Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition

This paper deals with the rotation synchronization problem, which arises in global registration of 3D point-sets and in structure from motion. The problem is formulated in an unprecedented way as a "low-rank and sparse" matrix decomposition that handles both outliers and missing data. A minimization strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against state-of-the-art algorithms on simulated and real data. The results show that R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript submitted to CVI

Robust Linear Regression Analysis - A Greedy Approach

The task of robust linear estimation in the presence of outliers is of particular importance in signal processing, statistics and machine learning. Although the problem has been stated a few decades ago and solved using classical (considered nowadays) methods, recently it has attracted more attention in the context of sparse modeling, where several notable contributions have been made. In the present manuscript, a new approach is considered in the framework of greedy algorithms. The noise is split into two components: a) the inlier bounded noise and b) the outliers, which are explicitly modeled by employing sparsity arguments. Based on this scheme, a novel efficient algorithm (Greedy Algorithm for Robust Denoising - GARD), is derived. GARD alternates between a least square optimization criterion and an Orthogonal Matching Pursuit (OMP) selection step that identifies the outliers. The case where only outliers are present has been studied separately, where bounds on the \textit{Restricted Isometry Property} guarantee that the recovery of the signal via GARD is exact. Moreover, theoretical results concerning convergence as well as the derivation of error bounds in the case of additional bounded noise are discussed. Finally, we provide extensive simulations, which demonstrate the comparative advantages of the new technique

Pentagon-Match (PMatch): Identification of View-Invariant Planar Feature for Local Feature Matching-Based Homography Estimation

In computer vision, finding correct point correspondence among images plays an important role in many applications, such as image stitching, image retrieval, visual localization, etc. Most of the research works focus on the matching of local feature before a sampling method is employed, such as RANSAC, to verify initial matching results via repeated fitting of certain global transformation among the images. However, incorrect matches may still exist. Thus, a novel sampling scheme, Pentagon-Match (PMatch), is proposed in this work to verify the correctness of initially matched keypoints using pentagons randomly sampled from them. By ensuring shape and location of these pentagons are view-invariant with various evaluations of cross-ratio (CR), incorrect matches of keypoint can be identified easily with homography estimated from correctly matched pentagons. Experimental results show that highly accurate estimation of homography can be obtained efficiently for planar scenes of the HPatches dataset, based on keypoint matching results provided by LoFTR. Besides, accurate outlier identification for the above matching results and possible extension of the approach for multi-plane situation are also demonstrated.Comment: arXiv admin note: text overlap with arXiv:2211.0300

Multiple structure recovery via robust preference analysis

2noThis paper address the extraction of multiple models from outlier-contaminated data by exploiting preference analysis and low rank approximation. First points are represented in the preference space, then Robust PCA (Principal Component Analysis) and Symmetric NMF (Non negative Matrix Factorization) are used to break the multi-model fitting problem into many single-model problems, which in turn are tackled with an approach inspired to MSAC (M-estimator SAmple Consensus) coupled with a model-specific scale estimate. Experimental validation on public, real data-sets demonstrates that our method compares favorably with the state of the art.openopenMagri, Luca; Fusiello, AndreaMagri, Luca; Fusiello, Andre