A Study of Graph Cuts Theoretic Concepts with Digital Signal Processing with Mathematical Concepts

Abstract

Optimization of variety of objective functions using graph cuts in different move spaces is studied in detail in the paper. The study concludes that, an objective function can be minimized using graph cuts provided it is FNO- optimizable. Characterizations of two classes of FNO- optimizable functions (O² and O³) are given and many mathematical results in this regard are proved in the paper. These characterizations contribute in easily identifying the image processing problems which can be addressed through graph cuts notion. However, further exploration of the concepts studied/ defined in the paper is required to strengthen the designed mathematical framework. Due to programming limitation on our part, we could not construct a computationally time-effective computer program encoding the graph-cuts model. There is a good scope of improvement in the implementation of graph theoretic models designed in the present work on appropriate programming platform.