Related papers: Geometric Separability using Orthogonal Objects
This paper considers the problem of designing a dynamical system to solve constrained optimization problems in a distributed way and in an anytime fashion (i.e., such that the feasible set is forward invariant). For problems with separable…
Artificial objects usually have very stable shape features, which are stable, persistent properties in geometry. They can provide evidence for object recognition. Shape features are more stable and more distinguishing than appearance…
Since specular reflection often exists in the real captured images and causes deviation between the recorded color and intrinsic color, specular reflection separation can bring advantages to multiple applications that require consistent…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
In this work, we study the challenging problem of identifying the irregular status of objects from images in an "open world" setting, that is, distinguishing the irregular status of an object category from its regular status as well as…
In this work, we propose a new segmentation algorithm for images containing convex objects present in multiple shapes with a high degree of overlap. The proposed algorithm is carried out in two steps, first we identify the visible contours,…
We establish that a simple polynomial-time algorithm that we call reweighted spectral partitioning obtains small 2/3-balanced vertex-separators for a number of graph classes, including $O(\sqrt{n})$-sized separators for planar graphs,…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…
We explicate a semi-automated statistical algorithm for object identification and segregation in both gray scale and color images. The algorithm makes optimal use of the observation that definite objects in an image are typically…
We focus on determining the separability of an unknown bipartite quantum state $\rho$ by invoking a sufficiently large subset of all possible entanglement witnesses given the expected value of each element of a set of mutually orthogonal…
Let $P$ be a set of points in $\mathbb{R}^d$, $B$ a bicoloring of $P$ and $\Oo$ a family of geometric objects (that is, intervals, boxes, balls, etc). An object from $\Oo$ is called balanced with respect to $B$ if it contains the same…
Recent advances in optical imaging and communication increasingly involve high-dimensional, partially coherent light, creating a growing need for scalable tools to measure and manipulate coherence. Here, we demonstrate the automatic…
A physical applicability of normed split-algebras, such as hyperbolic numbers, split-quaternions and split-octonions is considered. We argue that the observable geometry can be described by the algebra of split-octonions. In such a picture…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
In this paper we study the property of separability of functional space with the open-point and bi-point-open topologies.
It is important to design separation algorithms of low computational complexity in mixed integer programming. We study the separation problems of the two continuous knapsack polyhedra with divisible capacities. The two polyhedra are the…
An efficient geometric integrator is proposed for solving the perturbed Kepler motion. This method is stable and accurate over long integration time, which makes it appropriate for treating problems in astrophysics, like solar system…
The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is…
Recently a new formalism for perturbations of Maxwell's equations on the background of the Kerr-NUT-(A)dS spacetime was proposed, with which the equations are reduced to a equation of motion of a scalar field that can be solved by…