Localisation of topological features using 3D object representations

摘要

Holes, tunnels and cavities of two-dimensional (2D) and 3D objects are concise topological features used for object representation and recognition. In this study, the authors are representing any cubical tessellation (regular or not) of 2D and 3D objects and dealing with the extraction and the localisation of these features by using homology-based approach. The cubical tessellation (regular or not) of objects is translated into algebraic language suitable for building a reduced cell complex structure. The extraction of the homology information is equivalent to the estimation of the rank of the homology groups of the reduced complex. The localisation means the reconstruction of the object cycles from the generators of the homology groups. The reduction operation of the cell complex leads to an efficient algorithm. Note that, several objects can be analysed simultaneously by the algorithm conceived in our approach. This algorithm is validated by using 2D and 3D binary images.