Related papers: Algebraic Smooth Occluding Contours
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…
Existing computer vision systems can compete with humans in understanding the visible parts of objects, but still fall far short of humans when it comes to depicting the invisible parts of partially occluded objects. Image amodal completion…
We introduce a novel offset meshing approach that can robustly handle a 3D surface mesh with an arbitrary geometry and topology configurations, while nicely capturing the sharp features on the original input for both inward and outward…
Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to…
The paper is focused on the four-dimensional visualization of hypersurfaces represented by implicit equations without their parametrization. We describe a general method to find shadow boundaries in an arbitrary dimension and apply it in a…
In this paper, we formulate a simple algorithm that detects contours around a region of interest in an image. After an initial smoothing, the method is based on viewing an image as a topographic surface and finding convex and/or concave…
Learning-based 3D reconstruction methods have shown impressive results. However, most methods require 3D supervision which is often hard to obtain for real-world datasets. Recently, several works have proposed differentiable rendering…
We investigate the problem of finding the visible pieces of a scene of objects from a specified viewpoint. In particular, we are interested in the design of an efficient hidden surface removal algorithm for a scene comprised of iso-oriented…
We classify all complex surfaces with quotient singularities that do not contain any smooth rational curves, under the assumption that the canonical divisor of the surface is not pseudo-effective. As a corollary we show that if $X$ is a log…
We develop a theory for the representation of opaque solids as volumes. Starting from a stochastic representation of opaque solids as random indicator functions, we prove the conditions under which such solids can be modeled using…
Problems that require the parameterization of closed contours arise frequently in computer vision applications. This article introduces a new curve parameterization algorithm that is able to fit a closed curve to a set of points while being…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
In this paper which is the first of a series of papers on smooth structures, the concepts of C-structures and smooth structures are introduced and studied. The notion of smooth structure on semi-integral domains is given. It is shown that…
We present a novel neural surface reconstruction method called NeuralRoom for reconstructing room-sized indoor scenes directly from a set of 2D images. Recently, implicit neural representations have become a promising way to reconstruct…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
Reconstructing general dynamic scenes is important for many computer vision and graphics applications. Recent works represent the dynamic scene with neural radiance fields for photorealistic view synthesis, while their surface geometry is…
A ruled surface is a shape swept out by moving a line in 3D space. Due to their simple geometric forms, ruled surfaces have applications in various domains such as architecture and engineering. In the past, various approaches have been…
The Hessian Topology is a subject having interesting relations with several areas, for instance, differential geometry, implicit differential equations, analysis and singularity theory. In this article we study the problem of realization of…
In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the…