1. Introduction.- 1.1 Image Segmentation and Compression.- 1.2 Overview.- 2. Statistical Classification.- 2.1 Bayes Optimal Classification.- 2.2 Algorithms.- 2.3 Markov Random Fields.- 2.4 Markov Mesh.- 2.5 Multiresolution Image Classification.- 3. Vector Quantization.- 3.1 Introduction.- 3.2 Transform VQ.- 3.3 VQ as a Clustering Method.- 3.4 Bayes Vector Quantization.- 4 Two Dimensional Hidden Markov Model.- 4.1 Background.- 4.2 Viterbi Training.- 4.3 Previous Work on 2-D HMM.- 4.4 Outline of the Algorithm.- 4.5 Assumptions of 2-D HMM.- 4.6 Markovian Properties.- 4.7 Parameter Estimation.- 4.8 Computational Complexity.- 4.9 Variable-state Viterbi Algorithm.- 4.10 Intra- and Inter-block Features.- 4.11 Aerial Image Segmentation.- 4.12 Document Image Segmentation.- 5. 2-D Multiresolution Hmm.- 5.1 Basic Assumptions of 2-D MHMM.- 5.2 Related Work.- 5.3 The Algorithm.- 5.4 Fast Algorithms.- 5.5 Comparison of Complexity with 2-D HMM.- 5.6 Experiments.- 6. Testing Models.- 6.1 Hypothesis Testing.- 6.2 Test of Normality.- 6.3 Test of the Markovian Assumption.- 7. Joint Compression and Classification.- 7.1 Distortion Measure.- 7.2 Optimality Properties and the Algorithm.- 7.3 Initial Codebook.- 7.4 Optimal Encoding.- 7.5 Examples.- 7.6 Progressive Compression and Classification.- 8. Conclusions.- 8.1 Summary.- 8.2 Future Work.