Related papers: A two-level approach to implicit surface modeling …

Neural radiance fields (NeRF) have driven impressive progress in view synthesis by using ray-traced volumetric rendering. Splatting-based methods such as 3D Gaussian Splatting (3DGS) provide faster rendering by rasterizing 3D primitives.…

We introduce a framework for the recovery of points on a smooth surface in high-dimensional space, with application to dynamic imaging. We assume the surface to be the zero-level set of a bandlimited function. We show that the exponential…

We consider the problem of 3D shape reconstruction from multi-modal data, given uncertain calibration parameters. Typically, 3D data modalities can be in diverse forms such as sparse point sets, volumetric slices, 2D photos and so on. To…

Estimating subsurface dielectric properties is essential for applications ranging from environmental surveys of soils to nondestructive evaluation of concrete in infrastructure. Conventional wave inversion methods typically assume few…

Hyperplane is a set of non-injectivity of the spherical Radon transform (SRT) in the space of continuous functions in R^d. In this article, for the reconstruction of an unknown function f from C(R^3) (the support can be non-compact), using…

Personalised 3D vascular models are valuable for diagnosis, prognosis and treatment planning in patients with cardiovascular disease. Traditionally, such models have been constructed with explicit representations such as meshes and voxel…

Point set is a flexible and lightweight representation widely used for 3D deep learning. However, their discrete nature prevents them from representing continuous and fine geometry, posing a major issue for learning-based shape generation.…

Signed Distance Functions (SDFs) are vital implicit representations to represent high fidelity 3D surfaces. Current methods mainly leverage a neural network to learn an SDF from various supervisions including signed distances, 3D point…

Inspired by the seminal result that a graph and an associated rotation system uniquely determine the topology of a closed manifold, we propose a combinatorial method for reconstruction of surfaces from points. Our method constructs a…

Radial basis functions (RBFs) are prominent examples for reproducing kernels with associated reproducing kernel Hilbert spaces (RKHSs). The convergence theory for the kernel-based interpolation in that space is well understood and optimal…

Implicit representations have been widely applied in robotics for obstacle avoidance and path planning. In this paper, we explore the problem of constructing an implicit distance representation from a single image. Past methods for implicit…

A variational approach to the reconstruction of a shape (2D simple manifolds) as triangulated surface from given level set using shape gradients is presented. It involves an energy functional that depends on the local shape characteristics…

We propose a novel neural architecture for representing 3D surfaces, which harnesses two complementary shape representations: (i) an explicit representation via an atlas, i.e., embeddings of 2D domains into 3D; (ii) an implicit-function…

Radial basis functions are a common mathematical tool used to construct a smooth interpolating function from a set of data points. A spatial prior based on thin-plate spline radial basis functions can be easily implemented resulting in a…

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear…

This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…

This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified…

The Reduced Basis Method (RBM) is a rigorous model reduction approach for solving parametrized partial differential equations. It identifies a low-dimensional subspace for approximation of the parametric solution manifold that is embedded…

Neural implicit 3D representations have emerged as a powerful paradigm for reconstructing surfaces from multi-view images and synthesizing novel views. Unfortunately, existing methods such as DVR or IDR require accurate per-pixel object…

Reconstructing the high-fidelity surface from multi-view images, especially sparse images, is a critical and practical task that has attracted widespread attention in recent years. However, existing methods are impeded by the memory…