Spatially-Variant Structuring Elements Inspired by the Neurogeometry of the Visual Cortex

The V1-region of the primary visual cortex performs contour integration in the early mammalian visual system. The geometry of the neural connections of the V1-region has been mathematically described as a roto-translational continuous space. In this work, a bio-inspired methodology for processing 2D images based on the V1-region neurogeometrical structure is proposed. The input image is first transformed into the 3D roto-translational space. Then spatially-variant mathematical morphology operators using helicoidal structuring elements are applied in order to mimic the neural processing in the primary visual cortex. Finally, the output is projected back to the 2D cartesian space. Some illustrative straightforward applications of this methodology are presented for contour-completion and object-occlusion 2D problems.