# Hierarchical segmentation

Image segmentation starts by dividing a digital image into homogenous regions or objects according to a particular perceptual feature, such as homogeneity in color tone. Hierarchical segmentation algorithms analyse simultaneously the image at several different scales of analysis. Their output is not a single partition, but a hierarchy of regions or data structure that captures different partitions for different scales of analysis (Guigues 2003, Guigues et al. 2006, Trias-Sanz 2006). The algorithm starts with an initial over-segmentation (e.g. segmenting almost each pixel on a different own region) and uses this level as a base for the construction of subsequent significant levels.

The segmentation process is guided by an energy of the form:

E = D + µC

where,

*D* is a measure of goodness-of-fit (how well the segmentation fits to the original image, better fits give lower values of D); *C* is a measure of segmentation complexity (less complex solutions give lower values of C); and µ is a dimensional parameter, the scale parameter. The parameter balances between a perfect µ fit to the original data, consisting of one segmentation region for each pixel in the original image, and the simplest segmentation, consisting of a single region containing the whole image (Guigues et al. 2006) (see Figures 1 and 2 for a graphic representation of concepts related to hierarchical segmentation). The level of segmentation can be adjusted gradually from the finest to the coarsest depending of the image complexity.

Figure 1. Graphical depiction of concepts related to hierarchical segmentation. The diagram on the left shows partitions of an image at four different scales µ. The partition at the top has the highest µ and is therefore the coarsest (it is the trivial partition containing only one cell for the whole image); the partition at the bottom is the finest. The diagram on the right shows the cells of the corresponding hierarchy, with the links indicating merging events. Modified from Trias-Sanz (2006)

Figure 2. Graphical representation of concepts related to hierarchical segmentation. The figure shows partitions of an underwater benthic image at three different scales of segmentation. The partition on the left has the lowest µ and is the finest: (initial over-segmentation of the image), the partition on the right has a higher µ and is simpler (containing only few cells for the whole image). From Teixidó N, Albajes-Eizagirre A, Bolbo D, Le Hir E, Demestre M, Garrabou J, Guigues L, Gili JM, Piera J, Prelot T, Soria-Frisch A (2011) Hierarchical Segmentation based software for Cover Classification Analyses of Seabed Images (Seascape). Mar Ecol Prog Ser 431:45-53. Download the paper (3,42 Mb PDF).