Tensor maps for synchronizing heterogeneous shape collections

Huang, Qixing; Liang, Zhenxiao; Wang, Haoyun; Zuo, Simiao; Bajaj, Chandrajit L.

doi:10.1145/3306346.3322944

Cited by 12 publications

(7 citation statements)

References 77 publications

(140 reference statements)

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“…The art of consistently recovering absolute quantities from a collection of ratios is now a basic component of the classical multi-view / multi-shape analysis pipelines [59,15,16]. Various aspects of the problem have been vastly studied: different group structures [26,25,13,2,1,34,28,1,69,19,62,65,4,6], closed form solutions [4, 2, 1], robustness [18], certifiability [58], global optimality [14], learning-to-synchronize [35,53,23] and uncertainty quantification [64,11,10,13]. In this work, we are concerned with synchronizing correspondence sets, otherwise known as permutation synchronization (PS) [51] and motion segmentations [3].…”

Section: Related Workmentioning

confidence: 99%

MultiBodySync: Multi-Body Segmentation and Motion Estimation via 3D Scan Synchronization

Huang

Wang

Birdal

et al. 2021

Preprint

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We present MultiBodySync, a novel, end-to-end trainable multi-body motion segmentation and rigid registration framework for multiple input 3D point clouds. The two non-trivial challenges posed by this multi-scan multibody setting that we investigate are: (i) guaranteeing correspondence and segmentation consistency across multiple input point clouds capturing different spatial arrangements of bodies or body parts; and (ii) obtaining robust motionbased rigid body segmentation applicable to novel object categories.We propose an approach to address these issues that incorporates spectral synchronization into an iterative deep declarative network, so as to simultaneously recover consistent correspondences as well as motion segmentation. At the same time, by explicitly disentangling the correspondence and motion segmentation estimation modules, we achieve strong generalizability across different object categories. Our extensive evaluations demonstrate that our method is effective on various datasets ranging from rigid parts in articulated objects to individually moving objects in a 3D scene, be it single-view or full point clouds. Code at https://github.com/ huangjh-pub/multibody-sync.

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Section: Related Workmentioning

confidence: 99%

MultiBodySync: Multi-Body Segmentation and Motion Estimation via 3D Scan Synchronization

Huang

Wang

Birdal

et al. 2021

Preprint

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“…The problem is now very well studied, enjoying a rich set of algorithms. Primarily, there exists a plethora of works on group structures arising in different applications [49,48,16,5,4,57,55,4,101,28,97,99,6,9]. Some of the proposed solutions are closed form [6,5,73,4] or minimize robust losses [54,27].…”

Section: Related Workmentioning

confidence: 99%

Quantum Permutation Synchronization

Birdal¹,

Golyanik²,

Theobalt³

et al. 2021

Preprint

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We present QuantumSync, the first quantum algorithm for solving a synchronization problem in the context of computer vision. In particular, we focus on permutation synchronization which involves solving a non-convex optimization problem in discrete variables. We start by formulating synchronization into a quadratic unconstrained binary optimization problem (QUBO). While such formulation respects the binary nature of the problem, ensuring that the result is a set of permutations requires extra care. Hence, we: (i) show how to insert permutation constraints into a QUBO problem and (ii) solve the constrained QUBO problem on the current generation of the adiabatic quantum computers D-Wave. Thanks to the quantum annealing, we guarantee global optimality with high probability while sampling the energy landscape to yield confidence estimates. Our proofof-concepts realization on the adiabatic D-Wave computer demonstrates that quantum machines offer a promising way to solve the prevalent yet difficult synchronization problems.

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“…• joint matching and map synchronization: , Pachauri et al (2013), Shen et al (2016), Bajaj et al (2018), Sun et al (2018), Sun et al (2019), Huang et al (2019a)…”

Section: Notesmentioning

confidence: 99%

Spectral Methods for Data Science: A Statistical Perspective

Chen,

Chi,

Fan

et al. 2020

Preprint

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Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues (resp. singular values) and eigenvectors (resp. singular vectors) of some properly designed matrices constructed from data. A diverse array of applications have been found in machine learning, data science, and signal processing, including recommendation systems, community detection, ranking, structured matrix recovery, tensor completion, joint shape matching, blind deconvolution, financial investments, risk managements, econometric modeling, treatment evaluations, causal inference, amongst others. Due to their simplicity and effectiveness, spectral methods are not only used as a stand-alone estimator, but also frequently employed to initialize other more sophisticated algorithms to improve performance.While the studies of spectral methods can be traced back to classical matrix perturbation theory and methods of moments, the past decade has witnessed tremendous theoretical advances in demystifying their efficacy through the lens of statistical modeling, with the aid of nonasymptotic random matrix theory. This monograph aims to present a systematic, comprehensive, yet accessible introduction to spectral methods from a modern statistical perspective, highlighting their algorithmic implications in diverse large-scale applications. In particular, our exposition gravitates around several central questions that span various applications: how to characterize the sample efficiency of spectral methods in reaching a target level of statistical accuracy, and how to assess their stability in the face of random noise, missing data, and adversarial corruptions? In addition to conventional 2 perturbation analysis, we present a systematic ∞ and 2,∞ perturbation theory for eigenspace and singular subspaces, which has only recently become available owing to a powerful "leave-one-out" analysis framework.

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Tensor maps for synchronizing heterogeneous shape collections

Cited by 12 publications

References 77 publications

MultiBodySync: Multi-Body Segmentation and Motion Estimation via 3D Scan Synchronization

MultiBodySync: Multi-Body Segmentation and Motion Estimation via 3D Scan Synchronization

Quantum Permutation Synchronization

Spectral Methods for Data Science: A Statistical Perspective

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