Related papers: Minimum-norm interpolation for unknown surface rec…
This contribution presents a new analysis of properties of the interpolation using Radial Bases Functions (RBF) related to large data sets interpolation. The RBF application is convenient method for scattered d-dimensional interpolation.…
Deep learning based methods have recently pushed the state-of-the-art on the problem of Single Image Super-Resolution (SISR). In this work, we revisit the more traditional interpolation-based methods, that were popular before, now with the…
Radial basis function generated finite difference (RBF-FD) methods for PDEs require a set of interpolation points which conform to the computational domain $\Omega$. One of the requirements leading to approximation robustness is to place…
Realistic digital models of plant leaves are crucial to fluid dynamics simulations of droplets for optimising agrochemical spray technologies. The presence and nature of small features (on the order of 100$\mathrm{\mu m}$) such as ridges…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…
Recovering high quality surfaces from noisy point clouds, known as point cloud denoising, is a fundamental yet challenging problem in geometry processing. Most of the existing methods either directly denoise the noisy input or filter raw…
The fundamental purpose of the present work is to constitute an enhanced Euler method with adaptive inverse-quadratic and inverse-multi-quadratic radial basis function (RBF) interpolation technique to solve initial value problems. These…
Reconstructing a 3D surface from colonoscopy video is challenging due to illumination and reflectivity variation in the video frame that can cause defective shape predictions. Aiming to overcome this challenge, we utilize the…
Semantic scene understanding from point clouds is particularly challenging as the points reflect only a sparse set of the underlying 3D geometry. Previous works often convert point cloud into regular grids (e.g. voxels or bird-eye view…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
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…
We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface…
Single image surface normal estimation and depth estimation are closely related problems as the former can be calculated from the latter. However, the surface normals computed from the output of depth estimation methods are significantly…
Low-rank approximations are popular methods to reduce the high computational cost of algorithms involving large-scale kernel matrices. The success of low-rank methods hinges on the matrix rank of the kernel matrix, and in practice, these…
3D surface reconstruction from multi-view images is essential for scene understanding and interaction. However, complex indoor scenes pose challenges such as ambiguity due to limited observations. Recent implicit surface representations,…
We propose a fast and accurate surface reconstruction algorithm for unorganized point clouds using an implicit representation. Recent learning methods are either single-object representations with small neural models that allow for high…
We are interested in reconstructing the mesh representation of object surfaces from point clouds. Surface reconstruction is a prerequisite for downstream applications such as rendering, collision avoidance for planning, animation, etc.…
This paper aims to survey our recent work relating to the radial basis function (RBF) and its applications to numerical PDEs. We introduced the kernel RBF involving general pre-wavelets and scale-orthogonal wavelets RBF. A…
We present a comprehensive survey and benchmark of both traditional and learning-based methods for surface reconstruction from point clouds. This task is particularly challenging for real-world acquisitions due to factors such as noise,…
Man-made objects usually exhibit descriptive curved features (i.e., curve networks). The curve network of an object conveys its high-level geometric and topological structure. We present a framework for extracting feature curve networks…