Algorithms for homotopy classification of binary images

In this note using the concept of the index of pixel of a binary image [E. V. Shchepin and G. M. Nepomnyashchyi, On Topology Analysis of Images. MIP, Moscow (1990)], several algorithms for their homotopy classification are investigated. Defining the concept of a computer homotopy, we consider, in particular, the algorithm that assigns to any class of homotopy equivalent binary images a directed tree with a root