Related papers: A Robust Approach to Detect Intersections between …
We present a, hopefully, elementary mathematical treatment of the computational aspects of congruent numbers, such that an amateur could understand the problem and perform their own calculations.
Finding interactions between variables in large and high-dimensional datasets is often a serious computational challenge. Most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that…
Edge detection serves as a critical foundation for numerous computer vision applications, including object detection, semantic segmentation, and image editing, by extracting essential structural cues that define object boundaries and…
The primary objective of this study is to develop novel interpolation operators that interpolate the boundary values of a function defined on a triangle. This is accomplished by constructing New Generalized Boolean sum neural network…
Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
The number of triangles in a graph is a fundamental metric, used in social network analysis, link classification and recommendation, and more. Driven by these applications and the trend that modern graph datasets are both large and dynamic,…
Local-nonlocal coupling approaches combine the computational efficiency of local models and the accuracy of nonlocal models. However, the coupling process is challenging, requiring expertise to identify the interface between local and…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
An $\epsilon$-approximate incidence between a point and some geometric object (line, circle, plane, sphere) occurs when the point and the object lie at distance at most $\epsilon$ from each other. Given a set of points and a set of objects,…
A change point problem occurs in many statistical applications. If there exist change points in a model, it is harmful to make a statistical analysis without any consideration of the existence of the change points and the results derived…
Visual place recognition tasks often encounter significant challenges in landmark detection due to the presence of irrelevant objects such as humans, cars, and trees, despite the remarkable progress achieved by previous models, especially…
We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two…
A series of far-detector programs have been proposed for operation at various interaction points of the Large Hadron Collider during the upcoming runs. Investigating the potential and complementarity of these experiments for new-physics…
Large-scale parallel numerical simulations are essential for a wide range of engineering problems that involve complex, coupled physical processes interacting across a broad range of spatial and temporal scales. The data structures involved…
Visual object counting is a fundamental computer vision task underpinning numerous real-world applications, from cell counting in biomedicine to traffic and wildlife monitoring. However, existing methods struggle to handle the challenge of…
Parallel coordinates plot (PCP) is an excellent tool for multivariate visualization and analysis, but it may fail to reveal inherent structures for datasets with a large number of items. In this paper, we propose a suite of novel…
The paper introduces a novel representation for Generalized Planning (GP) problems, and their solutions, as C++ programs. Our C++ representation allows to formally proving the termination of generalized plans, and to specifying their…
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,…
Straightedge and compass construction problems are one of the oldest and most challenging problems in elementary mathematics. The central challenge, for a human or for a computer program, in solving construction problems is a huge search…