Related papers: Visible Points in Convex Sets and Best Approximati…
We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…
Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
We study the level sets of the distance function from a boundary point of a convex set in Euclidean space. We provide a lower bound for the range of connectivity of the level sets, in terms of the critical points of the distance function in…
Construction robots operate in unstructured construction sites, where effective visual perception is crucial for ensuring safe and seamless operations. However, construction robots often handle large elements and perform tasks across…
This paper introduces the point-axis representation for oriented object detection, emphasizing its flexibility and geometrically intuitive nature with two key components: points and axes. 1) Points delineate the spatial extent and contours…
In the paper three different characterizations of faces of convex sets, belonging to infinite-dimensional real vector spaces, are presented. The first one is formulated in the terms of generalized semispaces, the second -- in the terms of…
We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…
A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in…
Object detection is one of the most important and challenging branches of computer vision, which has been widely applied in peoples life, such as monitoring security, autonomous driving and so on, with the purpose of locating instances of…
Object pose estimation is a fundamental computer vision problem with broad applications in augmented reality and robotics. Over the past decade, deep learning models, due to their superior accuracy and robustness, have increasingly…
This paper gives some relating results for various concepts of convexity in metric spaces such as midpoint convexity, convex structure, uniform convexity and near-uniform convexity, Busemann curvature and its relation to convexity. Some…
A closed convex subset of a normed linear space is said to have the strong separation property if it can be strongly separated from every other disjoint closed and convex set by a closed hyperplane. In this paper we give some results on the…
Object Detection is the task of identifying the existence of an object class instance and locating it within an image. Difficulties in handling high intra-class variations constitute major obstacles to achieving high performance on standard…
We study relations of some classes of $k$-convex, $k$-visible bodies in Euclidean spaces. We introduce and study \textrm{circular projections} in normed linear spaces and classes of bodies related with families of such maps, in particular,…
Active visual perception refers to the ability of a system to dynamically engage with its environment through sensing and action, allowing it to modify its behavior in response to specific goals or uncertainties. Unlike passive systems that…
Projections onto sets are used in a wide variety of methods in optimization theory but not every method that uses projections really belongs to the class of projection methods as we mean it here. Here projection methods are iterative…
With the advent of state-of-the-art machine learning and deep learning technologies, several industries are moving towards the field. Applications of such technologies are highly diverse ranging from natural language processing to computer…