A Joint Segmentation, Registration, and Atlas Generation Model, and Deformation-Informed PCA.
vendredi 1 mars 2019, 14h00 - 16h00
In medical image analysis, constructing an atlas representing a meaningful statistical image of the global underlying anatomy from a set of images, as well as studying the variability inside a population, or retrieving the inherent dynamics of organs, are essential tasks which help the practitioners characterise and understand how geometrical and structural changes influence health. These involve identifying meaningful structures inside an image, process called segmentation, the mapping of a group of images to an unknown reference image, called registration, and a statistical analysis of the obtained deformations and structures. In this work, we address the issue of designing a unified variational model for joint segmentation, registration, and segmented atlas generation. We thus propose to segment and register a whole dataset of images to a mean representation of the ensemble (also an unknown of the model). The structures to be aligned are considered as isotropic, homogeneous and hyperelastic materials and more precisely as Ogden materials. The segmentation is based on the Potts model which allows to partition the image into more than two regions and the dissimilarity measure aims at aligning them. A representation of the deformations in a linear space equipped with a scalar product is then given in order to perform a geometry-driven Principal Component Analysis (PCA) and to extract the main modes of variations inside the initial set of images. Theoretical results highlighting the mathematical soundness of the model including existence of minimisers, analysis of a numerical method of resolution, asymptotic results and a PCA analysis, as well as numerical simulations are provided.
This is a joint work with John ASTON, Statslab, University of Cambridge, U.K., Fabien BONARDI, IBISC, Université d’Évry, France, Carole LE GUYADER, Institut National des Sciences Appliquées de Rouen Normandie, France, Marina ROMANCHIKOVA, National Physical Laboratory, Teddington, U.K., and Carola SCHÖNLIEB, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, U.K..