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We define singular points of the first kind and singular points of the second kind as singular points of mappings between surfaces. Typical examples of these singular points are fold singular points and cusp singular points, respectively.…
Demange (2012) generalized the classical single-crossing property to the intermediate property on median graphs and proved that the representative voter theorem still holds for this more general framework. We complement her result with…
A diagonal surface in a link exterior M is a properly embedded, incompressible, boundary incompressible surface which furthermore has the same number of boundary components and same slope on each component of the boundary of M. We derive a…
This is a review paper of traditional approaches for edge, corner, and boundary detection methods. There are many real-world applications of edge, corner, and boundary detection methods. For instance, in medical image analysis, edge…
This article presents a novel approach to identifying and classifying intersections for semantic and topological mapping. More specifically, the proposed novel approach has the merit of generating a semantically meaningful map containing…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an $n$-variate polynomial with bounded individual degree $d$ and…
In robotic surgery, pattern cutting through a deformable material is a challenging research field. The cutting procedure requires a robot to concurrently manipulate a scissor and a gripper to cut through a predefined contour trajectory on…
Boundary detection is essential for a variety of computer vision tasks such as segmentation and recognition. In this paper we propose a unified formulation and a novel algorithm that are applicable to the detection of different types of…
In general it requires at least 7 point correspondences to compute the fundamental matrix between views. We use the cross ratio invariance between corresponding epipolar lines, stemming from epipolar line homography, to derive a simple…
We study imbedded hypersurfaces in spacetime whose causal character is allowed to change from point to point. Inherited geometrical structures on these hypersurfaces are defined by two methods: first, the standard rigged connection induced…
Given a set of objects $O$ in the plane, the corresponding intersection graph is defined as follows. Each object defines a vertex and an edge joins two vertices whenever the corresponding objects intersect. We study here the case of unit…
We consider the complexity of the recognition problem for two families of combinatorial structures. A graph $G=(V,E)$ is said to be an intersection graph of lines in space if every $v\in V$ can be mapped to a straight line $\ell (v)$ in…
In this article, we investigate short topological decompositions of non-orientable surfaces and provide algorithms to compute them. Our main result is a polynomial-time algorithm that for any graph embedded in a non-orientable surface…
Consider p independent Brownian motions in R^d, each running up to its first exit time from an open domain B, and their intersection local time l as a measure on B. We give a sharp criterion for the finiteness of exponential moments,…
We consider systems of Laurent polynomials with support on a fixed point configuration. In the non-defective case, the closure of the locus of coefficients giving a non-degenerate multiple root of the system is defined by a polynomial…
We are introducing two methods for revealing the true inflection point of data that contains or not error. The starting point is a set of geometrical properties that follow the existence of an inflection point p for a smooth function. These…
The purpose of this paper is to present simple and fast methods for computing control points for polynomial curves and polynomial surfaces given explicitly in terms of polynomials (written as sums of monomials). We give recurrence formulae…
In this paper we study local routing strategies on geometric graphs. Such strategies use geometric properties of the graph like the coordinates of the current and target nodes to route. Specifically, we study routing strategies in the…
Two vertex-labelled polygons are \emph{compatible} if they have the same clockwise cyclic ordering of vertices. The definition extends to polygonal regions (polygons with holes) and to triangulations---for every face, the clockwise cyclic…