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In land surveying, the generation of maps was greatly simplified with the introduction of orthophotos and at a later stage with airborne LiDAR laser scanning systems. While the original purpose of LiDAR systems was to determine the altitude…
Given a surface with boundary and some points on its boundary, a polygon diagram is a way to connect those points as vertices of non-overlapping polygons on the surface. Such polygon diagrams represent non-crossing permutations on a surface…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
Deep learning has proven to yield fast and accurate predictions of quantum-chemical properties to accelerate the discovery of novel molecules and materials. As an exhaustive exploration of the vast chemical space is still infeasible, we…
This paper proposes a concise coding of the cells of n-dimensional finite regular grids. It induces a simple, generic and efficient framework for implementing classical digital topology data structures and algorithms. Discrete subsets of…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
We present an algorithm for computing the main topological characteristics of three-dimensional bodies. The algorithm is based on a discretization of Morse theory and uses discrete analogs of smooth functions with only nondegenerate (Morse)…
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…
Data generated in the fields of science, technology, business and in many other fields of research are increasing in an exponential rate. The way to extract knowledge from a huge set of data is a challenging task. This paper aims to propose…
Different types of neural networks have been used to solve the flow sensing problem in turbulent flows, namely to estimate velocity in wall-parallel planes from wall measurements. Generative adversarial networks (GANs) are among the most…
Scene graphs have been recently introduced into 3D spatial understanding as a comprehensive representation of the scene. The alignment between 3D scene graphs is the first step of many downstream tasks such as scene graph aided point cloud…
The precise characterization of plant morphology provides valuable insights into plant environment interactions and genetic evolution. A key technology for extracting this information is 3D segmentation, which delineates individual plant…
Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…
Knots, links and entangled filaments appear in many physical systems of interest in biology and engineering. Classifying knots and measuring entanglement is of interest both for advancing knot theory, as well as for analyzing large data…
Geometry and topology constitute complementary descriptors of three-dimensional shape, yet existing benchmark datasets primarily capture geometric information while neglecting topological structure. This work addresses this limitation by…
Deep neural networks for 3D point cloud understanding have achieved remarkable success in object classification and recognition, yet recent work shows that these models remain highly vulnerable to adversarial perturbations. Existing 3D…
In contrast to the literature where local patterns in 3D point clouds are captured by customized convolutional operators, in this paper we study the problem of how to effectively and efficiently project such point clouds into a 2D image…
Topology optimization is computationally demanding that requires the assembly and solution to a finite element problem for each material distribution hypothesis. As a complementary alternative to the traditional physics-based topology…
The remarkable success of Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) in 2D vision has spurred significant research in extending these architectures to the complex domain of 3D analysis. Yet, a core challenge arises…
Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two fields. On one hand, complexity theoretic results show that…