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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV. Part B5. Istanbul 2004 
area of the corresponding triangles; the later being normalised 
in terms of the total area of the artefact. 
The statistical distribution of the cords is described in terms of 
three histograms. The first histogram described the distribution 
of the cosine directions associated to the unit vector associated 
with the smallest Eigen value. The second histogram described 
the distribution of the cosine directions associated with the unit 
vector associated with the second smallest Eigen value. The 
third histogram described the distribution of the normalised 
spherical radius as defined in the previous paragraph. The 
ensemble of the three histograms constitutes the shape index of 
the corresponding artefact. A demonstration with a database of 
more than 4400 three-dimensional models can be seen at [8]. 
3.3 Characterization of virtual collections 
This section shows how to perform a comparative study on a 
collection by using the apparatus developed in the previous two 
sections. We saw that shape constitutes a universal language. 
This is obvious in art and architecture. Indeed, numerous styles 
can be characterized by the shape of their associated 
architectural elements. For instance, let us considerer the three 
classical orders of columns: Ionic, Doric and Corinthian. 
Columns of the same order are of course never identical but 
their shape is sufficiently similar so that it is relatively 
straightforward to identify them. The same can be said about 
cupolas, Roman arcs and Gothic arcs; the list is literally endless. 
While studying a collection, a scholar usually studies particular 
artefacts but he may as well want to compare similar artefacts in 
order to determine their common characteristics, their 
discrepancies or even the temporal evolution of a particular 
style. In order to be able to perform these actions, the scholar 
must be able to group or cluster similar artefacts within a 
common class. 
  
Figure 4. Creation of a palette of fragments for a broken vase. 
The top view corresponds to the central section of 
the vase while-the bottom view corresponds to the 
border. 
The same approach can be followed in the reconstitution of 
broken artefacts. Here, clustering (or cluster analysis) a data 
mining technique that deals with the extraction of the implicit 
knowledge, data relationship or other patterns not explicitly 
stored, by grouping or classifying related records together, is 
performed [10]. A cluster is a collection of objects that are 
similar to one another and are dissimilar to the objects in other 
clusters. The goal of clustering is to find intcr-cluster similarity 
and intra-cluster dissimilarity, through the discovery of a hidden 
pattern that gives meaningful groups (clusters) of objects. For 
example, the first step in the reconstitution of a broken artefact 
is to create a palette of similar fragments. Most of the time, 
similar fragments occupy adjacent regions on the artefact or 
belong to the same component: for instance a vase ear. 
Consequently, the palette facilitates the work of the scholar by 
providing him with a pre-classified ensemble of fragments into 
clusters. In practice this classification is performed manually: a 
time consuming approach. With the proposed method, it is 
possible to perform this classification semi-automatically. We 
first consider the general theory and then we apply the results to 
the creation of a palette of fragments for the reconstitution of a 
broken vase. 
Our system can find, in a collection, similar pictures and three- 
dimensional artefacts. We have seen that by following an 
iterative or spiral approach, the user can converge to the item of 
interest. Let us review this process from a more fundamental 
point of view. An index can be visualised as a point in an N- 
dimensional space where N depends on the number of channels. 
When the user chooses a prototype, he chooses a point or a seed 
in this space. Then, the search engine determines the closest 
points to the seed, with the proximity being defined according 
to a metric such as the Euclidian distance. It should be 
remembered that a point corresponds to an artefact in the 
collection. In this way, the nearest-neighbourhood approach is 
used to identify clusters of similar objects. 
If the outcome of the query corresponds to the foreseen results, 
it means that the seed point is approximately located near the 
centre of the cluster. If it is not the case, it means that the seed 
point is situated on the outskirt of the cluster. In that case, the 
user selects the best candidate from the closest M points 
obtained from the previous iteration and reiterates the process. 
After a few iterations, after a cluster has been constructed, the 
process converges to a point near the centre of the cluster. This 
point and its neighbourhood constitute the cluster and the 
corresponding artefacts form the class. 
We have applied this approach for the creation of a palette from 
a collection of 448 fragments from a broken vase (2000 AD!). 
We were able to group similar pieces such as the ear, the rim 
and the central region. Here, the Euclidian metric was used to 
create the clusters of similar pieces. Some results are illustrated 
in Figure 4. The top view shows two fragments of the central 
section that were grouped together while the bottom view shows 
two fragments of the border. A demonstration can be found in 
[8]. 
4. AN INTEGRATED APPROACH TO VIRTUAL 
COLLECTIONS MANAGEMENT 
In the previous sections, we have presented some considerations 
on virtualisation, a cost-effective stereo visualisation system for 
three-dimensional complex data, an indexation and retrieval 
system for images and three-dimensional artefacts based on 
composition and shape and, an approach for characterising a 
collection in terms of clusters and classes. In this section we 
present an integrated approach to virtual collections 
management. The proposed approach consists of five step: 
virtualisation, documentation, indexation, retrieval, 
characterisation and finally, visualisation. 
The first step is well known and thousands of scientific papers 
have been devoted to the subject. Although virtualisation is and