Collection Statistical Modeling for Shapes and Imaging
Organizer(s)
Date(s)
04/05/2024
From currents to oriented varifolds for data fidelity metrics; growth models for computational anatomy
In this talk, I present a general setting that extends the previous frameworks of currents and varifolds for the construction of data fidelity metrics between oriented or nonoriented geometric shapes like curves, curve sets or surfaces. The choice of the metric reduces to scalar functions with only one or two scale parameters that parametrize families of kernels which can be easily computed without requiring any kind of parametrization of shapes. In the second part of this talk, I present a growth model based on large diffeomorphic partial mappings. The evolution of the shape is described by the joint action of a deformation process and a creation process. The necessity for partial mappings leads 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.
