Hierarchical Clustering from ICA Mixtures - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 97

Table 4.2 Inter-object and
intra-object mean distances of
Fig. 4.7

Object box (a) onion (b)

box (a) 12.89 114.90

onion (b) 114.90 13.81

eight objects grouped into three main kinds of objects. The tree outlined by the
dendrogram clearly shows groupings of objects based on similar content and
suitable similarities between 'families' of objects, e.g., cars were more similar to
cans than onions. Thus, three groupings of the objects were found: cars, cans, and
vegetables.
Figure 4.9 shows a second set of object images from the COIL-100 database.
These objects were recognized and classified following the procedure explained
above; the results are shown in Fig. 4.10 . The clustering algorithm found mean-
ingful groupings that describe the objects at higher hierarchy levels from the basis
extracted in ICA mixtures at the bottom of the hierarchy.

4.5.2 Image Segmentation

The proposed algorithm was applied to segmentation of natural images. The goal
was to obtain a meaningful bottom-up structure merging several zones of an
image. Figure 4.11 shows an image with nine zones, some of which are clearly
different and other which are more or less similar to each other. The total size of
the image is 449 9 512 pixels. In all the experiments of image segmentation the
following was done: (i) a set of 1,000 image patches (windows) of 8 9 8 pixels
were taken at random location from each zone, (ii) the normalization, whitening,
and dewhitening procedure explained above was applied, (iii) the number of
classes of the Mixca algorithm was configured to be the number of zones of the
image, (iv) supervised training was used to estimate the ICA parameters for
the lowest level of the hierarchy, and (v) a hierarchical representation using the
proposed clustering algorithm was obtained.
The dendrogram in Fig. 4.11 shows how the zones are merged from the basis
functions. Four segments have been found: sky, cone, structure (roof) and persons,
and stairs. These segments are grouped into two broad segments distinguishing the
kinds of basis functions that correspond to the part of the image that mainly
contains portions of sky, and those zones that correspond to patches where there is
a predominant portion of stairs (high frequency). The dendrogram also shows the
distances at which the clusters are merged; it can be used as a similarity measure of
the zones of the image. The bottom zones are merged at low distances due to the
high similarity in borders. Therefore, the hierarchical structures obtained from the
zones of the natural image allow for an intuitive interpretation of the scene from
different degrees of generalization. This is significant since it can be related with a
complex abstraction process.