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Given two curves in $\PP^3$, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the…
In the classic polyline simplification problem we want to replace a given polygonal curve $P$, consisting of $n$ vertices, by a subsequence $P'$ of $k$ vertices from $P$ such that the polygonal curves $P$ and $P'$ are as close as possible.…
This paper presents an algorithm for detecting and computing the cusp points in the joint space of 3-RPR planar parallel manipulators. In manipulator kinematics, cusp points are special points, which appear on the singular curves of the…
In this paper, we propose a novel shape optimization approach for the source identification of elliptic equations. This identification problem arises from two application backgrounds: actuator placement in PDE-constrained optimal controls…
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…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational…
As the spherical object can be seen everywhere, we should extract the ellipse image accurately and fit it by implicit algebraic curve in order to finish the 3D reconstruction. In this paper, we propose a new ellipse fitting algorithm which…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
The elliptic curve discrete logarithm problem is of fundamental importance in public-key cryptography. It is in use for a long time. Moreover, it is an interesting challenge in computational mathematics. Its solution is supposed to provide…
Visual localization is the task of estimating a 6-DoF camera pose of a query image within a provided 3D reference map. Thanks to recent advances in various 3D sensors, 3D point clouds are becoming a more accurate and affordable option for…
Many problems arising in image processing and signal recovery with multi-regularization can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
A given six dimensional vector represents a 3D straight line in Plucker coordinates if its coordinates satisfy the Klein quadric constraint. In many problems aiming to find the Plucker coordinates of lines, noise in the data and other…
Estimating the position and orientation of a camera with respect to an observed scene is one of the central problems in computer vision, particularly in the context of camera calibration and multi-sensor systems. This paper addresses the…
In recent years, the task of learned point cloud compression has gained prominence. An important type of point cloud, the spinning LiDAR point cloud, is generated by spinning LiDAR on vehicles. This process results in numerous circular…
Usual mathematical method for creating trochoids is based on a solid rule that requires a pure rolling motion of a circle along another one. In this vision a trochoid defined as a traced path by an attached point (a non-conceptive issue) to…
We study how an irreducible closed algebraic curve X embedded in CP^3 can be recovered using its projections from points onto embedded projective planes. The different embeddings are unknown. The only input is the defining equation of each…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…
We present novel retrospective change point detection approach based on optimal transport and geometric discrepancy. The method does not require any parametric assumptions about distributions separated by change points. It can be used both…