  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 rigidi motions of simple shapes.

Analysis of PDEs;Metric Geometry