## Recursive Hierarchical Image Segmentation (RHSEG)

With the addition of alternating iterations of spectral clustering in the HSEG algorithm, the computational demands significantly increase. This is caused primarily because of the requirement to update or calculate the dissimilarity criterion values for all pairs of regions in steps 2 and 8. For a 1024 x 1024 pixel image, this leads to the order of 10000000 comparisons in the initial processing stage.

Nevertheless, this computational obstacle is surmounted by the recursive formulation of the HSEG algorithm, RHSEG. This recursive form not only limits the number of comparisons bwetween spatially non-adjacent regions to a more reasonable number, but also lens itself to a straightforward and efficient implementation on parallel computing platforms.

In regards to the definition of RHSEG, it follows the same as the RHSWO and includes the definition of processing window artifact elimination.

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Fig. 8. Segmentation results for RHSEG with spclust_wght=0.1, processing window artifact elimination, and with the BSMSE dissimilarity function. (a) Region mean image for the 13 region segmentation result and global dissimilarity value of 9.9326. (b) Hierarchical boundary map for (a). (c) Region mean image for the 9 region segmentation and global dissimilarity value of 11.6204. (d) Hierarchical boundary for (c).