Fuzzy image processing with topological theory

We extend the theory of finite topology that we constructed before to a fuzzy topological space by using fuzzy sets. Gray-scale images can be processed based on this fuzzy topology and color images can be processed by regarding the color image as multi-dimensional gray-scale images. We aim to construct a theory for systematic image processing by examining methods of image processing with fuzzy topology. We believe these theories will help organize and provide a theoretical foundation for image processing techniques.