GEOGINE: a formal oncological model for shape/texture optimal synthetic description

GEOGINE© (GEOmetrical enGINE), a formal Ontological Model Generator (OMG) for multidimensional shape/texture optimal synthetic understanding, description and classification is presented. In general, reliable computer object recognition of even elementary geometric forms of any dimension, subjected to geometric transformation on a rigorous mathematical level, can be a difficult task that can be greatly facilitated by using suitable descriptors computed from image. To assure effective computational result robustness those descriptors must be invariant from object position, orientation, viewing angle, and degradations introduced by imaging system; in other words, the obvious way to obtain image features which are not affected by the action of a transformation group is to use invariants of the group action: we need to find a set of separating invariants (i.e. an object model) such that two images are in the same orbit if and only if the values of these invariants evaluated on the two images are the same. On the other hand, an ontology can be regarded as a logical theory accounting for the intended meaning of a formal dictionary, i.e., its ontological commitment to a particular conceptualization of the world. The intended models of a logical language using such a dictionary are constrained by its ontological commitment. An ontology indirectly reflects this commitment by approximating these intended models. Therefore, it could be useful to think about an ontological model that grows incrementally so that the representation of the real world would be more accurate as the model is incrementally developed and refined. This statement can be considered an axiom of our work. Another significant aspect of developing an ontological model is that of its formalization, which is basic for being considered a valid model. Therefore, another axiom of our work is that all the aspects defined in our incremental ontological model must be completely formalized. So an ontology can be seen as an approximation to what exists in the real world. An ontological model is the kernel used for specifying ontologies so that how close an ontology can be from the real world depends on the possibilities offered by the ontological model. The present paper introduces a new approach for automatic model generation based on n-Dimensional Tensor Invariants as a formal dictionary. Main operational advantages over previous approaches are: 1) Automated Model Generation, 2) Invariant Minimal Complete Set for computational efficiency, 3) Arbitrary Model Precision for robust object description. GEOGINE© computational kernel results are validated by carefully designed experiments with certified 2-D geometric reference database, for sake of presentation simplicity. In this way, n-Dimensional extensions are quite straightforward. GEOGINE© computational complexity and error analysis are discussed.