Multi-band image classification using membership functions

We propose a method for remotely sensed multi-band image classification using membership function. Our aim is to classify the image as classes with use-defined number from a prior knowledge of remote sensing, and every point is finally labeled as the class with the highest value of membership function. This classification is reduced to a minimization problem of a functional whose arguments are membership functions. The minimization problem is solved via iteration with the initial value from the classification result of fuzzy C-means. Our method refines the result of fuzzy C-means and produces a smoother and less cluttered classification. Two novelties compared with traditional membership methods are in this paper. First, unconstrained functional is used. Constraints are added in the literature since membership functions need to be positive and with sum equal to one, which is avoided here by variable substitution. Second, intermediate variables are introduced so that a big complicated functional is separated as three relatively easy functionals that can be solved with fast speed. The experimental results from Google Map and Quickbird images show the validity of this approach.