Editing Image segmentation (section)

== Dual clustering method ==

This method is a combination of three characteristics of the image: partition of the image based on histogram analysis is checked by high compactness of the clusters (objects), and high gradients of their borders. For that purpose two spaces have to be introduced: one space is the one-dimensional histogram of brightness ''H'' =&nbsp;''H''(''B''); the second space is the dual 3-dimensional space of the original image itself ''B'' =&nbsp;''B''(''x'',&nbsp;''y''). The first space allows to measure how compactly the brightness of the image is distributed by calculating a minimal clustering kmin. Threshold brightness T corresponding to kmin defines the binary (black-and-white) image&nbsp;– bitmap ''b'' =&nbsp;''φ''(''x'',&nbsp;''y''), where ''φ''(''x'',&nbsp;''y'') =&nbsp;0, if ''B''(''x'',&nbsp;''y'')&nbsp;<&nbsp;''T'', and ''φ''(''x'',&nbsp;''y'') =&nbsp;1, if ''B''(''x'',&nbsp;''y'')&nbsp;≥&nbsp;''T''. The bitmap ''b'' is an object in dual space. On that bitmap a measure has to be defined reflecting how compact distributed black (or white) pixels are. So, the goal is to find objects with good borders. For all ''T'' the measure ''M''<sub>DC</sub> =&nbsp;''G''/(''k''&nbsp;×&nbsp;''L'') has to be calculated (where ''k'' is difference in brightness between the object and the background, ''L'' is length of all borders, and ''G'' is mean gradient on the borders). Maximum of MDC defines the segmentation.<ref>[http://gth.krammerbuch.at/sites/default/files/articles/AHAH%20callback/01_Guberman_KORR.pdf] {{Webarchive|url=https://web.archive.org/web/20171013224758/http://gth.krammerbuch.at/sites/default/files/articles/AHAH%20callback/01_Guberman_KORR.pdf|date=13 October 2017}}[[Guberman Shelia (Shelija)|Shelia Guberman]]<span>, Vadim V. Maximov, Alex Pashintsev Gestalt and Image Understanding. GESTALT THEORY 2012, Vol. 34, No.2, 143–166.</span></ref>