On satellite image segmentation via piecewise constant approximation of selective smoothed target mapping

Abstract

Mostly motivated by the crop field classification problem and the automated computational methodology for the extraction of agricultural fields with a uniform crop distribution from satellite data, we propose an indirect approach for the image segmentation which is based on the concept of a piecewise constant approximation of the slope-based vegetation indices. We discuss in detail the consistency of the new statement of segmentation problem and its solvability. We mainly focus on the rigor mathematical substantiation of the proposed approach, deriving the corresponding optimality conditions, and we show that the new optimization problem is rather a flexible and powerful model of variational image segmentation problems. We illustrate the efficiency of the proposed algorithm by numerical experiences with images that have been delivered by satellite Sentinel-2.