Representing 3D objects and computing homology and localization using homology-based approach.

What is it about?

The approach we propose has the same philosophy as state-of-art approaches: giving an object representation of 2D or 3D image in its initial subdivision; converting this initial subdivision to block-based representation with its irregular grid; modelling each rectangular block as cubical box and using splitting process to standardise common boundaries with adjacent boxes; building the corresponding cell complex using collections of cubical boxes (new complex structure for homology and localization).

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Why is it important?

Representing any cubical tessellation (regular or not cubical subdivision) of 2D and 3D objects using cubical box entities to generate new complex structure with few cells that is topologically equivalelent to original data. This structure leads to compute the homology and realize the localization of homology cycles with less run time and memory.