Some Properties of Interpolations Using Mathematical Morphology

The Problem of interpolation between two images is defined as - given two images, one at time t=0 and another at t=T, one must estimate the series of intermediate images for all intermediate time steps. This problem is not well posed, in the sense that without further constraints, there are many possible solutions. The solution is thus usually dictated by the choice of the constraints/assumptions, which in turn relies on the domain of application. In this article, we follow the approach of obtaining a solution to the interpolation problem using the operators from mathematical morphology (MM). These operators have an advantage of preserving structures since the operators are defined on sets. In this paper, we explore the solutions obtained using MM, and provide several results along with proofs which corroborates the validity of the assumptions, provide links among existing methods and intuition about them. We also summarize few possible extensions and prospective problems of current interest.