Skip to Main content Skip to Navigation
Conference papers

Symmetric Algorithmic Components for Shape Analysis with Diffeomorphisms

Abstract : In computational anatomy, the statistical analysis of temporal deformations and inter-subject variability relies on shape registration. However, the numerical integration and optimization required in diffeomorphic registration often lead to important numerical errors. In many cases, it is well known that the error can be drastically reduced in the presence of a symmetry. In this work, the leading idea is to approximate the space of deformations and images with a possibly non-metric symmetric space structure using an involution, with the aim to perform parallel transport. Through basic properties of symmetries, we investigate how the implementations of a midpoint and the involution compare with the ones of the Riemannian exponential and logarithm on diffeomorphisms and propose a modification of these maps using registration errors. This leads us to identify transvections, the composition of two symmetries, as a mean to measure how far from symmetric the underlying structure is. We test our method on a set of 138 cardiac shapes and demonstrate improved numerical consistency in the Pole Ladder scheme.
Complete list of metadata

https://hal.inria.fr/hal-02148832
Contributor : Nicolas Guigui <>
Submitted on : Wednesday, June 5, 2019 - 7:35:14 PM
Last modification on : Wednesday, January 6, 2021 - 9:00:01 AM

Files

55-Guigui.pdf
Files produced by the author(s)

Identifiers

Citation

Nicolas Guigui, Shuman Jia, Maxime Sermesant, Xavier Pennec. Symmetric Algorithmic Components for Shape Analysis with Diffeomorphisms. GSI 2019 - 4th conference on Geometric Science of Information, F. Nielsen and F. Barbaresco, Aug 2019, Toulouse, France. pp.759--768, ⟨10.1007/978-3-030-26980-7_79⟩. ⟨hal-02148832⟩

Share

Metrics

Record views

259

Files downloads

1394