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We present a new framework for multi-view geometry in computer vision. A camera is a mapping between $\mathbb{P}^3$ and a line congruence. This model, which ignores image planes and measurements, is a natural abstraction of traditional…
Part-aware panoptic segmentation is a problem of computer vision that aims to provide a semantic understanding of the scene at multiple levels of granularity. More precisely, semantic areas, object instances, and semantic parts are…
The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well established since many decades. This topic was mostly studied for variational formulations…
Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution…
Platforms such as robots, security cameras, drones and satellites are used in multi-view imaging for three-dimensional (3D) recovery by stereoscopy or tomography. Each camera in the setup has a field of view (FOV). Multi-view analysis…
With the help of the deep learning paradigm, many point cloud networks have been invented for visual analysis. However, there is great potential for development of these networks since the given information of point cloud data has not been…
We study a wide spectrum of incidence problems involving points and curves or points and surfaces in $\mathbb R^3$. The current (and in fact the only viable) approach to such problems, pioneered by Guth and Katz [2010,2015], requires a…
Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
Let $S$ be a set of $n$ points in the plane. We present several different algorithms for finding a pair of points in $S$ such that any disk that contains that pair must contain at least $cn$ points of $S$, for some constant $c>0$. The first…
We consider radial solutions of a general elliptic equation involving a weighted $p$-Laplace operator with a subcritical nonlinearity. By a shooting method we prove the existence of solutions with any prescribed number of nodes. The method…
Among the main goals in multiple change point problems are the estimation of the number and positions of the change points, as well as the regime structure in the clusters induced by those changes. The product partition model (PPM) is a…
By enabling capturing of 3D point clouds that reflect the geometry of the immediate environment, LiDAR has emerged as a primary sensor for autonomous systems. If a LiDAR scan is too sparse, occluded by obstacles, or too small in range,…
LiDAR-based 3D detection has made great progress in recent years. However, the performance of 3D detectors is considerably limited when deployed in unseen environments, owing to the severe domain gap problem. Existing domain adaptive 3D…
Correspondence is a ubiquitous problem in computer vision and graph matching has been a natural way to formalize correspondence as an optimization problem. Recently, graph matching solvers have included higher-order terms representing…
The chosen tool of this thesis is an extremal type approach. The lesson drawn by the theorems proved in the thesis is that surprisingly small compromise is necessary on the efficacy of the solutions to make the approach work. The problems…
With the advent of integrated sensor technology (smart flow meters and pressure sensors), various new numerical algorithms for leak localization (a core element of water distribution system operation) have been developed. However, there is…
This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…
For a class of quasilinear elliptic equations involving the p-Laplace operator, we develop an abstract critical point theory in the presence of sub-supersolutions. Our approach is based upon the proof of the invariance under the gradient…
This paper is concerned with the study of multiple positive solutions to the following elliptic problem involving a nonhomogeneous operator with nonstandard growth of $p$-$q$ type and singular nonlinearities \begin{equation*} \left\{…