Shape Analogies via Group Shape Difference Analysis

In this project, we proposed a novel framework to solve the shape analogies problem between 3D shape collections. Instead of using geometric features based on individuals to describe each shape, we leveraged the idea that fine grained characteristic of a shape can be defined by other similar shapes, and used relationship within collections to depict shapes. To capture the abstract relationship, a novel shape descriptor, average shape difference, was proposed. Based on the descriptor, we formulated the shape analogies problem as a graph matching task and solved it via a coarse to fine algorithm. We tested our algorithm on several datasets and the result shows our framework effectively solves the shape analogies problem without knowing the cross-collection point correspondence information, which is a key factor for traditional shape matching techniques but usually not easy to get.