Principal Component Analysis-based Mesh Decomposition

Abstract

In this paper, we propose an automatic mesh decomposition technique based on principal component analysis (PCA) and Boolean operations. First, we calculate the normalized protrusion degree of each dual vertex on the smoothed 3-D mesh. The protrusion degree of a vertex and the vertex's 3-D coordinates form a 4-D feature vector, which we use to represent the polygon mesh. Since a 3-D object is composed of a large number of polygon meshes, we apply PCA to the set of 4-D feature vectors. We take the axes corresponding to the top three principal components as the three axes of a new coordinate system and project the set of 4-D vectors onto the system. Surprisingly, the projected data along the first axis reveals the salient structures of the 3-D object. Therefore, using the first component axis as the search basis, we can identify all the salient parts of an arbitrary 3-D object.