Projects:GeodesicShapeRegression

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Ongoing Work (Updated 10/2014)

Geodesic Regression for Anatomical Shape Complexes

Shape regression is of crucial importance for statistical shape analysis. It is useful to find correlations between shape configuration and a continuous scalar parameter such as age, disease progression, drug delivery, or cognitive scores. When only few follow-up observations are available, regression is also a necessary tool to interpolate between data points and provide a scenario of continuous shape evolution over the parameter range. Longitudinal studies also require to compare such regressions across different subjects.

Multi-Object Shape Complexes

Medical imaging data is available in many formats. From volumetric imaging data, anatomical structures are extracted. The structures can be represented in several ways (in 2D or 3D): triangular meshes for surfaces, landmarks, point clouds, curves, etc. It is important to consider image data in anatomical context, which motivates regression on image and shape data in different combinations (a multi-object complex).

Geodesic Growth Model

Fig. 1. Conceptual overview of geodesic regression on multi-object complexes containing both image and shape data. The framework estimates parameters at t = 0 which consist of the baseline image I0 and shape X0 along with the deformation model parameterized by control points c0 and initial momenta α0 such that overall distance between the deformed objects and the observations are minimal.

Literature

[1] Fishbaugh, J., Prastawa, M., Gerig, G., Durrleman, S. Geodesic regression of image and shape data for improved modeling of 4D trajectories. IEEE International Symposium on Biomedical Imaging (ISBI '14)

[2] Fishbaugh, J., Prastawa, M., Gerig, G., Durrleman, S. Geodesic image regression with a sparse parameterization of diffeomorphisms. Geometric Science of Information (GSI '13). LNCS vol 8085, pp. 95-102. (2013)

[3] Fishbaugh, J., Prastawa, M., Gerig, G., Durrleman, S. Geodesic shape regression in the framework of currents. Proc. of Information Processing in Medical Imaging (IPMI '13). Vol 23, pp. 718-729. (2013)

Key Investigators

• Utah: James Fishbaugh, Marcel Prastawa, Guido Gerig
• INRIA/ICM, Pitie Salpetriere Hospital: Stanley Durrleman

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