Related papers: Local Surface Parameterizations via Smoothed Geode…

We introduce a statistical extension of the classic Poisson Surface Reconstruction algorithm for recovering shapes from 3D point clouds. Instead of outputting an implicit function, we represent the reconstructed shape as a modified Gaussian…

Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…

Extracting robust and general 3D local features is key to downstream tasks such as point cloud registration and reconstruction. Existing learning-based local descriptors are either sensitive to rotation transformations, or rely on classical…

Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…

Shape from texture refers to the extraction of 3D information from 2D images with irregular texture. This paper introduces a statistical framework to learn shape from texture where convex texture elements in a 2D image are represented…

We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying…

The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…

A promising approach to accurate positioning of robots is ground texture based localization. It is based on the observation that visual features of ground images enable fingerprint-like place recognition. We tackle the issue of efficient…

Splines are central objects for the interpolation of discrete data via piecewise smooth paths. Their iterated-integral signature is an infinite collection of tensors which characterizes paths almost uniquely. We study truncations of this…

Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…

In this paper we introduce and describe an implementation of curved (surface) geometries within the Dune framework for grid-based discretizations. Therefore, we employ the abstraction of geometries as local-functions bound to a grid…

The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit…

We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth…

Mapping the environment has been an important task for robot navigation and Simultaneous Localization And Mapping (SLAM). LIDAR provides a fast and accurate 3D point cloud map of the environment which helps in map building. However,…

We introduce a conceptually simple and efficient algorithm for seamless parametrization, a key element in constructing quad layouts and texture charts on surfaces. More specifically, we consider the construction of parametrizations with…

Given a birational parameterization of an algebraic surface S in the projective space, the purpose of this paper is to investigate the sets of points on S whose preimage consists in k or more points, counting multiplicities. They are…

As commonly used implicit geometry representations, the signed distance function (SDF) is limited to modeling watertight shapes, while the unsigned distance function (UDF) is capable of representing various surfaces. However, its inherent…

Learning a dense 3D model with fine-scale details from a single facial image is highly challenging and ill-posed. To address this problem, many approaches fit smooth geometries through facial prior while learning details as additional…

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 present an approach to learning features that represent the local geometry around a point in an unstructured point cloud. Such features play a central role in geometric registration, which supports diverse applications in robotics and 3D…