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

Reconstruction of high-fidelity 3D objects or scenes is a fundamental research problem. Recent advances in RGB-D fusion have demonstrated the potential of producing 3D models from consumer-level RGB-D cameras. However, due to the discrete…

Recently, neural implicit surfaces learning by volume rendering has become popular for multi-view reconstruction. However, one key challenge remains: existing approaches lack explicit multi-view geometry constraints, hence usually fail to…

Recent advances in learning 3D shapes using neural implicit functions have achieved impressive results by breaking the previous barrier of resolution and diversity for varying topologies. However, most of such approaches are limited to…

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…

We present a method for differentiable rendering of 3D surfaces that supports both explicit and implicit representations, provides derivatives at occlusion boundaries, and is fast and simple to implement. The method first samples the…

We present a novel two-view geometry estimation framework which is based on a differentiable robust loss function fitting. We propose to treat the robust fundamental matrix estimation as an implicit layer, which allows us to avoid…

In this article we present a modification of classical Radial Basis Function (RBF) interpolation techniques aimed at reducing oscillations near discontinuities in one and two dimensions. Our approach introduces an adaptive mechanism by…

Given only a set of images, neural implicit surface representation has shown its capability in 3D surface reconstruction. However, as the nature of per-scene optimization is based on the volumetric rendering of color, previous neural…

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is…

The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [3], provides a way of representing immersed surfaces in $\mathbb R^3$, and equipping the set of these immersions with a "distance function" (to be precise, a pseudometric)…

Optimization-based trajectory generation methods are widely used in whole-body planning for robots. However, existing work either oversimplifies the robot's geometry and environment representation, resulting in a conservative trajectory, or…

Surface reconstruction is very challenging when the input point clouds, particularly real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual…

We present a general method for computing local parameterizations rooted at a point on a surface, where the surface is described only through a signed implicit function and a corresponding projection function. Using a two-stage process, we…

Real-world 3D data may contain intricate details defined by salient surface gaps. Automated reconstruction of these open surfaces (e.g., non-watertight meshes) is a challenging problem for environment synthesis in mixed reality…

Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data.…

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set…

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…

Recent works on implicit neural representations have made significant strides. Learning implicit neural surfaces using volume rendering has gained popularity in multi-view reconstruction without 3D supervision. However, accurately…

Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…

Neural Signed Distance Functions (SDFs) excel at reconstructing watertight manifolds but fail on thin structures and open boundaries due to strict inside--outside constraints. Conversely, Unsigned Distance Fields (UDFs) accommodate general…