Deep-PE: A Learning-Based Pose Evaluator for Point Cloud Registration

In the realm of point cloud registration, the most prevalent pose evaluation approaches are statistics-based, identifying the optimal transformation by maximizing the number of consistent correspondences. However, registration recall decreases significantly when point clouds exhibit a low overlap rate, despite efforts in designing feature descriptors and establishing correspondences. In this paper, we introduce Deep-PE, a lightweight, learning-based pose evaluator designed to enhance the accuracy of pose selection, especially in challenging point cloud scenarios with low overlap. Our network incorporates a Pose-Aware Attention (PAA) module to simulate and learn the alignment status of point clouds under various candidate poses, alongside a Pose Confidence Prediction (PCP) module that predicts the likelihood of successful registration. These two modules facilitate the learning of both local and global alignment priors. Extensive tests across multiple benchmarks confirm the effectiveness of Deep-PE. Notably, on 3DLoMatch with a low overlap rate, Deep-PE significantly outperforms state-of-the-art methods by at least 8% and 11% in registration recall under handcrafted FPFH and learning-based FCGF descriptors, respectively. To the best of our knowledge, this is the first study to utilize deep learning to select the optimal pose without the explicit need for input correspondences.

ComboStoc: Combinatorial Stochasticity for Diffusion Generative Models

In this paper, we study an under-explored but important factor of diffusion generative models, i.e., the combinatorial complexity. Data samples are generally high-dimensional, and for various structured generation tasks, there are additional attributes which are combined to associate with data samples. We show that the space spanned by the combination of dimensions and attributes is insufficiently sampled by existing training scheme of diffusion generative models, causing degraded test time performance. We present a simple fix to this problem by constructing stochastic processes that fully exploit the combinatorial structures, hence the name ComboStoc. Using this simple strategy, we show that network training is significantly accelerated across diverse data modalities, including images and 3D structured shapes. Moreover, ComboStoc enables a new way of test time generation which uses insynchronized time steps for different dimensions and attributes, thus allowing for varying degrees of control over them.

NeurCross: A Self-Supervised Neural Approach for Representing Cross Fields in Quad Mesh Generation

Quadrilateral mesh generation plays a crucial role in numerical simulations within Computer-Aided Design and Engineering (CAD/E). The quality of the cross field is essential for generating a quadrilateral mesh. In this paper, we propose a self-supervised neural representation of the cross field, named NeurCross, comprising two modules: one to fit the signed distance function (SDF) and another to predict the cross field. Unlike most existing approaches that operate directly on the given polygonal surface, NeurCross takes the SDF as a bridge to allow for SDF overfitting and the prediction of the cross field to proceed simultaneously. By utilizing a neural SDF, we achieve a smooth representation of the base surface, minimizing the impact of piecewise planar discretization and minor surface variations. Moreover, the principal curvatures and directions are fully encoded by the Hessian of the SDF, enabling the regularization of the overall cross field through minor adjustments to the SDF. Compared to state-of-the-art methods, NeurCross significantly improves the placement of singular points and the approximation accuracy between the input triangular surface and the output quad mesh, as demonstrated in the teaser figure.

CWF: Consolidating Weak Features in High-quality Mesh Simplification

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach prioritizes accuracy and can preserve strong feature lines/points as well but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset, along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding.

NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature

Despite recent advances in reconstructing an organic model with the neural signed distance function (SDF), the high-fidelity reconstruction of a CAD model directly from low-quality unoriented point clouds remains a significant challenge. In this paper, we address this challenge based on the prior observation that the surface of a CAD model is generally composed of piecewise surface patches, each approximately developable even around the feature line. Our approach, named NeurCADRecon, is self-supervised, and its loss includes a developability term to encourage the Gaussian curvature toward 0 while ensuring fidelity to the input points. Noticing that the Gaussian curvature is non-zero at tip points, we introduce a double-trough curve to tolerate the existence of these tip points. Furthermore, we develop a dynamic sampling strategy to deal with situations where the given points are incomplete or too sparse. Since our resulting neural SDFs can clearly manifest sharp feature points/lines, one can easily extract the feature-aligned triangle mesh from the SDF and then decompose it into smooth surface patches, greatly reducing the difficulty of recovering the parametric CAD design. A comprehensive comparison with existing state-of-the-art methods shows the significant advantage of our approach in reconstructing faithful CAD shapes.

OAAFormer: Robust and Efficient Point Cloud Registration Through Overlapping-Aware Attention in Transformer

In the domain of point cloud registration, the coarse-to-fine feature matching paradigm has received substantial attention owing to its impressive performance. This paradigm involves a two-step process: first, the extraction of multi-level features, and subsequently, the propagation of correspondences from coarse to fine levels. Nonetheless, this paradigm exhibits two notable limitations.Firstly, the utilization of the Dual Softmax operation has the potential to promote one-to-one correspondences between superpoints, inadvertently excluding valuable correspondences. This propensity arises from the fact that a source superpoint typically maintains associations with multiple target superpoints. Secondly, it is imperative to closely examine the overlapping areas between point clouds, as only correspondences within these regions decisively determine the actual transformation. Based on these considerations, we propose {\em OAAFormer} to enhance correspondence quality. On one hand, we introduce a soft matching mechanism, facilitating the propagation of potentially valuable correspondences from coarse to fine levels. Additionally, we integrate an overlapping region detection module to minimize mismatches to the greatest extent possible. Furthermore, we introduce a region-wise attention module with linear complexity during the fine-level matching phase, designed to enhance the discriminative capabilities of the extracted features. Tests on the challenging 3DLoMatch benchmark demonstrate that our approach leads to a substantial increase of about 7\% in the inlier ratio, as well as an enhancement of 2-4\% in registration recall. =

For A More Comprehensive Evaluation of 6DoF Object Pose Tracking

Previous evaluations on 6DoF object pose tracking have presented obvious limitations along with the development of this area. In particular, the evaluation protocols are not unified for different methods, the widely-used YCBV dataset contains significant annotation error, and the error metrics also may be biased. As a result, it is hard to fairly compare the methods, which has became a big obstacle for developing new algorithms. In this paper we contribute a unified benchmark to address the above problems. For more accurate annotation of YCBV, we propose a multi-view multi-object global pose refinement method, which can jointly refine the poses of all objects and view cameras, resulting in sub-pixel sub-millimeter alignment errors. The limitations of previous scoring methods and error metrics are analyzed, based on which we introduce our improved evaluation methods. The unified benchmark takes both YCBV and BCOT as base datasets, which are shown to be complementary in scene categories. In experiments, we validate the precision and reliability of the proposed global pose refinement method with a realistic semi-synthesized dataset particularly for YCBV, and then present the benchmark results unifying learning&non-learning and RGB&RGBD methods, with some finds not discovered in previous studies.

Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian

Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural function to possess the properties of a Signed Distance Function (SDF). However, inferring the actual topology and geometry of the underlying surface from poor-quality unoriented point clouds remains challenging. In accordance with Differential Geometry, the Hessian of the SDF is singular for points within the differential thin-shell space surrounding the surface. Our approach enforces the Hessian of the neural implicit function to have a zero determinant for points near the surface. This technique aligns the gradients for a near-surface point and its on-surface projection point, producing a rough but faithful shape within just a few iterations. By annealing the weight of the singular-Hessian term, our approach ultimately produces a high-fidelity reconstruction result. Extensive experimental results demonstrate that our approach effectively suppresses ghost geometry and recovers details from unoriented point clouds with better expressiveness than existing fitting-based methods.

Guided Linear Upsampling

Guided upsampling is an effective approach for accelerating high-resolution image processing. In this paper, we propose a simple yet effective guided upsampling method. Each pixel in the high-resolution image is represented as a linear interpolation of two low-resolution pixels, whose indices and weights are optimized to minimize the upsampling error. The downsampling can be jointly optimized in order to prevent missing small isolated regions. Our method can be derived from the color line model and local color transformations. Compared to previous methods, our method can better preserve detail effects while suppressing artifacts such as bleeding and blurring. It is efficient, easy to implement, and free of sensitive parameters. We evaluate the proposed method with a wide range of image operators, and show its advantages through quantitative and qualitative analysis. We demonstrate the advantages of our method for both interactive image editing and real-time high-resolution video processing. In particular, for interactive editing, the joint optimization can be precomputed, thus allowing for instant feedback without hardware acceleration.

Mesh-MLP: An all-MLP Architecture for Mesh Classification and Semantic Segmentation

With the rapid development of geometric deep learning techniques, many mesh-based convolutional operators have been proposed to bridge irregular mesh structures and popular backbone networks. In this paper, we show that while convolutions are helpful, a simple architecture based exclusively on multi-layer perceptrons (MLPs) is competent enough to deal with mesh classification and semantic segmentation. Our new network architecture, named Mesh-MLP, takes mesh vertices equipped with the heat kernel signature (HKS) and dihedral angles as the input, replaces the convolution module of a ResNet with Multi-layer Perceptron (MLP), and utilizes layer normalization (LN) to perform the normalization of the layers. The all-MLP architecture operates in an end-to-end fashion and does not include a pooling module. Extensive experimental results on the mesh classification/segmentation tasks validate the effectiveness of the all-MLP architecture.