Convex Joint Graph Matching and Clustering via Semidefinite Relaxations

TL;DR

This paper introduces a novel convex semidefinite relaxation approach for jointly solving graph matching and clustering without training data, improving performance on noisy and complex 3D scene graphs.

Contribution

It is the first to unify graph matching and clustering in a joint, training-free framework using spectral embeddings and semidefinite relaxations.

Findings

Outperforms state-of-the-art methods on challenging noisy graphs

Effective in real 3D compound scene applications

No training data required for joint reasoning

Abstract

This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages for identifying similar arbitrary objects in compound 3D scenes and matching them. For joint reasoning, we first rephrase graph matching as a rigid point set registration problem operating on spectral graph embeddings. Consequently, we utilise efficient convex semidefinite program relaxations for aligning points in Hilbert spaces and add coupling constraints to model the mutual dependency and exploit synergies between both tasks. We outperform state of the art in challenging cases with non-perfectly matching and noisy graphs, and we show successful applications on real compound scenes with multiple 3D elements. Our source code and data are publicly available.