Image Segmentation: A Rough-set Theoretic Approach - Rough Fuzzy Image Analysis: Foundations and Methodologies - page 196

(10.3a) (10.3b)

(10.3c) (10.3d)

FIGURE 10.3: Segmentation comparison. (a)Test image22013(b)Histogram based seg-
mentation (c)Histon based segmentation (d)Roughness index based segmentation

TheProbabilisticRandIndex(PRI)
The Probabilistic Rand Index (PRI) proposed by Unnikrishnan and Hebert (Unnikrishnan
et al., 2005) is a generalization of Rand Index (RI) (Rand, 1971), which allows comparison
of test segmentation with multiple ground-truth images through soft non-uniform weighting
of pixel pairs as a function of the variability in the ground-truth set. The RI counts the
fraction of pairs of pixels whose labels are consistent between the computed segmentation
and the ground truth. PRI is an extension of RI which averages the result across all manual
segmentations of a given image.

Consider an image I = fI 1 ;I 2 ;:::;I N g consisting ofNpixels. Let the set of manual
segmentations (ground-truth images) of the imageIbe fS 1 ;S 2 ;:::;S K g and let S t be the
test segmentation which is to be compared with manually labeled set. Let the label of a
point I i be denoted by l S t i in segmentation S t and by l S i in the manually segmented image