2018/01/29 by Hsi-Wei Hsieh, Hsieh, Hsi-Wei, Nicolas Charon +1
Computer Science · Engineering · #3D Shape Modeling and Analysis #49J15 #49M25 #49Q20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Medical Image Segmentation Techniques #Optimization and Control (math.OC) #Robotics and Sensor-Based Localization
paper · pdf · doi:10.48550/arxiv.1801.09778
openalex publication_date 2018/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both the large deformation diffeomorphic metric mapping (LDDMM) model and the concept of oriented varifolds introduced in previous works like [Kaltenmark 2017]. Unlike previous approaches in which varifold representations are only used as surrogates to define and evaluate fidelity terms, the specificity of this paper is to derive direct deformation models and corresponding matching algorithms for discrete varifolds. We show that it gives on the one hand an alternative numerical setting for curve and surface matching but that it can also handle efficiently more general shape structures, including multi-directional objects or multi-modal images represented as distributions of unit gradient vectors.