Related papers: Reconstruction of surfaces with ordinary singulari…
We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the `apparent contour' of a single projection to the projective plane. We deal with the case of tangent developables and of general…
We investigate the problem of existence of degenerations of surfaces in $\mathbb P^3$ with ordinary singularities into plane arrangements in general position.
Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as…
The surface reconstruction problem from sets of planar parallel slices representing cross sections through 3D objects is presented. The final result of surface reconstruction is always based on the correct estimation of the structure of the…
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…
We present a local classification of smooth projective surfaces in 3-space via projective transformations in accordance with singularity types of central projections up to codimension 4. We also discuss relations between our classification…
We develop recursive formulas for the horizontal and vertical monodromies of a quasi-ordinary surface. These are monodromies associated to the Milnor fiber of a slice transverse to a component of the singular locus. In the course of working…
We use normal sections to relate the curvature locus of regular (resp. singular corank 1) 3-manifolds in $\mathbb{R}^6$ (resp. $\mathbb R^5$) with regular (resp. singular corank 1) surfaces in $\mathbb R^5$ (resp. $\mathbb R^4$). For…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
We present a method to learn single-view reconstruction of the 3D shape, pose, and texture of objects from categorized natural images in a self-supervised manner. Since this is a severely ill-posed problem, carefully designing a training…
In this article we pose the problem of existence and uniqueness of convex body for which the projection curvature radius function coincides with given function. We find a necessary and sufficient condition that ensures a positive answer to…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive…
Generic 3D reconstruction from a single image is a difficult problem. A lot of data loss occurs in the projection. A domain based approach to reconstruction where we solve a smaller set of problems for a particular use case lead to greater…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
From a single image, humans are able to perceive the full 3D shape of an object by exploiting learned shape priors from everyday life. Contemporary single-image 3D reconstruction algorithms aim to solve this task in a similar fashion, but…
Numerous techniques have been proposed for reconstructing 3D models for opaque objects in past decades. However, none of them can be directly applied to transparent objects. This paper presents a fully automatic approach for reconstructing…
In this paper we address the problem of visual quality of images reconstructed from block-wise random projections. Independent reconstruction of the blocks can severely affect visual quality, by displaying artifacts along block borders. We…
Recent years have seen the development of mature solutions for reconstructing deformable surfaces from a single image, provided that they are relatively well-textured. By contrast, recovering the 3D shape of texture-less surfaces remains an…
Actions as simple as grasping an object or navigating around it require a rich understanding of that object's 3D shape from a given viewpoint. In this paper we repurpose powerful learning machinery, originally developed for object…