Related papers: L-systems in Geometric Modeling
Centerline graphs, crucial for path planning in autonomous driving, are traditionally learned using deterministic methods. However, these methods often lack spatial reasoning and struggle with occluded or invisible centerlines. Generative…
Finding semantic correspondences is a challenging problem. With the breakthrough of CNNs stronger features are available for tasks like classification but not specifically for the requirements of semantic matching. In the following we…
We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…
Graph Neural Networks (GNNs) are a popular class of machine learning models. Inspired by the learning to explain (L2X) paradigm, we propose L2XGNN, a framework for explainable GNNs which provides faithful explanations by design. L2XGNN…
Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few…
The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding: (1) Hausdorff distance, and (2) a sum…
Analysis of human sketches in deep learning has advanced immensely through the use of waypoint-sequences rather than raster-graphic representations. We further aim to model sketches as a sequence of low-dimensional parametric curves. To…
In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different…
Boundary representation (B-rep) models are the standard way 3D shapes are described in Computer-Aided Design (CAD) applications. They combine lightweight parametric curves and surfaces with topological information which connects the…
We give an algorithmic introduction to Lagrangian coherent structures (LCSs) using a newly developed computational engine, LCS Tool. LCSs are most repelling, attracting and shearing material lines that form the centerpieces of observed…
A Lie system is a non-autonomous system of first-order ordinary differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional real Lie algebra of vector fields, a so-called…
Deep ReLU Networks can be decomposed into a collection of linear models, each defined in a region of a partition of the input space. This paper provides three results extending this theory. First, we extend this linear decompositions to…
Datasets that exhibit non-Gaussian characteristics are common in many fields, while the current modeling framework and available software for non-Gaussian models is limited. We introduce Linear Latent Non-Gaussian Models (LLnGMs), a unified…
This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…
Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and…
We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in…
Based on the seminal work on Array-RQMC methods and rank-1 lattice sequences by Pierre L'Ecuyer and collaborators, we introduce efficient deterministic algorithms for image synthesis. Enumerating a low discrepancy sequence along the Hilbert…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
This paper considers the multi-parametric linear complementarity problem (pLCP) with sufficient matrices. The main result is an algorithm to find a polyhedral decomposition of the set of feasible parameters and to construct a piecewise…