Geodesic regression of image and shape data for improved modeling of 4D trajectories

A variety of regression schemes have been proposed on images or shapes, although available methods do not handle them jointly. In this paper, we present a framework for joint image and shape regression which incorporates images as well as anatomical shape information in a consistent manner. Evolution is described by a generative model that is the analog of linear regression, which is fully characterized by baseline images and shapes (intercept) and initial momenta vectors (slope). Further, our framework adopts a control point parameterization of deformations, where the dimensionality of the deformation is determined by the complexity of anatomical changes in time rather than the sampling of the image and/or the geometric data. We derive a gradient descent algorithm which simultaneously estimates baseline images and shapes, location of control points, and momenta. Experiments on real medical data demonstrate that our framework effectively combines image and shape information, resulting in improved modeling of 4D (3D space + time) trajectories.

[1]  Guido Gerig,et al.  Toward a Comprehensive Framework for the Spatiotemporal Statistical Analysis of Longitudinal Shape Data , 2012, International Journal of Computer Vision.

[2]  Guido Gerig,et al.  Quantifying regional growth patterns through longitudinal analysis of distances between multimodal MR intensity distributions , 2012, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI).

[3]  Michael I. Miller,et al.  Landmark matching via large deformation diffeomorphisms , 2000, IEEE Trans. Image Process..

[4]  Guido Gerig,et al.  Optimal Data-Driven Sparse Parameterization of Diffeomorphisms for Population Analysis , 2011, IPMI.

[5]  Ali R. Khan,et al.  Representation of time-varying shapes in the large deformation diffeomorphic framework , 2008, 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[6]  P. Thomas Fletcher,et al.  A vector momenta formulation of diffeomorphisms for improved geodesic regression and atlas construction , 2013, 2013 IEEE 10th International Symposium on Biomedical Imaging.

[7]  P. Thomas Fletcher,et al.  Population Shape Regression from Random Design Data , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[8]  François-Xavier Vialard,et al.  Geodesic Regression for Image Time-Series , 2011, MICCAI.

[9]  G. Pearlson,et al.  Rate of caudate atrophy in presymptomatic and symptomatic stages of Huntington's disease , 2000, Movement disorders : official journal of the Movement Disorder Society.

[10]  Guido Gerig,et al.  Geodesic Shape Regression in the Framework of Currents , 2013, IPMI.

[11]  Nicholas Ayache,et al.  Iconic feature based nonrigid registration: the PASHA algorithm , 2003, Comput. Vis. Image Underst..