Consistent Partial Matching of Shape Collections via Sparse Modeling

Abstract

Recent efforts in the area of joint object matching approach the problem by taking as input a set of pairwise maps, which are then jointly optimized across the whole collection so that certain accuracy and consistency criteria are satisfied. One natural requirement is cycle‐consistency—namely the fact that map composition should give the same result regardless of the path taken in the shape collection. In this paper, we introduce a novel approach to obtain consistent matches without requiring initial pairwise solutions to be given as input. We do so by optimizing a joint measure of metric distortion directly over the space of cycle‐consistent maps; in order to allow for partially similar and extra‐class shapes, we formulate the problem as a series of quadratic programs with sparsity‐inducing constraints, making our technique a natural candidate for analysing collections with a large presence of outliers. The particular form of the problem allows us to leverage results and tools from the field of evolutionary game theory. This enables a highly efficient optimization procedure which assures accurate and provably consistent solutions in a matter of minutes in collections with hundreds of shapes.Recent efforts in the area of joint object matching approach the problem by taking as input a set of pairwise maps, which are then jointly optimized across the whole collection so that certain accuracy and consistency criteria are satisfied. One natural requirement is cycleconsistency— namely the fact that map composition should give the same result regardless of the path taken in the shape collection. In this paper, we introduce a novel approach to obtain among partially similar shapes consistent matches without requiring initial pairwise solutions to be given as input.