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There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
Precise 3D measurements of rigid surfaces are desired in many fields of application like quality control or surgery. Often, views from all around the object have to be acquired for a full 3D description of the object surface. We present a…
The linear complementarity problem (LCP) provides a unified approach to many problems such as linear programs, convex quadratic programs, and bimatrix games. The general LCP is known to be NP-hard, but there are some promising results that…
We consider the high-resolution imaging problem of 3D point source image recovery from 2D data using a method based on point spread function (PSF) engineering. The method involves a new technique, recently proposed by S.~Prasad, based on…
This work presents two novel solvers for estimating the relative poses among views with known vertical directions. The vertical directions of camera views can be easily obtained using inertial measurement units (IMUs) which have been widely…
We present for the first time an explicit, complete and closed-form solution to the three-dimensional problem of two fixed centres, based on Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our…
We consider several problems that involve lines in three dimensions, and present improved algorithms for solving them. The problems include (i) ray shooting amid triangles in $R^3$, (ii) reporting intersections between query lines…
Multi-perspective cameras are quickly gaining importance in many applications such as smart vehicles and virtual or augmented reality. However, a large system size or absence of overlap in neighbouring fields-of-view often complicate their…
Deep learning method is of great importance in solving partial differential equations. In this paper, inspired by the failure-informed idea proposed by Gao et.al. (SIAM Journal on Scientific Computing 45(4)(2023)) and as an improvement, a…
This paper investigates singular configurations of the P3P problem. Using local dual space, a systematic algebraic-computational framework is proposed to give a complete geometric stratification for the P3P singular configurations with…
The paper is an introduction to the use of the classical Newton-Puiseux procedure, oriented to an algorithmic description of it. This procedure enables to get polynomial approximations for parameterizations of branches of an algebraic plane…
Using the normalized B-bases of vector spaces of trigonometric and hyperbolic polynomials of finite order, we specify control point configurations for the exact description of higher dimensional (rational) curves and (hybrid) multivariate…
The problem of finding a next best viewpoint for 3D modeling or scene mapping has been explored in computer vision over the last decade. This paper tackles a similar problem, but with different characteristics. It proposes a method for…
The three-dimensional linear regression problem is a problem of finding a spacial straight line best fitting a group of points in three-dimensional Euclidean space. This problem is considered in the present paper and a solution to it is…
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…
We study the \emph{Proximal Alternating Predictor-Corrector} (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle to solve nonsmooth structured convex-concave saddle point problems consisting of the sum of a smooth convex…
In this paper, we propose an object-based camera pose estimation from a single RGB image and a pre-built map of objects, represented with ellipsoidal models. We show that contrary to point correspondences, the definition of a cost function…
This paper aims to answer an open question recently posed in the literature, that is to find a fast exact method for solving the p-dispersion-sum problem (PDSP), a nonconcave quadratic binary maximization problem. We show that, since the…
Methods of three-dimensional deconvolution (3DD) or volumetric deconvolution of optical complex-valued wavefronts diffracted by 3D samples with the 3D point spread function are presented. Particularly, the quantitative correctness of the…
This work focuses on Registration or Alignment of 3D point sets. Although the Registration problem is a well established problem and it's solved using multiple variants of Iterative Closest Point (ICP) Algorithm, most of the approaches in…