Image segmentation by Dirac needles

A novel fuzzy set evolution is proposed for digital image binary segmentation into foreground and background areas. The scheme is derived from a goal function which considers only within-class variances for pixel values. The discrete form of the cost function gradient leads to a simple recurrent equation for membership functions. The equation has the single impulsive factor approximating Diracpsilas delta functional. The fuzzy set sequence stabilizes rapidly and the resulting binary segmentation has high degree of matching with intuition of human image observer. The experiments with synthetic and natural images show the high potential of the proposed method. It can be applied to grayscale, color, and multi-spectral images with smooth and crisp edges, as well.