The generalized spherical homeomorphism theorem for digital images

The spherical homeomorphism conjecture, proposed by Shattuck and Leahy in 2001, serves as the backbone of their algorithm to correct the topology of magnetic resonance images of the human cerebral cortex. Using a canonical image-thickening technique and the authors' previously proven 'spherical homeomorphism theorem for surfaces,' we formulate and provea spherical homeomorphism theorem which is valid for all digital images when utilizing the (26,6)-connectivity rule. Index Terms--Digital topology, spherical homeomorphism.