Statistical Region Merging (SRM)
Statistical Region Merging (SRM) [1] is a clustering technique also used directly for image segmentation.
A region $R$ is a set of pixels and the cardinality $\lvert R \rvert$ determines how many pixels are in a region.
Starting with a sorted set of connected regions (w. r. t. some distance function $f$), two regions $R$ and $R'$ are merged if the qualification criteria $\vert \overline{R'}-\overline{R} \vert \leq \sqrt{b^2(R)+b^2(R')}$ with $b(R) = g \cdot \sqrt{\frac{\ln \frac{\mathcal{R}_{\lvert R \rvert}}{\delta}}{2Q\lvert R \rvert}}$ is fulfilled.
Therefore, $\mathcal{R}_{\lvert R \rvert}$ is the set of regions with $\lvert R \rvert$ pixels.
Typically $Q$ is chosen as $Q \in \lbrack 256, 1\rbrack$ and $\delta = \frac{1}{\lvert I \rvert^2}$.
The $Q$ parameter mainly influences the merging process. An example is given in Figure \ref{fig:srmcolor}. Choosing lower values for $Q$, the regions are becoming more coarse. Using a union-find structure, the segmentation does not need to be recalculated for each $Q$ level. For the step from $q$ to $\frac{q}{2}$, simply the qualification criteria needs to be applied to the regions from the $q$ result. A MATLAB implementation can be found in [2].
[1] Nock R, Nielsen F. Statistical region merging. IEEE Transactions on PAMI. 2004;26:1452–8.
[2] Boltz S. Statistical region merging matlab implementation; 2014. Available
from: http://www.mathworks.com/matlabcentral/fileexchange/
25619-image-segmentation-using-statistical-region-merging. Accessed 12 Dec 2013.
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