Geometric realization conjecture for path triangulations in digital images

A path triangulation is a triangulation obtained from paths in a planar cell complex, and a triangulated digital image is a digital image equipped with such a triangulation. Geometric realization conjecture. Every path triangulation has a geometric realization in some triangulated digital image. This conjecture proposes a bridge from path triangulations of planar cell complexes to digital topology, where geometric realizations could relate the resulting complexes to digital fundamental groups and related invariants.