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Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often…
Afshani, Barbay and Chan (2017) introduced the notion of instance-optimal algorithm in the order-oblivious setting. An algorithm A is instance-optimal in the order-oblivious setting for a certain class of algorithms A* if the following…
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.…
In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying…
We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to $\mathbb{R}^d$ containing a distorted reflection symmetry pattern. We pose the problem of detecting…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Designing and analyzing algorithms with provable performance guarantees enables efficient optimization problem solving in different application domains, e.g.\ communication networks, transportation, economics, and manufacturing. Despite the…
Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on…
We consider the $(1+\epsilon)$-approximate nearest neighbor search problem: given a set $X$ of $n$ points in a $d$-dimensional space, build a data structure that, given any query point $y$, finds a point $x \in X$ whose distance to $y$ is…
The proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of nonpositive curvature. We…
For any two point sets $A,B \subset \mathbb{R}^d$ of size up to $n$, the Chamfer distance from $A$ to $B$ is defined as $\text{CH}(A,B)=\sum_{a \in A} \min_{b \in B} d_X(a,b)$, where $d_X$ is the underlying distance measure (e.g., the…
Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…
In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
To reach human performance on complex tasks, a key ability for artificial systems is to understand physical interactions between objects, and predict future outcomes of a situation. This ability, often referred to as intuitive physics, has…
Since edge detection is in the forefront of image processing for object detection, it is crucial to have a good understanding of edge detection algorithms. The reason for this is that edges form the outline of an object. An edge is the…
Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…
A method is developed to calculate collision probability in this paper. Based on the encounter geometric features of space objects, it is reasonable to separate the radial orbital motions from that in the cross section for most encounter…