Shape Indexing Using Relational Vectors and Neural Networks

In this paper, we propose a novel approach to generating topology preserving mapping of structural shapes using the self-organising maps (SOM). The structural information of the geometrical shapes is captured by the relational vectors. These relational attribute vectors are quantised using an SOM. Using this quatisation SOM, a histogram is generated for every shape. These histograms are treated as inputs to train another SOM which yields a topology preserving mapping of the geometric shapes. By appropriately choosing the relational vectors, it is possible to generate the mapping invariant to some chosen transformations such as rotation, translation, scale, aÆne or perspective. These SOMs may be organised into a tree-structure so that during the application phase the histogram of the query shape and the shapes most similar to the query shape can be retrieved eÆciently.