A probabilistic approach to spectral graph matching.

Spectral Matching (SM) is a computationally efficient approach to approximate the solution of pairwise matching problems that are np-hard. In this paper, we present a probabilistic interpretation of spectral matching schemes and derive a novel Probabilistic Matching (PM) scheme that is shown to outperform previous approaches. We show that spectral matching can be interpreted as a Maximum Likelihood (ML) estimate of the assignment probabilities and that the Graduated Assignment (GA) algorithm can be cast as a Maximum a Posteriori (MAP) estimator. Based on this analysis, we derive a ranking scheme for spectral matchings based on their reliability, and propose a novel iterative probabilistic matching algorithm that relaxes some of the implicit assumptions used in prior works. We experimentally show our approaches to outperform previous schemes when applied to exhaustive synthetic tests as well as the analysis of real image sequences.

Improving shape retrieval by spectral matching and meta similarity.

We propose two computational approaches for improving the retrieval of planar shapes. First, we suggest a geometrically motivated quadratic similarity measure, that is optimized by way of spectral relaxation of a quadratic assignment. By utilizing state-of-the-art shape descriptors and a pairwise serialization constraint, we derive a formulation that is resilient to boundary noise, articulations and nonrigid deformations. This allows both shape matching and retrieval. We also introduce a shape meta-similarity measure that agglomerates pairwise shape similarities and improves the retrieval accuracy. When applied to the MPEG-7 shape dataset in conjunction with the proposed geometric matching scheme, we obtained a retrieval rate of 92.5%.