Related papers: Genus Computing for 3D digital objects: algorithm …

In this paper, we propose a novel 3D registration paradigm, Generative Point Cloud Registration, which bridges advanced 2D generative models with 3D matching tasks to enhance registration performance. Our key idea is to generate cross-view…

A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…

The topological analysis of four-dimensional (4D) image-type data is challenged by the immense size that these datasets can reach. This can render the direct application of methods, like persistent homology and convolutional neural networks…

Fix a finite group $G$. We analyze the computational complexity of the problem of counting homomorphisms $\pi_1(X) \to G$, where $X$ is a topological space treated as computational input. We are especially interested in requiring $G$ to be…

In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue…

The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and…

Given a graph embedded in an orientable surface, a process consisting of random excitations and random node and face balancing is constructed and analyzed. It is shown that given a priori bounds g' on the genus and n' on the number of…

Genetic algorithms (GAs) are an optimization technique that has been successfully used on many real-world problems. There exist different approaches to their theoretical study. In this paper we complete a recently presented approach to…

We give several algorithms addressing computations of intersections of conjugate subgroups.

This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…

Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution. Quantum computation is a new computational paradigm which exploits quantum resources to speed up information processing tasks. Therefore, it is…

We propose a topology-constrained quantized nnUNet framework for efficient and anatomically accurate 3D tooth segmentation, addressing the challenges of spatial distortion introduced by quantization in deep learning models. The proposed…

In the current era of neural networks and big data, higher dimensional data is processed for automation of different application areas. Graphs represent a complex data organization in which dependencies between more than one object or…

This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…

Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…

Geometric 3D scene classification is a very challenging task. Current methodologies extract the geometric information using only a depth channel provided by an RGB-D sensor. These kinds of methodologies introduce possible errors due to…

We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…

We describe some theoretical results on triangulations of surfaces and we develop a theory on roots, decompositions and genus-surfaces. We apply this theory to describe an algorithm to list all triangulations of closed surfaces with at most…

Recent text-to-3D models can render high-quality assets, yet they still stumble on objects with complex attributes. The key obstacles are: (1) existing text-to-3D approaches typically lift text-to-image models to extract semantics via text…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…