It is proposed a novel method that optimizes nonlinear filters by unsupervised learning using a novel definition of morphological pattern spectrum, called "morphological opening/closing spectrum (MOCS)." The MOCS can separate smaller portions of image objects from approximate shapes even if the shapes are degraded by noisy pixels. Our optimization method analogizes the linear low-pass filtering and Fourier spectrum: filter parameters are adjusted to reduce the portions of smaller sizes in MOCS, since they are regarded as the contributions of noises like high-frequency components. This method has an advantage that it uses only target noisy images and requires no example of ideal outputs. Experimental results of applications of this method to optimization of morphological open-closing filter for binary images are presented.
mathematical morphology, pattern spectrum, nonlinear filter, filter optimization, learning, genetic algorithm