Multi-surface quasi-isometric flattening of the cortex

Mapping convoluted surface of the cortex to a canonical space has been widely used in brain functional imaging. Apart from different geometrical features proposed to be preserved during mapping, geometrical features of the cortex tissue differ when traveling from the white matter to the pial boundaries. We propose, for the first time, to represent cortical volume with a set of partial iso-surfaces. Iso-surfaces are defined as the locus of points at constant distance ratio from the cortex boundaries. Such representation provides a specialized frame of reference within the cortex which advocates physiological evidence that active neurons are mainly oriented locally normal to the cortex surface. Furthermore, multi-surface representation is applied to flatten the whole set of iso-surfaces on a planar environment simultaneously. Multi-surface flattening improves flattening performance in terms of lowering distortion variance on the set of iso-surfaces.