A Diffeomorphism Groupoid and Algebroid Framework for Discontinuous Image Registration
In this paper, we propose a novel mathematical framework for piecewise diffeomorphic image registration that involves discontinuous sliding motion using a diffeomorphism groupoid and algebroid approach. The traditional Large Deformation Diffeomorphic Metric Mapping (LDDMM) registration method builds on Lie groups, which assume continuity and smoothness in velocity fields, limiting its applicability in handling discontinuous sliding motion. To overcome this limitation, we extend the diffeomorphism Lie groups to a framework of discontinuous diffeomorphism Lie groupoids, allowing for discontinuities along sliding boundaries while maintaining diffeomorphism within homogeneous regions. We prov...
| Authors | Lili Bao, Bin Xiao, Shihui Ying et al. |
|---|---|
| Primary category | math.GR |
| Published | 12 March 2026 |
| Last updated at source | 29 April 2026 |
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