Related papers: Point-Normal Subdivision Curves and Surfaces
Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…
We prove a Diophantine approximation inequality for closed subschemes on surfaces which can be viewed as a joint generalization of recent inequalities of Ru-Vojta and Heier-Levin in this context. As applications, we study various…
A new method is proposed to divide a spherical surface into equal-area cells. The method is based on dividing a sphere into several latitudinal bands of near-constant span with further division of each band into equal-area cells. It is…
As 3D point clouds become the representation of choice for multiple vision and graphics applications, the ability to synthesize or reconstruct high-resolution, high-fidelity point clouds becomes crucial. Despite the recent success of deep…
We present a novel parametric finite element approach for simulating the surface diffusion of curves and surfaces. Our core strategy incorporates a predictor-corrector time-stepping method, which enhances the classical first-order temporal…
We propose a novel normal estimation method called HSurf-Net, which can accurately predict normals from point clouds with noise and density variations. Previous methods focus on learning point weights to fit neighborhoods into a geometric…
This paper presents an end-to-end differentiable algorithm for robust and detail-preserving surface normal estimation on unstructured point-clouds. We utilize graph neural networks to iteratively parameterize an adaptive anisotropic kernel…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all…
Change point detection (CPD) methods aim to identify abrupt shifts in the distribution of input data streams. Accurate estimators for this task are crucial across various real-world scenarios. Yet, traditional unsupervised CPD techniques…
We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embedding method, which uses an implicit representation of the…
This paper addresses the problem of generating uniform dense point clouds to describe the underlying geometric structures from given sparse point clouds. Due to the irregular and unordered nature, point cloud densification as a generative…
Domain generalization in 3D segmentation is a critical challenge in deploying models to unseen environments. Current methods mitigate the domain shift by augmenting the data distribution of point clouds. However, the model learns global…
In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific…
In this work, we present a novel approach for reconstructing shape point clouds using planar sparse cross-sections with the help of generative modeling. We present unique challenges pertaining to the representation and reconstruction in…
In this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space $E^3$. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal…
In recent years, Convolutional Neural Networks (CNN) have proven to be efficient analysis tools for processing point clouds, e.g., for reconstruction, segmentation and classification. In this paper, we focus on the classification of edges…
We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics…
Modeling statistical regularity plays an essential role in ill-posed image processing problems. Recently, deep learning based methods have been presented to implicitly learn statistical representation of pixel distributions in natural…
Reconstruction of a continuous surface of two-dimensional manifold from its raw, discrete point cloud observation is a long-standing problem. The problem is technically ill-posed, and becomes more difficult considering that various sensing…