[2604.04299] A Persistent Homology Design Space for 3D Point Cloud Deep Learning

Computer Science > Computer Vision and Pattern Recognition arXiv:2604.04299 (cs) [Submitted on 5 Apr 2026] Title:A Persistent Homology Design Space for 3D Point Cloud Deep Learning Authors:Prachi Kudeshia, Jiju Poovvancheri, Amr Ghoneim, Dong Chen View a PDF of the paper titled A Persistent Homology Design Space for 3D Point Cloud Deep Learning, by Prachi Kudeshia and 3 other authors View PDF HTML (experimental) Abstract:Persistent Homology (PH) offers stable, multi-scale descriptors of intrinsic shape structure by capturing connected components, loops, and voids that persist across scales, providing invariants that complement purely geometric representations of 3D data. Yet, despite strong theoretical guarantees and increasing empirical adoption, its integration into deep learning for point clouds remains largely ad hoc and architecturally peripheral. In this work, we introduce a unified design space for Persistent-Homology driven learning in 3D point clouds (3DPHDL), formalizing the interplay between complex construction, filtration strategy, persistence representation, neural backbone, and prediction task. Beyond the canonical pipeline of diagram computation and vectorization, we identify six principled injection points through which topology can act as a structural inductive bias reshaping sampling, neighborhood graphs, optimization dynamics, self-supervision, output calibration, and even internal network regularization. We instantiate this framework through a controll...