SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid Registration

Existing optimization-based methods for non-rigid registration typically minimize an alignment error metric based on the point-to-point or point-to-plane distance between corresponding point pairs on the source surface and target surface. However, these metrics can result in slow convergence or a loss of detail. In this paper, we propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration. The symmetrized point-to-plane distance relies on both the positions and normals of the corresponding points, resulting in a more accurate approximation of the underlying geometry and can achieve higher accuracy than existing methods. To solve this optimization problem efficiently, we propose an alternating minimization solver using a majorization-minimization strategy. Moreover, for effective initialization of the solver, we incorporate a deformation graph-based coarse alignment that improves registration quality and efficiency. Extensive experiments show that the proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency. The code is publicly available at https://github.com/yaoyx689/spare.

Neural-ABC: Neural Parametric Models for Articulated Body with Clothes

In this paper, we introduce Neural-ABC, a novel parametric model based on neural implicit functions that can represent clothed human bodies with disentangled latent spaces for identity, clothing, shape, and pose. Traditional mesh-based representations struggle to represent articulated bodies with clothes due to the diversity of human body shapes and clothing styles, as well as the complexity of poses. Our proposed model provides a unified framework for parametric modeling, which can represent the identity, clothing, shape and pose of the clothed human body. Our proposed approach utilizes the power of neural implicit functions as the underlying representation and integrates well-designed structures to meet the necessary requirements. Specifically, we represent the underlying body as a signed distance function and clothing as an unsigned distance function, and they can be uniformly represented as unsigned distance fields. Different types of clothing do not require predefined topological structures or classifications, and can follow changes in the underlying body to fit the body. Additionally, we construct poses using a controllable articulated structure. The model is trained on both open and newly constructed datasets, and our decoupling strategy is carefully designed to ensure optimal performance. Our model excels at disentangling clothing and identity in different shape and poses while preserving the style of the clothing. We demonstrate that Neural-ABC fits new observations of different types of clothing. Compared to other state-of-the-art parametric models, Neural-ABC demonstrates powerful advantages in the reconstruction of clothed human bodies, as evidenced by fitting raw scans, depth maps and images. We show that the attributes of the fitted results can be further edited by adjusting their identities, clothing, shape and pose codes.

DynoSurf: Neural Deformation-based Temporally Consistent Dynamic Surface Reconstruction

This paper explores the problem of reconstructing temporally consistent surfaces from a 3D point cloud sequence without correspondence. To address this challenging task, we propose DynoSurf, an unsupervised learning framework integrating a template surface representation with a learnable deformation field. Specifically, we design a coarse-to-fine strategy for learning the template surface based on the deformable tetrahedron representation. Furthermore, we propose a learnable deformation representation based on the learnable control points and blending weights, which can deform the template surface non-rigidly while maintaining the consistency of the local shape. Experimental results demonstrate the significant superiority of DynoSurf over current state-of-the-art approaches, showcasing its potential as a powerful tool for dynamic mesh reconstruction. The code is publicly available at https://github.com/yaoyx689/DynoSurf.

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

Non-rigid registration, which deforms a source shape in a non-rigid way to align with a target 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 $\ell_{p}$ 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.

A Survey of Non-Rigid 3D Registration

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.

A Robust Loss for Point Cloud Registration

The performance of surface registration relies heavily on the metric used for the alignment error between the source and target shapes. Traditionally, such a metric is based on the point-to-point or point-to-plane distance from the points on the source surface to their closest points on the target surface, which is susceptible to failure due to instability of the closest-point correspondence. In this paper, we propose a novel metric based on the intersection points between the two shapes and a random straight line, which does not assume a specific correspondence. We verify the effectiveness of this metric by extensive experiments, including its direct optimization for a single registration problem as well as unsupervised learning for a set of registration problems. The results demonstrate that the algorithms utilizing our proposed metric outperforms the state-of-the-art optimization-based and unsupervised learning-based methods.

Fast and Robust Iterative Closet Point

The Iterative Closest Point (ICP) algorithm and its variants are a fundamental technique for rigid registration between two point sets, with wide applications in different areas from robotics to 3D reconstruction. The main drawbacks for ICP are its slow convergence as well as its sensitivity to outliers, missing data, and partial overlaps. Recent work such as Sparse ICP achieves robustness via sparsity optimization at the cost of computational speed. In this paper, we propose a new method for robust registration with fast convergence. First, we show that the classical point-to-point ICP can be treated as a majorization-minimization (MM) algorithm, and propose an Anderson acceleration approach to improve its convergence. In addition, we introduce a robust error metric based on the Welsch's function, which is minimized efficiently using the MM algorithm with Anderson acceleration. On challenging datasets with noises and partial overlaps, we achieve similar or better accuracy than Sparse ICP while being at least an order of magnitude faster. Finally, we extend the robust formulation to point-to-plane ICP, and solve the resulting problem using a similar Anderson-accelerated MM strategy. Our robust ICP methods improve the registration accuracy on benchmark datasets while being competitive in computational time.

Quasi-Newton Solver for Robust Non-Rigid Registration

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 $\ell_{p}$ 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.

Fast K-Means Clustering with Anderson Acceleration

We propose a novel method to accelerate Lloyd's algorithm for K-Means clustering. Unlike previous acceleration approaches that reduce computational cost per iterations or improve initialization, our approach is focused on reducing the number of iterations required for convergence. This is achieved by treating the assignment step and the update step of Lloyd's algorithm as a fixed-point iteration, and applying Anderson acceleration, a well-established technique for accelerating fixed-point solvers. Classical Anderson acceleration utilizes m previous iterates to find an accelerated iterate, and its performance on K-Means clustering can be sensitive to choice of m and the distribution of samples. We propose a new strategy to dynamically adjust the value of m, which achieves robust and consistent speedups across different problem instances. Our method complements existing acceleration techniques, and can be combined with them to achieve state-of-the-art performance. We perform extensive experiments to evaluate the performance of the proposed method, where it outperforms other algorithms in 106 out of 120 test cases, and the mean decrease ratio of computational time is more than 33%.