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This paper proposes a novel object detection framework named Grid R-CNN, which adopts a grid guided localization mechanism for accurate object detection. Different from the traditional regression based methods, the Grid R-CNN captures the…
This paper is concerned with Lagrange interpolation by total degree polynomials in moderate dimensions. In particular, we are interested in characterising the optimal choice of points for the interpolation problem, where we define the…
We propose a differentiable imaging framework to address uncertainty in measurement coordinates such as sensor locations and projection angles. We formulate the problem as measurement interpolation at unknown nodes supervised through the…
The point inclusion tests for polygons, in other words the point-in-polygon (PIP) algorithms, are fundamental tools for many scientific fields related to computational geometry, and they have been studied for a long time. The PIP algorithms…
We present a new method, called the pixel array method, for approximating all solutions in a bounding box for an arbitrary nonlinear system of relations. In contrast with other solvers, our approach requires that the user must specify which…
In contrast to sparse keypoints, a handful of line segments can concisely encode the high-level scene layout, as they often delineate the main structural elements. In addition to offering strong geometric cues, they are also omnipresent in…
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. This is applied by Du (2010) [A note on cone…
Suspensions of small anisotropic particles, termed 'rheoscopic fluids', are used for flow visualisation. By illuminating the fluid with light of three different colours, it is possible to determine Poincare indices for vector fields formed…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
We present a method that detects boundaries of parts in 3D shapes represented as point clouds. Our method is based on a graph convolutional network architecture that outputs a probability for a point to lie in an area that separates two or…
A novel method has been introduced to solve a point inclusion in a polygon problem. The method is applicable to convex as well as non-convex polygons which are not self-intersecting. The introduced method is independent of rounding off…
Negative dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the method simultaneously gives solutions in different regions of…
Two new algorithms are described for matching two dimensional coordinate lists of point sources that are signifcantly faster than previous methods. By matching rarely occurring triangles (or more complex shapes) in the two lists, and by…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…
Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum…
The goal of this primer is to provide a relatively short exposition of the basics of multigrid methods, simplified by focusing on fundamental concepts in a variational setting. This is done by way of a quadratic energy minimization…
We consider a geometrical system of equations for a three dimensional Riemannian manifold. This system of equations has been constructed as to include several physically interesting systems of equations, such as the stationary Einstein…
The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence properties. In order to present our method the concept of…
This paper introduces a novel, lightweight method to solve the visibility problem for 2D grids. The proposed method evaluates the existence of lines-of-sight from a source point to all other grid cells in a single pass with no preprocessing…