4 papers
Smooth Reparameterizations of Functions on Simplicial Product Spaces: Applications to Probabilistic Tensor Decomposition and Functional Data Registration
Shashwat Kumar, Arafat Rahman, Anuj Srivastava +1
We consider optimization problems defined on product spaces of simplices. Examples of this class of problems include learning low-rank discrete multivariate probability distributio…
TreeSRNF: Square-Root Normal Fields for Generative Modelling of the Geometric and Structural Variability in Tree-like 3D Objects
Tahmina Khanam, Hamid Laga, Mohammed Bennamoun +4
We introduce a novel mathematical framework for analyzing and generating complex tree-shaped 3D objects, such as botanical trees and plants, which deform both in their 3D geometry…
Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis
Awais Nizamani, Hamid Laga, Guanjin Wang +3
We propose a novel framework for the statistical analysis of genus-zero 4D surfaces, i.e., 3D surfaces that deform and evolve over time. This problem is particularly challenging du…
A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-shaped Structures
Tahmina Khanam, Hamid Laga, Mohammed Bennamoun +5
We propose the first comprehensive approach for modeling and analyzing the spatiotemporal shape variability in tree-like 4D objects, i.e., 3D objects whose shapes bend, stretch, an…