Geodesic shape regression with multiple geometries and sparse parameters

James Fishbaugh, Stanley Durrleman, Marcel Prastawa, Guido Gerig

    Research output: Contribution to journalArticlepeer-review


    Many problems in medicine are inherently dynamic processes which include the aspect of change over time, such as childhood development, aging, and disease progression. From medical images, numerous geometric structures can be extracted with various representations, such as landmarks, point clouds, curves, and surfaces. Different sources of geometry may characterize different aspects of the anatomy, such as fiber tracts from DTI and subcortical shapes from structural MRI, and therefore require a modeling scheme which can include various shape representations in any combination. In this paper, we present a geodesic regression model in the large deformation (LDDMM) framework applicable to multi-object complexes in a variety of shape representations. Our model decouples the deformation parameters from the specific shape representations, allowing the complexity of the model to reflect the nature of the shape changes, rather than the sampling of the data. As a consequence, the sparse representation of diffeomorphic flow allows for the straightforward embedding of a variety of geometry in different combinations, which all contribute towards the estimation of a single deformation of the ambient space. Additionally, the sparse representation along with the geodesic constraint results in a compact statistical model of shape change by a small number of parameters defined by the user. Experimental validation on multi-object complexes demonstrate robust model estimation across a variety of parameter settings. We further demonstrate the utility of our method to support the analysis of derived shape features, such as volume, and explore shape model extrapolation. Our method is freely available in the software package deformetrica which can be downloaded at

    Original languageEnglish (US)
    Pages (from-to)1-17
    Number of pages17
    JournalMedical Image Analysis
    StatePublished - Jul 1 2017


    • 4D shape modeling
    • Geodesic
    • LDDMM
    • Multi-object complex
    • Shape regression
    • Spatiotemporal

    ASJC Scopus subject areas

    • Radiological and Ultrasound Technology
    • Radiology Nuclear Medicine and imaging
    • Computer Vision and Pattern Recognition
    • Health Informatics
    • Computer Graphics and Computer-Aided Design


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