• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Splines for diffeomorphisms

Thumbnail
View/Open
singh2015_diffeosplines.pdf (8.259Mb)
Date
2015
Dewey
Probabilités et mathématiques appliquées
Sujet
LDDMM; Diffeomorphisms; Splines; Image Regression; Polynomials; Time Series
Journal issue
Medical Image Analysis
Volume
25
Number
1
Publication date
2015
Article pages
56-71
Publisher
Oxford University Press
DOI
http://dx.doi.org/10.1016/j.media.2015.04.012
URI
https://basepub.dauphine.fr/handle/123456789/16397
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Singh, Nikhil
Vialard, François-Xavier
Niethammer, Marc
Type
Article accepté pour publication ou publié
Abstract (EN)
This paper develops a method for higher order parametric regression on diffeomorphisms for image regression. We present a principled way to define curves with nonzero acceleration and nonzero jerk. This work extends methods based on geodesics which have been developed during the last decade for computational anatomy in the large deformation diffeomorphic image analysis framework. In contrast to previously proposed methods to capture image changes over time, such as geodesic regression, the proposed method can capture more complex spatio-temporal deformations.We take a variational approach that is governed by an underlying energy formulation, which respects the nonflat geometry of diffeomorphisms. Such an approach of minimal energy curve estimation also provides a physical analogy to particle motion under a varying force field. This gives rise to the notion of the quadratic, the cubic and the piecewise cubic splines on the manifold of diffeomorphisms. The variational formulation of splines also allows for the use of temporal control points to control spline behavior. This necessitates the development of a shooting formulation for splines.The initial conditions of our proposed shooting polynomial paths in diffeomorphisms are analogous to the Euclidean polynomial coefficients. We experimentally demonstrate the effectiveness of using the parametric curves both for synthesizing polynomial paths and for regression of imaging data. The performance of the method is compared to geodesic regression.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.