How many zero crossings? A method for structure-texture image decomposition

Structure-texture image decomposition aims to interpret an image as the superposition of a structural component and a textural component, which is a very challenging problem, yet opens the door to many applications once solved successfully. The number of zero crossings in derivatives is utilized as a type of coarseness measure to perform structure-aware image smoothing. By this measure, the smoothed signal is required to have a smaller number of intervals over which it is monotonically increasing or decreasing (convex or concave), as well as to be similar to the original signal. We propose an efficient method for evaluating the proximity operator of the number of zero crossings to solve the resulting optimization problem. Our method is also validated with applications in inverse halftoning, smoothing photos captured from screen, and text image deblurring.