Technology modification for distance calculation between pairs of adjacent clusters in multilevel thresholding

DOI: 10.34759/trd-2021-118-13

Аuthors

Khanykov I. G.

Saint Petersburg State University of Aerospace Instrumentation, 67, Bolshaya Morskaya str., Saint Petersburg, 190000, Russia

e-mail: igorioniak@mail.ru

Abstract

The article considers the multi-threshold images processing technology, which consists in generating a series of partitions into clusters for the original grayscale image. Each image is being assigned to its own brightness histogram, which every column is a separate cluster of pixels. A cluster is being characterized by the number of pixels it contains and the average brightness value. All pairs of adjacent clusters are being browsed while traversing over the brightness histogram. The pair of clusters with the minimum distance between them is being selected for merging at the end of the histogram traversing. In general case, 256 partitions are available by the number of the gray levels. In a special case, when the image consists of K grey levels (K < 256), and there is a need to find a partition from t levels of grey, the necessity to generate K — t partition into clusters will arise. With the original version of the multi-threshold processing method, the distance between the pairs of adjacent clusters was computed through the product of the intra-class and interclass dispersions, which requires considering the brightness histogram as a function of the probability density. The original technique is full of complex design equations. The modification proposed in the presented work allows computing the distance between the pairs of adjacent clusters by the increment of the total quadratic error. This modification is justified by a number of reasons. Firstly, the number of computational operations reduces twofold. Secondly, the accumulated value of the total quadratic error, expressed through the mean-square deviation, serves as the quality indicator of the image partitioning to clusters. Thirdly, the set of the total quadratic errors, characterizing the series of partitions into clusters, forms optimal sequence of partitions as evidenced by the convex curve.

Keywords:

multilevel thresholding, standard deviation, piecewise-constant partition, grayscale image, pixel clusters

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