule-based systems. In our case,the IF part contains

available data,that is,partial or incomplete input. The THEN

part is the factual knowledge extracted from old

photographs,historical sources,analogies or ethnographic

description. The rule is a piece of heuristic knowledge

linking two bits of factual knowledge:

IF b (X,Y,Z) FITS MODEL A

THEN b (SHAPE) DERIVES FROM MODEL A

Of course,the most obvious problem is how to represent

factual knowledge to be used in such a way. We can use a

representation framework,called frame,schema,or list

structure,which is an assemblage of associated knowledge

about an entity to be represented. Typically,a unit consists

of a list of properties of the entity and associated values for

those properties. Since every task domain consists of many

entities that stand in various relations,the properties can

also be used to specify relations,and the values of these

properties are the names of other units that are linked

according to the relations. One frame can also represent

knowledge that is a ?special case?of another unit,or some

units can be ?parts of?another unit. In fact,frames and

properties are nothing more than verbal labels,but we can

link any property to an algorithm or command able to

execute some computer action (drawing a line,interpolating

a surface,adding a texture,etc.). For instance:

BUILDING:

Contains:walls

Contains:ceiling

Contains:floor

WALL:

Is_made_of:bricks

Dimensions:15x0.2x3

Heuristic knowledge organises and controls factual

knowledge. One common but powerful paradigm involves

chaining of IF-THEN rules to form a line of reasoning. For

instance:

If the geometric model of (x) has geometric

properties A,B,C

THEN (x) is an example of MODEL ABC

If (x) is an example of MODEL ABC

AND (x) has not property D

THEN JOIN property D to the geometric model of

(x)

where JOIN is an operator implemented as a command able

to add some geometric unit to those already present in a

preliminary model of the partial input.

Each rule should be understood as a knowledge unit about

how to use a specific piece of information. If the chaining

starts from a set of conditions and moves toward some

conclusion,the method is called forward chaining. If the

conclusion is known (for example,a goal to be achieved)

but the path to that conclusion is not known,then reasoning

backwards is called for,and the method is backward

chaining. These problem-solving methods are built into

program modules called inference engines or inference

procedures that manipulate and use knowledge in the

knowledge base to form a line of reasoning.

This representation of heuristic knowledge eliminates flow

charting by repeatedly:

?determining the set of applicable rules

?selecting a rule to be applied

?executing the actions (the then part) of the selected rule

Knowledge is almost always incomplete and uncertain. To

deal with uncertain knowledge,a rule may have associated

with it a confidence factor or a weight. The set of methods

for using uncertain knowledge in combination with uncertain

data in the reasoning process is called reasoning with

uncertainty. An important subclass of methods for reasoning

with uncertainty is called ?fuzzy logic,?and the systems that

use them are known as ?fuzzy systems?. For instance:

If the geometric model of (x) has geometric properties

A,B,C but not properties D,E

THEN (x) is an example of MODEL ABC (with

probability 0.7)

If the geometric model of (x) has geometric properties

A,B,C,D,E

THEN (x) is an example of MODEL ABC (with

probability 1.0)

If (x) APPROXIMATELY fits MODEL ABC

THEN VISUALISE the incomplete parts of (x) using

ABC properties

Because an expert system uses uncertain or heuristic

knowledge (as we humans do) its credibility is often in

question,as is the case with humans. When an answer to a

problem is questionable,we tend to want to know the

rationale. If the rationale seems plausible,we tend to believe

the answer. So it is with expert systems.

One of the main examples of using expert systems for the

simulation of archaeological missing data is the estimation

of the general shape of a building by OZAWA (1992,1996).

The geometric model was based on a contour map of

keyhole tomb mounds of ancient Japan. When

archaeological information is not enough to produce the

contour map,an expert system creates an estimated contour

map of the original tomb mound in co-operation with

archaeologists. The expert system holds the statistical

knowledge for classifying any tomb into its likeliest type

and the geometrical knowledge for drawing contour lines of

the tomb mound. The user for each contour map introduces

shape parameters,and the system classifies the mound as

one of the seven types,according to specific parameters

(diameter,length,weight,height,etc.). The estimated shape

layout is then used as input for the 3D solid modelling and

rendering (OZAWA 1992).

FLORENZANO et al. (1999) give a further advance in this

artificial intelligence approach. They use an Object-

Oriented Knowledge-Base containing a theoretical model of

existing architecture. They have chosen classical

architecture as the first field of experiment of the process.

This architecture can be modelled easily enough. The

proportion ratios linking the diverse parts of architectural

entities to the module allows a simple description of each

entity?s morphology. The main hypothesis of this research is

about comparing the theoretical model of the building to the

incomplete input data (preserved remains) acquired by

photogrammetry. Abstract models are organised with the

aim of isolating elementary entities that share common

morphological characteristics and function,on which rules

of composition can be used to re-order the building. The

concept of architectural entity gathers in a single class the

architectural data describing the entity,the interface with

survey mechanisms and the representation methods. Each

24

architectural entity,each element of the predefined

architectural corpus,is therefore described through

geometrical primitives corresponding to its morphological

characteristics:a redundant number of measurable

geometrical primitives are added to each entity?s definition,

as previously mentioned.

1.Splitting of the object into a cloud of points measured on

its surface.

2.Linking of the points to architectural entities.

3.Data processing.

4.Definition of geometrical models reconstructed on these

points.

5.Definition of the architectural model,which is informed

by the geometrical model.

6.Consistency-making on the whole set of entities.

LEWIS and S?GUIN (1998) give another approach to building

reconstruction. They have created the Building Model

Generator (BMG) which accepts 2D floor plans in a common

DXF geometry description format. The program first

converts these plans into a suitable internal data structure

that permits,not only efficient geometric manipulation and

analysis,but also the integration of non-geometrical data,as

the definition and identity of all rooms,doors,windows,

columns,etc. It then corrects small local geometrical

inconsistencies and makes the necessary adjustments to

obtain a consistent layout topology. This clean floor plan is

then analysed to extract semantic information (room

identities,connecting portals,the function of columns or

arches,etc.). With that information the pure walls are

extruded to a specified (by the user) height,and door,

window and ceiling geometries are inserted where

appropriate. This generates a 3D representation of the

building shell,which can then be visualised and some local

adjustment on parts of the building or material properties

can be made with an interactive editor.

Archaeological structures can be reconstructed from aerial

images,the initial body of a structure (building box) derives

from known structures footprints from a multi-purpose

digital map,this is being extended in the vertical direction

up to the archaeological entity. Detected elements are then

phototextured from aerial images,the building box is

phototextured after improvements with automated

measurements of archaeological remains from field level

photography. As an input dataset for the archaeological

reconstruction not only aerial images with known

orientation parameters can be used,but also digital elevation

models (DEM) and GIS-data (structures footprints at the

ground level and approximate elevation of the structure

contour from the multi-purpose digital map). The idea is to

obtain first an estimate of the archaeological entity

boundaries in the image plane using the GIS data,then to add

detected lines coming from an image segmentation with the

algorithm proposed by Burns,Hanson & Riseman. The

detected entity boundaries generate a 2D archaeological

skeleton (monocular) creating a correct topological

description of the archaeological elements polygons for an

automated production of the 3D archaeological skeleton.

Then the reconstruction of 3D archaeological detail takes

place,using external knowledge (historical sources or

ethnographical analogy). Finally it is needed to obtain the

phototexture from aerial images with consideration of

correspondence between geometric and texture detail. This

serves to relax the requirements for the 3D archaeological

skeleton. The proposed approach has been used at the

University of Graz (Austria) for roof building

reconstruction,and promises automation and speed in the

detection and reconstruction of the roofs using the GIS data.

It supports a feedback between 3D models of buildings and

the GIS,preserves the correspondence between geometric

and texture detail and creates parametric models for future

work.(http://www.icg.tu-graz.ac.at/ORGroup/research/

3D_Aerial_Building.html).

An interesting future development is the possibility of using

visualisations in a case-based reasoning framework (FOLEY

and RIBARSKY 1994). The fundamental strategy is to

organise a large collection of existing visualisations as cases

and to design new visualisations by adapting and combining

the past cases. New problems in the case-based approach

are solved by adapting the solutions to similar problems

encountered in the past. The important issues in building a

case-based visualisation advisor are developing a large

library of visualisations,developing an indexing scheme to

access relevant cases,and determining a closeness metric to

find the best matches from the case library.

3.2 QUANTITATIVE MODELS

Sometimes,the archaeological record to be visualised

cannot be seen because most of it is hidden,or we have only

some partial information about its physical location and

properties. In this case,fragmented data are represented as

scattered x,y,z input data sampled at irregular locations.

The fragmented spatial information available must be

extrapolated to complete closed surfaces. So,the

reconstruction of a given object or a given building structure

as an architectural frame is a generalization of fragmented

observable data by mathematical object description.

The procedure may be illustrated by the mathematical ovoid

and the eggshell compared. The eggshell is a solid formed

by a fine closed surface. Continuity and dynamics are bound

to the shape of the eggshell,in such a way that it is possible

to locate the fragments of a broken eggshell as well as to

define the whole by only very few spatial measurements.

Evidently,to model the physics of an eggshell,it is

sufficient to pick from the fragments of a broken eggshell

some spatial world data to simulate the entire eggshell. The

spatial continuity and dynamics of the ovoid is included in

the mathematical description,to simulate the missing

information. The algorithm for the mathematical ovoid

serves as a generalized constructive solid geometry,and just

some additional information will tell the specification and

the modification of the individual eggshell,its capacity and

the location of the centre of gravity. This kind of fact-based

solid simulation by mathematical guidelines is including the

physical measurement of a shell,just as a recursive

calculation (STECKNER 1993,1996). In other words,we

should create a geometric model (the mathematical ovoid)

of the interpreted reality,and then use information deduced

from the model to fit the partially observed reality.

The idea is very similar to the previous one,but instead of a

qualitative model we have geometric models. Several

measurements ? like volume,width,maximal perimeter,etc

? are computed from observable data. Comparing the actual

measurements or interpolated surface with the parameters

and surfaces defining the theoretical model makes

simulation possible. In this case,prior knowledge can be

represented in terms of simple geometrical models,and we

can still follow the general rule:?The most similar is taken

for the complete simulation?.

25

For example,consider the case where we have not all-

relevant 3D information for a shape model,but a series of

2D sections,irregularly sampled over a 2D area. This is a

very common situation in geology,archaeology and in all

disciplines using computer tomography scanners.

The purpose is to generalize 2D sampled data into a

homogenous 3D model. A grid,which can be envisioned,

represents an interpolated parametric surface,as two

orthogonal sets of parallel,equally spaced lines representing

the co-ordinate system. The points where grid lines intersect

are called grid nodes. Values of the surface must be known or

estimated at each of these nodes using ?gridding?techniques.

The first step is to extend the 2D sections normally,in such a

way that different samples meet at common planes. The

method begins with a rough surface interpolating only

boundary points,and in successive steps,refines those points

(and the resulting surface) by adding the maximum error

point at a time until the desired approximation accuracy is

reached. (WATSON 1992,HOULDING 1994,PARK and KIM

1995,ALGORRI and SCHMITT 1996,EGGLI et al. 1996,MA and

HE 1998,PIEGL and TILLER 1999).

In the previous case,fragmented data were represented as

scattered x,y,z input data sampled at irregular locations. In

other cases,we do not have an irregularly sampled surface,

but an interrupted surface. In those cases,we should add

new geometrical information,instead of merely calculating

missing information from nearest neighbour points. This is

the situation in pottery analysis,when we try to reconstruct

the shape of the vessel from the preserved sherds. STECKNER

(2000) uses simple interpolation to solve the same problem.

Here,a surface is interpolated on some points sampled

along the contour of the sherd. Several measurements ? like

volume,width,maximal perimeter,etc ? are computed from

sherd data (contour). Comparing the actual contour or

interpolated surface with the contour lines and surfaces

already computed for complete vessels makes

reconstructions of pots from sherds. The most similar is

taken for the complete reconstruction and classification (see

also STECKNER & STECKNER 1987). A similar approach has

been developed in the qualitative case by BARCEL?(1996b)

using a fuzzy logic approach to compute the similarity

between the sherd information and the complete vase

already known. A Generalized Hough transformation,

instead of surface interpolation,has been used by DURHAM,

LEWIS and SHENNAN (1993). ROWNER (1993) uses a similar

approach for lithic analysis (projectile points). Alternatively,

contour reconstruction can be computed from interpoint

distances. BERGER et al. (1999) presents an algorithm for

doing this task,even when the precise location of each point

is uncertain.

A neural network (see BARCEL?1993,1996a,GU and YAN

1995) can be used also to reconstruct a surface. A neural

network (NN) is a system composed of many simple

processing elements operating in parallel whose function is

determined by network structure,connection strengths,and

the processing performed at computing elements or nodes.

(Definition by the DARPA Neural Network Study 1988,

AFCEA International Press:60). That is to say,an NN is a

network of many simple processors (?units?),each possibly

having a small amount of local memory. Communication

channels (?connections?) which usually carry numeric (as

opposed to symbolic) data,encoded by any of various

means connect the units. The units operate only on their

local data and on the inputs they receive via the connections.

The restriction to local operations is often relaxed during

training. Most NNs have some sort of ?training?rule

whereby the weights of connections are adjusted on the

basis of data. In other words,NNs ?learn?from examples

and exhibit some capability for generalization beyond the

training data.

During learning,the outputs of a supervised neural net come

to approximate the target values given the inputs in the

training set. This ability may be useful in itself,but more

often the purpose of using a neural net is to generalize ? i.e.,

to have the outputs of the net approximate target values

given inputs that are not in the training set. Generalization

is not always possible. There are two conditions that are

typically necessary (although not sufficient) for good

generalization.

The first necessary condition is that the function you are

trying to learn (that relates inputs to correct outputs) be,in

some sense,smooth. In other words,a small change in the

inputs should,most of the time,produce a small change in

the outputs. For continuous inputs and targets,smoothness

of the function implies continuity and restrictions on the

first derivative over most of the input space. Some neural

nets can learn discontinuities as long as the function

consists of a finite number of continuous pieces. Very no

smooth functions such as those produced by pseudo-random

number generators and neural nets cannot generalize

encryption algorithms. Often a nonlinear transformation of

the input space can increase the smoothness of the function

and improve generalization.

In practice,NNs are especially useful for simulating missing

data in an incomplete geometric model of archaeological

entities. These algorithms suppose a way of classification

and function approximation/mapping problems which are

tolerant of some imprecision,which have lots of training

data available,but to which hard and fast rules (such as

those that might be used in an expert system) cannot easily

be applied. The Neural Network is trained using ?complete

geometric models?(real objects). Then,given a partially

damaged input (incomplete surface),the network is able to

generalize the model and it generates those points that were

not available. That is to say,the computer program

?remembers?when it retrieves previously stored

information in response to associated data. If you have an

adequate sample for your training set,every case in the

population will be close to a sufficient number of training

cases. Hence,under these conditions and with proper

training,a neural net will be able to generalize reliably to

the population.

If you have more information about the function,you can

often take advantage of this information by placing

constraints on the network. Among the constraints,there are

geometric constraints (related to shape) and feature-

extrinsic constraints (ALGORRI and SCHMITT 1996,LEWIS

and S?GUIN 1998,WERGHI et al.,1999). This is an

alternative approach to missing data simulation. Since

preserved data are not arbitrary,a generic model having a

known shape is a logical starting point for a curve or surface

fitting process. Pertinent features within the data are

incorporated into the basic structure of the model. The

model is then deformed to fit the unique characteristics of

each data set (DOBSON et al. 1995).

TSINGOS et al (1995) use a modification of this approach:

implicit iso-surfaces generated by a skeleton for shape

reconstruction. An initial skeleton is positioned at the center

of mass of the data points,and divided until the process

26

reaches a correct approximation level. Local control for the

reconstructed shape is possible through a local field

function,which enables the definition of local energy terms

associated with each skeleton. The method works as a semi-

automatic process:the user can visualize the data,initially

position some skeleton thanks to an interactive implicit

surfaces editor,and further optimize the process by

specifying several ?reconstruction windows?,that slightly

overlap,and where surface reconstruction follows a local

criterion. THALMANN et al. (1995) use a similar approach for

reconstructing the Xian Terra-cotta Soldiers. A geometric

model of these Chinese sculptures is produced through a

method similar to modeling of clay,which essentially

consists of adding or eliminating parts of material and

turning the object around when the main shape has been set

up. They use a sphere as a starting point for the heads of

soldiers,and they add or remove polygons according to the

details needed and apply local deformations to alter the

shape. This process helps the user towards a better

understanding about the final proportions of a human?s

head. Scaling deformations were first applied to the sphere

to give an egg shape aspect,then various regions selected

with triangles were moved by translation. At this point

vertices were selected one by one and then lifted to the

desired locations. The modeling of different regions was

started,sculpting and pushing back and forth vertices and

regions to make the nose,jaws,eyes and various landmarks.

Using a similar approach,ATTARDI et al. (2000) use a

distortion (warping) of the 3D model of a reference scanned

head,until its hard tissues match those of the scanned data.

The subsequent stage is the construction of the hybrid

model composed by the hard tissues of the mummy plus the

soft ones of the reference head. Another example of warping

to reconstruction is BROGNI et al (2000).

4. CONCLUSIONS

In all these approaches,we have been using general models

and particular constraints as mechanisms for modifying a

preliminary hypothetical geometrical model of a

?complete?reality into another that simulate the missing

parts by satisfying constraints. Finding the geometric

configurations that satisfy the constraints is the crucial

issue. We have examined two strategies:

a) The use of specific values of the constraints and looks

for geometric configurations satisfying these

constraints.

b) The user investigates first whether the geometric

elements could be placed given the constraints

independently of their values.

Among the constraints,there are geometric constraints

(related to shape) and feature-extrinsic constraints.

However,we should take into account that the world is not

made of images,but it is a series of perceptual information

waiting for an observer that imposes order by recognising

an object and by describing it. Visual models are only a

spatial pattern of luminance contrasts that explains how the

light is reflected,and we use them as a ?virtual?model of

something that does not exist,that cannot be seen.

A description of what cannot be seen is not an explanation

of reality?s missing parts; it is only a part of the explanatory

process. I?m suggesting using VR techniques not only for

description,but also for building all the explanatory

process,from data acquisition to understanding. An

explanation can be presented as a visual model,that is as a

virtual dynamic environment,where the user ask questions

in the same way a scientist use a theory to understand the

empirical world. A virtual world should be,then a model,a

set of concepts,laws,tested hypotheses and hypotheses

waiting for testing. If in standard theories,concepts are

expressed linguistically or mathematically,in virtual

environments,theories are expressed computationally,by

using images and rendering effects. Nothing should be

wrong or ?imaginary?in a virtual reconstruction,but should

follow what we know,be dynamical,and be interactively

modifiable. A virtual experience is then a way of studying a

geometrical model ? a scientific theory expressed with a

geometric language ? instead of studying empirical reality.

As such it should be related with work on the empirical

reality (excavation,laboratory analysis). As a result we can

act virtually with inaccessible realities through their

models.

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