Percolation approach to digital comparative holography via optical flow investigation

Abstract

Digital comparative holography is an important method deployed for working on verifying the body or contortion of two corresponding entities with different micro architecture. The percolation theory is a useful mathematical theory that describes the behavior of connected clusters in a randomly generated graph which can be derived from a picture. Percolation theory is also regarded as a model for displaying a phase transition and it demonstrates the so called critical phenomenon. This in digital comparative holography context implies a drastic change in characteristics. In this paper a novel approach has been taken by utilizing a mathematical theory being the percolation theory to transfer the image achieved by comparative holography in three-dimensional site-percolated form. This operation empowers us to analyze the test object and the behavior of its cluster representation by the help of an image investigation technique being the optical flow investigation. Finally the universality principle will be used to explain and demonstrate the interaction of clusters and how distance and rotation can remarkably affect the optical flow directions.