Related papers: A numerical framework for elastic surface matching…
We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with…
Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an…
Implicit Neural Representations (INRs), characterized by neural network-encoded signed distance fields, provide a powerful means to represent complex geometries continuously and efficiently. While successful in computer vision and…
With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…
Multimodal tasks, such as image-text retrieval and generation, require embedding data from diverse modalities into a shared representation space. Aligning embeddings from heterogeneous sources while preserving shared and modality-specific…
Neural radiance fields have recently revolutionized novel-view synthesis and achieved high-fidelity renderings. However, these methods sacrifice the geometry for the rendering quality, limiting their further applications including…
Glass-like objects are widespread in daily life but remain intractable to be segmented for most existing methods. The transparent property makes it difficult to be distinguished from background, while the tiny separation boundary further…
1. Parameter inference from distorted measurements is discussed. 2. Smeared measurements are unfolded without explicit regularization. The corresponding results are unbiased and permit to fit parameters and to apply quantitative…
In this paper, we propose several mathematical models for 3D surface reconstruction and volume estimation from a set of scattered cloud data. Three meshless methods including the interpolation-based method by RBF, PDE-based approach by…
Map-to-map matching is a critical task for aligning spatial data across heterogeneous sources, yet it remains challenging due to the lack of ground truth correspondences, sparse node features, and scalability demands. In this paper, we…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…
Surface matching usually provides significant deformations that can lead to structural failure due to the lack of physical policy. In this context, partial surface matching of non-linear deformable bodies is crucial in engineering to govern…
Implicit Neural Representations have gained prominence as a powerful framework for capturing complex data modalities, encompassing a wide range from 3D shapes to images and audio. Within the realm of 3D shape representation, Neural Signed…
Scene and object reconstruction is an important problem in robotics, in particular in planning collision-free trajectories or in object manipulation. This paper compares two strategies for the reconstruction of nonvisible parts of the…
The Laplace eigenvalue problem on circular sectors has eigenfunctions with corner singularities. Standard methods may produce suboptimal approximation results. To address this issue, a novel numerical algorithm that enhances standard…
A conformal flattening maps a curved surface to the plane without distorting angles---such maps have become a fundamental building block for problems in geometry processing, numerical simulation, and computational design. Yet existing…
Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We…
We describe new approaches for distances between pairs of 2-dimensional surfaces (embedded in 3-dimensional space) that use local structures and global information contained in inter-structure geometric relationships. We present algorithms…