Huber-$$L_1$$-based non-isometric surface registration

Computer Graphics Forum

Dyke

et al. 2022

Non-rigid registration computes an alignment between a source surface with a target surface in a non-rigid manner. In the past decade, with the advances in 3D sensing technologies that can measure time-varying surfaces, non-rigid registration has been applied for the acquisition of deformable shapes and has a wide range of applications. This survey presents a comprehensive review of non-rigid registration methods for 3D shapes, focusing on techniques related to dynamic shape acquisition and reconstruction. In particular, we review different approaches for representing the deformation field, and the methods for computing the desired deformation. Both optimization-based and learning-based methods are covered. We also review benchmarks and datasets for evaluating non-rigid registration methods, and discuss potential future research directions.

Section: Extrinsic Methodsmentioning

confidence: 99%

A Survey of Non‐Rigid 3D Registration

Computer Graphics Forum

Dyke

et al. 2022

“…Wu et al [35] introduced an as-conformal-as-possible energy to avoid mesh distortion. Jiang et al [17] applied a Huber-norm regularization to induce piecewise smooth transformation.…”

Section: Related Workmentioning

confidence: 99%

“…Compute gradient G(X (j) ) with ( 15); Compute direction d (j) with Alg. 1; Perform line search for X (j+1) that satisfies condition (17);…”

Section: Numerical Minimizationmentioning

confidence: 99%

“…Such large localized errors will be inhibited by the 2 formulations, which can lead to erroneous alignment results. To improve the alignment accuracy, recent works have utilized sparsity-promoting norms for these terms, such as the 1 -norm [36,22,17] and the 0 -norm [12]. The sparsity optimization enforces small error metrics on most parts of the point cloud while allowing for large errors in some local regions, improving the robustness of the registration process.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quasi-Newton Solver for Robust Non-Rigid Registration

2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

et al. 2020

Imperfect data (noise, outliers and partial overlap) and high degrees of freedom make non-rigid registration a classical challenging problem in computer vision. Existing methods typically adopt the p type robust estimator to regularize the fitting and smoothness, and the proximal operator is used to solve the resulting non-smooth problem. However, the slow convergence of these algorithms limits its wide applications. In this paper, we propose a formulation for robust non-rigid registration based on a globally smooth robust estimator for data fitting and regularization, which can handle outliers and partial overlaps. We apply the majorization-minimization algorithm to the problem, which reduces each iteration to solving a simple least-squares problem with L-BFGS. Extensive experiments demonstrate the effectiveness of our method for non-rigid alignment between two shapes with outliers and partial overlap, with quantitative evaluation showing that it outperforms state-of-the-art methods in terms of registration accuracy and computational speed. The source code is available at https://github.com/Juyong/Fast_RNRR.

“…The ℓ 2 formulations can inhibit such large localized errors and lead to erroneous alignment. To improve the alignment accuracy, recent works have utilized sparsity-promoting norms for these terms, such as the ℓ 1 -norm [4], [5], [6] and the ℓ 0norm [7]. The sparsity optimization enforces small error values on most parts of the surface while allowing for large errors in some local regions, improving the robustness of the registration process.…”

Section: Introductionmentioning

confidence: 99%

Fast and Robust Non-Rigid Registration Using Accelerated Majorization-Minimization

IEEE Trans. Pattern Anal. Mach. Intell.

et al. 2023

Non-rigid 3D registration, which deforms a source 3D shape in a non-rigid way to align with a target 3D shape, is a classical problem in computer vision. Such problems can be challenging because of imperfect data (noise, outliers and partial overlap) and high degrees of freedom. Existing methods typically adopt the ℓp type robust norm to measure the alignment error and regularize the smoothness of deformation, and use a proximal algorithm to solve the resulting non-smooth optimization problem. However, the slow convergence of such algorithms limits their wide applications. In this paper, we propose a formulation for robust non-rigid registration based on a globally smooth robust norm for alignment and regularization, which can effectively handle outliers and partial overlaps. The problem is solved using the majorization-minimization algorithm, which reduces each iteration to a convex quadratic problem with a closed-form solution. We further apply Anderson acceleration to speed up the convergence of the solver, enabling the solver to run efficiently on devices with limited compute capability. Extensive experiments demonstrate the effectiveness of our method for non-rigid alignment between two shapes with outliers and partial overlaps, with quantitative evaluation showing that it outperforms state-of-the-art methods in terms of registration accuracy and computational speed. The source code is available at https://github.com/yaoyx689/AMM NRR.