Fig. 1: General structure of the AD-SVFD model.

The proposed approach leverages deep learning techniques to perform the diffeomorphic registration of vascular anatomies to a reference. Invertible ambient space deformations are modeled as solutions at unit time of ODEs, whose right-hand sides are parametrized by neural networks. The source and template geometries, represented as point clouds, are provided as input to AD-SVFD. The direct (top part of the image) and inverse (bottom part of the image) transforms are obtained by integrating the flow equations forward and backward in time, respectively. Geodesic paths can be visualized by morphing the input shapes at intermediate stages during the ODE integration. Generalization capabilities are enabled by associating each source shape with a trainable latent code (in green). The baseline model is optimized by minimizing the Chamfer distance (CD) between the mapped and the target geometries. Pointwise errors are quantified through the forward local distance (FLD), expressed in cm, namely the distance of each point in the mapped geometry from the closest one in the target.