Computer Aided Geometric Design最新文献

Establishing accurate and representative matches is a crucial step in addressing the point cloud registration problem. A commonly employed approach involves detecting keypoints with salient geometric features and subsequently mapping these keypoints from one frame of the point cloud to another. However, methods within this category are hampered by the repeatability of the sampled keypoints. In this paper, we introduce a saliency-guided transformer, referred to as D3Former, which entails the joint learning of repeatable Dense Detectors and feature-enhanced Descriptors. The model comprises a Feature Enhancement Descriptor Learning (FEDL) module and a Repetitive Keypoints Detector Learning (RKDL) module. The FEDL module utilizes a region attention mechanism to enhance feature distinctiveness, while the RKDL module focuses on detecting repeatable keypoints to enhance matching capabilities. Extensive experimental results on challenging indoor and outdoor benchmarks demonstrate that our proposed method consistently outperforms state-of-the-art point cloud matching methods. Notably, tests on 3DLoMatch, even with a low overlap ratio, show that our method consistently outperforms recently published approaches such as RoReg and RoITr. For instance, with the number of extracted keypoints reduced to 250, the registration recall scores for RoReg, RoITr, and our method are 64.3%, 73.6%, and 76.5%, respectively.

This paper addresses the challenge of representing geodesic distance fields on triangular meshes in a piecewise linear manner. Unlike general scalar fields, which often assume piecewise linear changes within each triangle, geodesic distance fields pose a unique difficulty due to their non-differentiability at ridge points, where multiple shortest paths may exist. An interesting observation is that the geodesic distance field exhibits an approximately linear change if each triangle is further decomposed into sub-regions by the ridge curve. However, computing the geodesic ridge curve is notoriously difficult. Even when using exact algorithms to infer the ridge curve, desirable results may not be achieved, akin to the well-known medial-axis problem. In this paper, we propose a two-stage algorithm. In the first stage, we employ Dijkstra's algorithm to cut the surface open along the dual structure of the shortest path tree. This operation allows us to extend the surface outward (resembling a double cover but with distinctions), enabling the discovery of longer geodesic paths in the extended surface. In the second stage, any mature geodesic solver, whether exact or approximate, can be employed to predict the real ridge curve. Assuming the fast marching method is used as the solver, despite its limitation of having a single marching direction in a triangle, our extended surface contains multiple copies of each triangle, allowing various geodesic paths to enter the triangle and facilitating ridge curve computation. We further introduce a simple yet effective filtering mechanism to rigorously ensure the connectivity of the output ridge curve. Due to its merits, including robustness and compatibility with any geodesic solver, our algorithm holds great potential for a wide range of applications. We demonstrate its utility in accurate geodesic distance querying and high-fidelity visualization of geodesic iso-lines.

Learning the skill of human bimanual grasping can extend the capabilities of robotic systems when grasping large or heavy objects. However, it requires a much larger search space for grasp points than single-hand grasping and numerous bimanual grasping annotations for network learning, making both data-driven or analytical grasping methods inefficient and insufficient. We propose a framework for bimanual grasp saliency learning that aims to predict the contact points for bimanual grasping based on existing human single-handed grasping data. We learn saliency corresponding vectors through minimal bimanual contact annotations that establishes correspondences between grasp positions of both hands, capable of eliminating the need for training a large-scale bimanual grasp dataset. The existing single-handed grasp saliency value serves as the initial value for bimanual grasp saliency, and we learn a saliency adjusted score that adds the initial value to obtain the final bimanual grasp saliency value, capable of predicting preferred bimanual grasp positions from single-handed grasp saliency. We also introduce a physics-balance loss function and a physics-aware refinement module that enables physical grasp balance, capable of enhancing the generalization of unknown objects. Comprehensive experiments in simulation and comparisons on dexterous grippers have demonstrated that our method can achieve balanced bimanual grasping effectively.

For large data fitting, the least squares progressive iterative approximation (LSPIA) methods have been proposed by Lin and Zhang (2013) and Deng and Lin (2014), in which a constant step size is used. In this paper, we further accelerate the LSPIA method in terms of a Chebyshev semi-iterative scheme and present an asynchronous LSPIA (denoted by ALSPIA) method. The control points in ALSPIA are updated by using an extrapolated variant in which an adaptive step size is chosen according to the roots of Chebyshev polynomial. Our convergence analysis shows that ALSPIA is faster than the original LSPIA method in both singular and non-singular least squares fitting cases. Numerical examples show that the proposed algorithm is feasible and effective.

By lifting the pre-trained 2D diffusion models into Neural Radiance Fields (NeRFs), text-to-3D generation methods have made great progress. Many state-of-the-art approaches usually apply score distillation sampling (SDS) to optimize the NeRF representations, which supervises the NeRF optimization with pre-trained text-conditioned 2D diffusion models such as Imagen. However, the supervision signal provided by such pre-trained diffusion models only depends on text prompts and does not constrain the multi-view consistency. To inject cross-view consistency into diffusion priors, some recent works finetune the 2D diffusion model via multi-view data, but still lack fine-grained view coherence. To tackle this challenge, we incorporate multi-view image conditions into the supervision signal of NeRF optimization, which explicitly enforces fine-grained view consistency. With such stronger supervision, our proposed text-to-3D method effectively mitigates the generation of floaters (due to excessive densities) and completely empty spaces (due to insufficient densities). Our quantitative evaluations on the T³Bench dataset demonstrate that our method achieves state-of-the-art performance over existing text-to-3D methods. We will make the code publicly available.

Tooth arrangement is a crucial step in orthodontics treatment, in which aligning teeth could improve overall well-being, enhance facial aesthetics, and boost self-confidence. To improve the efficiency of tooth arrangement and minimize errors associated with unreasonable designs by inexperienced practitioners, some deep learning-based tooth arrangement methods have been proposed. Currently, most existing approaches employ MLPs to model the nonlinear relationship between tooth features and transformation matrices to achieve tooth arrangement automatically. However, the limited datasets (which to our knowledge, have not been made public) collected from clinical practice constrain the applicability of existing methods, making them inadequate for addressing diverse malocclusion issues. To address this challenge, we propose a general tooth arrangement neural network based on the diffusion probabilistic model. Conditioned on the features extracted from the dental model, the diffusion probabilistic model can learn the distribution of teeth transformation matrices from malocclusion to normal occlusion by gradually denoising from a random variable, thus more adeptly managing real orthodontic data. To take full advantage of effective features, we exploit both mesh and point cloud representations by designing different encoding networks to extract the tooth (local) and jaw (global) features, respectively. In addition to traditional metrics ADD, PA-ADD, CSA, and ${\mathrm{ME}}_{rot}$, we propose a new evaluation metric based on dental arch curves to judge whether the generated teeth meet the individual normal occlusion. Experimental results demonstrate that our proposed method achieves state-of-the-art tooth alignment results and satisfactory occlusal relationships between dental arches. We will publish the code and dataset.

It has been recently discovered that a certain class of nanocarbon materials has geometrical properties related to the geometry of discrete surfaces with a pre-constant discrete curvature, based on a discrete surface theory for trivalent graphs proposed in 2017 by Kotani et al. In this paper, with the aim of an application to the nanocarbon materials, we will study discrete constant principal curvature (CPC) surfaces. Firstly, we develop the discrete surface theory on a full 3-ary oriented tree so that we define a discrete analogue of principal directions on them and investigate it. We also construct some interesting examples of discrete constant principal curvature surfaces, including discrete CPC tori.

For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design and has found a wide range of applications in fields such as scientific computing and discrete geometry, to name but a few. With increasing interest in nonlinear data science, its constructive approach has been shown to provide a principled way to generalize parametric smooth curves to manifolds. These curves have found remarkable new applications in the analysis of parameter-dependent, geometric data. This article provides a survey of the recent theoretical developments in this exciting area as well as its applications in fields such as geometric morphometrics and longitudinal data analysis in medicine, archaeology, and meteorology.

Finding parameterizations of spatial point data is a fundamental step for surface reconstruction in Computer Aided Geometric Design. Especially the case of unstructured point clouds is challenging and not widely studied. In this work, we show how to parameterize a point cloud by using barycentric coordinates in the parameter domain, with the aim of reproducing the parameterizations provided by quadratic triangular Bézier surfaces. To this end, we train an artificial neural network that predicts suitable barycentric parameters for a fixed number of data points. In a subsequent step we improve the parameterization using non-linear optimization methods. We then use a number of local parameterizations to obtain a global parameterization using a new overdetermined barycentric parameterization approach. We study the behavior of our method numerically in the zero-residual case (i.e., data sampled from quadratic polynomial surfaces) and in the non-zero residual case and observe an improvement of the accuracy in comparison to standard methods. We also compare different approaches for non-linear surface fitting such as tangent distance minimization, squared distance minimization and the Levenberg Marquardt algorithm.

A state-of-the-art survey is presented on various formulations of multi-sided parametric surface patches, with a focus on methods that interpolate positional and cross-derivative information along boundaries.