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Reconstructing the 3D mesh of a general object from a single image is now possible thanks to the latest advances of deep learning technologies. However, due to the nontrivial difficulty of generating a feasible mesh structure, the…
Converting hand-drawn sketches into structured 3D geometries remains challenging due to the difficulty of representing non-Euclidean surfaces and maintaining topological consistency. Existing generative models such as GANs, NeRFs, and…
Recovering high quality surfaces from noisy triangulated surfaces is a fundamental important problem in geometry processing. Sharp features including edges and corners can not be well preserved in most existing denoising methods except the…
Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a…
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
We introduce and analyze numerical companion matrix methods for the reconstruction of hypersurfaces with crossings from smooth interpolants given unordered or, without loss of generality, value-sorted data. The problem is motivated by the…
The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…
Domain discretization is an essential part of the solution procedure in numerical simulations. Meshless methods simplify the domain discretization to positioning of nodes in the interior and on the boundary of the domain. However, generally…
We present a technique for a complete 3D reconstruction of small objects moving in front of a textured background. It is a particular variation of multibody structure from motion, which specializes to two objects only. The scene is captured…
Currently, the area of geometric modeling and the construction of 3D models based on point clouds from laser sensors is actively developing. One of the basic tasks of geometric modeling is the reconstruction of a surface from a cloud of…
We present a novel method for 3D surface reconstruction from multiple images where only a part of the object of interest is captured. Our approach builds on two recent developments: surface reconstruction using neural radiance fields for…
This paper investigates the problem of recovering hyperspectral (HS) images from single RGB images. To tackle such a severely ill-posed problem, we propose a physically-interpretable, compact, efficient, and end-to-end learning-based…
Shape-from-Template (SfT) methods estimate 3D surface deformations from a single monocular RGB camera while assuming a 3D state known in advance (a template). This is an important yet challenging problem due to the under-constrained nature…
Obtaining high quality particle distribution representing clean geometry in pre-processing is essential for the simulation accuracy of the particle-based methods. In this paper, several level-set based techniques for cleaning up `dirty'…
This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…
We consider the problem of few-viewpoint 3D surface reconstruction using raw measurements from a lidar system. Lidar captures 3D scene geometry by emitting pulses of light to a target and recording the speed-of-light time delay of the…
The three-dimensional reconstruction of scenes from multiple views has made impressive strides in recent years, chiefly by methods correlating isolated feature points, intensities, or curvilinear structure. In the general setting, i.e.,…
This paper is concerned with the nonconforming finite element discretization of geometric partial differential equations. In specific, we construct a surface Crouzeix-Raviart element on the linear approximated surface, analogous to a flat…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…