Optimization of chamfer masks using Farey sequences and kernel dimensionality

Farey sequences have captured the attention of several researchers because of their wide applications in polygonal approximation, generation of Ford circles, and shape analysis. In this work, we extend the applications of these sequences to optimize chamfer masks for computation of distance maps in images. Compared with previous methods, the proposed method can more effectively generate optimal weights from larger chamfer masks without considering multiple and rather complex defining variables of the masks. Furthermore, our work demonstrates the relationship between size of the chamfer kernel, Farey sequence, and optimal weights of the chamfer mask. This interesting relationship, which may be useful in various image processing and computer vision tasks, has never been revealed by any other previous study. Results from the current research may advance our understanding on the applications of Farey sequences in computational geometry and vision-related tasks. To allow reproducibility of the results, implementation codes and datasets can be accessed in the public repository at https://www.mathworks.com/matlabcentral/fileexchange/71652-optimization-of-chamfer-masks.