Contents 3.3 Partitional Clustering 89 3.4 Clustering Software 133 3.5 Clustering Methodology 135 3.6 Summary 141 4 CLUSTER VALIDITY 143 4.1 Background 143 4.2 Indices of Cluster Validity 160 4.3 Validity of Hierarchical Structures 165 4.4 Validity of Partitional Structures 172 4.5 Validity of Individual Clusters 188 4.6 Clustering Tendency 201 4.7 Summary 222 5 APPLICATIONS 223 5.1 Image Processing 224 5.2 Image Segmentation by Clustering 225 5.3 Segmentation of Textured Images 227 5.4 Segmentation of Range Images 232 5.5 Segmentation of Multispectral Images 235 5.6 Image Registration 237 5.7 Summary 240 A PATTERN RECOGNITION 241 B DISTRIBUTIONS 246 B.1 The Gaussian Distribution 246 B.2 The Hypergeometric Distribution 249 LINEAR ALGEBRA 252 D SCATTER MATRICES 258 E FACTOR ANALYSIS 260