Section: New Results

Sparse Adaptive Parameterization of Variability in Image Ensembles

Participants : Stanley Durrleman [Correspondant] , Sarang Joshi, Stéphanie Allassonnière.

We introduce a new parameterization of diffeomorphic deformations for the characterization of the variability in image ensembles. Dense diffeomorphic deformations are built by interpolating the motion of a finite set of control points that forms a Hamiltonian flow of self-interacting particles. The proposed approach estimates a template image representative of a given image set, an optimal set of control points that focuses on the most variable parts of the image, and template-to-image registrations that quantify the variability within the image set. The method automatically selects the most relevant control points for the characterization of the image variability and estimates their optimal positions in the template domain. The optimization in position is done during the estimation of the deformations without adding any computational cost at each step of the gradient descent. The selection of the control points is done by adding a $L^1$ prior to the objective function, which is optimized using the FISTA algorithm.

Figure 2. Left: template image estimated from 20 images of the US postal database. Momentum vectors are placed at the most variable places and paramterize mappings from the template to each image in the data set. Right: sample images from the data set (top) and template image deformed to match the corresponding sample image (bottom)

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