3-D Mesh Representation and Retrieval Using Isomap Manifold

Abstract

We propose a compact 3-D object representation scheme that can greatly assist the search/retrieval process in a network environment. A 3-D mesh-based object is transformed into a new coordinate frame by using the Isomap (isometric feature mapping) method. During the transformation process, not only the structure of the salient parts of an object will be kept, but also the geometrical relationships will be preserved. From the viewpoint of cognitive psychology, the data distributed on the Isomap manifold can be regarded as a set of significant features of a 3-D mesh-based object. To perform efficient matching, we project the Isomap domain 3-D object onto two different 2-D maps, and the two 2-D feature descriptors are used as the basis to measure the degree of similarity between two 3-D mesh-based objects. Experiments demonstrate that the proposed method in retrieving similar 3-D models is very effective. Most importantly, the proposed 3-D mesh retrieval scheme is still valid even if a 3-D mesh undergoes a mesh simplification process.