CLAP: Concave Linear APproximation for Quadratic Graph Matching

Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem (QAP) with node-wise and edge-wise constraints. However, solving such a QAP can be both expensive and difficult due to numerous local extreme points. In this work, we introduce a novel linear model and solver designed to accelerate the computation of graph matching. Specifically, we employ a positive semi-definite matrix approximation to establish the structural attribute constraint.We then transform the original QAP into a linear model that is concave for maximization. This model can subsequently be solved using the Sinkhorn optimal transport algorithm, known for its enhanced efficiency and numerical stability compared to existing approaches. Experimental results on the widely used benchmark PascalVOC showcase that our algorithm achieves state-of-the-art performance with significantly improved efficiency. Source code: https://github.com/xmlyqing00/clap

A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Parts

Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes of individual pieces and establishing matches between different pieces. Many approaches also model priors of the underlying complete object. Existing approaches are tightly connected problems of shape segmentation, shape matching, and learning shape priors. We provide existing algorithms in this context and emphasize their similarities and differences to general-purpose approaches. We also survey the trends from early non-deep learning approaches to more recent deep learning approaches. In addition to algorithms, this survey will also describe existing datasets, open-source software packages, and applications. To the best of our knowledge, this is the first comprehensive survey on this topic in computer graphics.