Tensor based sparse decomposition of 3D shape for visual detection of mirror symmetry

Abstract

This study explores an approach for analysing the mirror (reflective) symmetry of 3D shapes with tensor based sparse decomposition. The approach combines non-negative tensor decomposition and directional texture synthesis, with symmetry information about 3D shapes that is represented by 2D textures synthesised from sparse, decomposed images. This technique requires the center of mass of 3D objects to be at the origin of the coordinate system. The decomposition of 3D shapes and analysis of their symmetry are useful for image compression, pattern recognition, as well as there being an emerging interest in the medical community due to its potential to find morphological changes between healthy and pathological structures. This paper postulates that sparse texture synthesis can be used to describe the decomposed basis images acting as symmetry descriptors for a 3D shape. We apply the theory of non-negative tensor decomposition and sparse texture synthesis, deduce the new representation, and show some application examples.