Topology-based reasoning on non-manifold shapes


Topological information is a promising resource to research in shape-understanding as it provides a high-level description of the characteristics of a shape, and such high-level description often has strong association with the semantics of an object. The Shape Acquisition and Processing (SAP) ontology has been designed to maintain useful information of a model. We propose here an extension to the SAP ontology, that addresses the non-manifold properties of a model. Useful information about the connectivity of an object can be obtained based on an analysis of its non-manifold properties, because the structure of a non-manifold object can be considered as a graph of manifold parts connected together at non-manifold joints. The manifold parts are often pieces that have strong semantic associations. In this work, we describe the type of non-manifold properties, the various types of connected components in a non-manifold object and their semantical significance. We address how the Euler’ characteristics of a non-manifold object can be found based on such information. All such information are extractable from a model using TopMesh, a tool that we have developed. In this work, we also describe the features of TopMesh, namely, all the topological properties it extracts.

Proceedings of the 1st International Symposium on Shapes and Semantics