Elastic Net Constraints for Shape Matching

Abstract

We consider a parametrized relaxation of the widely adopted quadratic assignment problem (QAP) formulation for minimum distortion correspondence between deformable shapes. In order to control the accuracy/sparsity trade-off we introduce a weighting parameter on the combination of two existing relaxations, namely spectral and game-theoretic. This leads to the introduction of the elastic net penalty function into shape matching problems. In combination with an efficient algorithm to project onto the elastic net ball, we obtain an approach for deformable shape matching with controllable sparsity. Experiments on a standard benchmark confirm the effectiveness of the approach.