Geometrical growth models for computational anatomy

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Date(s) - 23/02/2018
14 h 00 min - 15 h 00 min

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After brief illustrations of shape representations by currents, varifolds and oriented varifolds, I will present a growth model for longitudinal shape analysis grounded on the geometric concept of a group of deformations acting on embedded shapes that has proved to be highly efficient to compare and quantify diffeomorphic morphometric changes. However, the analysis of medical imaging data also requires the processing of more complex transformations that may not be diffeomorphic, at least in a biological sense. One reason might be a gradual creation of new material. The evolution of the shape can then be described by the joint action of a deformation process and a creation process. The necessity for partial mappings leads then to a time-varying dynamic that modifies the action of the group of deformations. Ultimately, growth priors are integrated into a new optimal control problem for assimilation of time-varying surface data represented by currents or varifolds. This new model is inspired by the deployment of animal horns and will be applied to it.

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