Cortically Based Optimal Transport

We introduce a model for image morphing in the primary visual cortex V1 to perform completion of missing images in time. We model the output of simple cells through a family of Gabor filters and the propagation of the neural signal accordingly to the functional geometry induced by horizontal connectivity. Then we model the deformation between two images as a path relying two different outputs. This path is obtained by optimal transport considering the Wasserstein distance geodesics associated to some probability measures naturally induced by the outputs on V1. The frame of Gabor filters allows to project back the output path, therefore obtaining an associated image stimulus deformation. We perform a numerical implementation of our cortical model, assessing its ability in reconstructing rigid motions of simple shapes.