A Homology-based Algorithm for the Analysis of Structures

Observations of the microstructure of objects by means of a microscope are carried out in different technical fields. The state organization of iron with quenching-annealing and the human tissue by biopsy are typical examples. Since the results of such observations depend on the skills of the technician, objective methods are required for the quantification of structures. When the observed structures are very complex, the performance of pattern recognition and Fourier methods is not satisfactory. In this talk, I will introduce an algorithm based on the concept of homology. By applying this method, we obtain rigorous quantitative estimates of a structure. Several examples of its application will be presented.