Related papers: Efficient computation of topological integral tran…

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

We present a novel topology-preserving 3D medial axis computation framework based on volumetric restricted power diagram (RPD), while preserving the medial features and geometric convergence simultaneously, for both 3D CAD and organic…

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on…

The use of vectorial parameterization to create geometrical representations in computational models has a large number of applications. One particular application is the calculation of the 3D rotational motion of rigid bodies, that could be…

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the…

A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…

Transformer-based language models have set new benchmarks across a wide range of NLP tasks, yet reliably estimating the uncertainty of their predictions remains a significant challenge. Existing uncertainty estimation (UE) techniques often…

Many known Radon-type transforms of symmetric (radial or zonal) functions are represented by one-dimensional Riemann-Liouville fractional integrals or their modifications. The present article contains new examples of such transforms in the…

A new predictor-corrector type incremental algorithm is proposed for the exact construction of weighted straight skeletons of 2D general planar polygons of arbitrary complexity based on the notion of deforming polygon. In the proposed…

To enhance the interpretability of multimodal unified representations, many studies have focused on discrete unified representations. These efforts typically start with contrastive learning and gradually extend to the disentanglement of…

Topological descriptors, such as the Euler characteristic function and the persistence diagram, have grown increasingly popular for representing complex data. Recent work showed that a carefully chosen set of these descriptors encodes all…

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest…

The Euclid mission is expected to image millions of galaxies with high resolution, providing an extensive dataset to study galaxy evolution. We investigate the application of deep learning to predict the detailed morphologies of galaxies in…

Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…

The early detection and nuanced subtype classification of non-small cell lung cancer (NSCLC), a predominant cause of cancer mortality worldwide, is a critical and complex issue. In this paper, we introduce an innovative integration of…

High-confidence overlap prediction and accurate correspondences are critical for cutting-edge models to align paired point clouds in a partial-to-partial manner. However, there inherently exists uncertainty between the overlapping and…

Many data representations are vectors of continuous values. In particular, deep learning embeddings are data-driven representations, typically either unconstrained in Euclidean space, or constrained to a hypersphere. These may also be…

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide…

We propose a Transformer architecture for volumetric segmentation, a challenging task that requires keeping a complex balance in encoding local and global spatial cues, and preserving information along all axes of the volume. Encoder of the…