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Object detection is a main task in computer vision. Template matching is the reference method for detecting objects with arbitrary templates. However, template matching computational complexity depends on the rotation accuracy, being a…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
The contouring methods described by Lewis et al. (1993) and Witt (1993) are very efficient and elegant for obtaining the magnification of a point source moving along a straight track in the source plane. The method is, however, not very…
The focus of this paper is on a thin obstacle problem where the obstacle is defined on the intersection between a hyper-plane $\Gamma$ in $\mathbb{R}^n$ and a periodic perforation $\mathcal{T}_\varepsilon$ of $\mathbb{R}^n$, depending on a…
We propose an experimental scheme to construct an optical lattice where the atoms are confined to the surface of a torus. This construction can be realized with spatially shaped laser beams which could be realized with recently developed…
Image tracing is a foundational component of the workflow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean…
A new algorithm for clipping a line segment against a pyramid in E3 is presented. This algorithm avoids computation of intersection points which are not end-points of the output line segment. It also allows solving all cases more…
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of…
One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
We show that any set of distinct homotopy classes of simple closed curves on the torus that pairwise intersect at most $k$ times has size $k + O(\sqrt{k} \log k)$. Prior to this work, a lemma of Agol, together with the state of the art…
Detecting polygons defined by a set of line segments in a plane is an important step in analyzing vector drawings. This paper presents an approach combining several algorithms to detect basic polygons from arbitrary line segments. The…
An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart,…
Vector-based algorithms are novel algorithms in optimal any-angle path planning that are motivated by bug algorithms, bypassing free space by directly conducting line-of-sight checks between two queried points, and searching along obstacle…
On a smooth variety, Serre's intersection formula computes intersection multiplicities via an alternating sum of the lengths of Tor groups. When the variety is singular, the corresponding sum can be a divergent series. But there are…
A polygon C is an intersecting polygon for a set O of objects in the plane if C intersects each object in O, where the polygon includes its interior. We study the problem of computing the minimum-perimeter intersecting polygon and the…
This paper presents a novel method for the reconstruction of interaction vertices in particle collision data. The algorithm is an agglomerative clustering technique designed for high-luminosity environments in current and future…
A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…
We introduce \textcolor{red}{general} new techniques for computing the geometric index of a link $L$ in the interior of a solid torus $T$. These techniques simplify and unify previous ad hoc methods used to compute the geometric index in…
Finding the intersection of two conics is a commonly occurring problem. For example, it occurs when identifying patterns of craters on the lunar surface, detecting the orientation of a face from a single image, or estimating the attitude of…