Particle Based Shape Regression of Open Surfaces with Applications to Developmental Neuroimaging
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
Schild's Ladder for the parallel transport of deformations in time series of images
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Estimation of smooth growth trajectories with controlled acceleration from time series shape data
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Geodesic regression for image time-series
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Analysis of longitudinal shape variability via subject specific growth modeling
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Sparse Adaptive Parameterization of Variability in Image Ensembles
International Journal of Computer Vision
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Shape regression is emerging as an important tool for the statistical analysis of time dependent shapes. In this paper, we develop a new generative model which describes shape change over time, by extending simple linear regression to the space of shapes represented as currents in the large deformation diffeomorphic metric mapping (LDDMM) framework. By analogy with linear regression, we estimate a baseline shape (intercept) and initial momenta (slope) which fully parameterize the geodesic shape evolution. This is in contrast to previous shape regression methods which assume the baseline shape is fixed. We further leverage a control point formulation, which provides a discrete and low dimensional parameterization of large diffeomorphic transformations. This flexible system decouples the parameterization of deformations from the specific shape representation, allowing the user to define the dimensionality of the deformation parameters. We present an optimization scheme that estimates the baseline shape, location of the control points, and initial momenta simultaneously via a single gradient descent algorithm. Finally, we demonstrate our proposed method on synthetic data as well as real anatomical shape complexes.