Operations, Methods and Algorithm for Quasi-Optimal Clustering in the Problem of Preprocessing of Aerospace Earth Images

This paper considers operations on pixel clusters, image segments; methods of intermediate quality improvement of a given partition and algorithm for generating a hierarchical sequence of piecewise-constant partitions of the original image. The algorithm utilizes total squared error E or standard deviation σ to assess the partition quality. The basis of software-algorithmic toolkit are four operations on pixel clusters and image segments: "merge"–merging the pair of clusters into one, "divide"–dividing cluster into two source ones, "split"–selecting a subset of pixels into a separate cluster and "correct"–reclassifying parts of pixels by excluding them from one cluster and assigning them to another. A coarse hierarchy of clusters (segments) is constructed using the "merge" and "divide" operations. The pair of "split" and "correct" operations modifies an existing hierarchy. The combination of "merge" and "divide" operations forms SI-method for quality improvement of the image partition. SI-method executes as long as there is a triple of segments, the separation of one of which and combination of two other is accompanied by decrease of standard deviation. The "correct" operation generates K-meanless method – the extension of K-means method. K-meanless method redistributes groups of pixels from cluster to cluster until this process reduces the overall value of standard deviation. Aerospace Earth images, including full-dimension, from SIPI USC open international database were used to test run the proposed quasi-optimal clustering algorithm in segmentation and clustering modes. It has been established that clustering in comparison with segmentation gives significantly more accurate results, both in visual perception and in the standard deviation value.