Information theory (IT) tools, widely used in many scientific fields such as engineering, physics, genetics, neuroscience, and many others, are also useful transversal tools in image processing. In this book, we present the basic concepts of IT and how they have been used in the image processing areas of registration, segmentation, video processing, and computational aesthetics. Some of the approaches presented, such as the application of mutual information to registration, are the state of the art in the field. All techniques presented in this book have been previously published in peer-reviewed conference proceedings or international journals. We have stressed here their common aspects, and presented them in an unified way, so to make clear to the reader which problems IT tools can help to solve, which specific tools to use, and how to apply them. The IT basics are presented so as to be self-contained in the book. The intended audiences are students and practitioners of image processing and related areas such as computer graphics and visualization. In addition, students and practitioners of IT will be interested in knowing about these applications.

1. Information theory basics -- 1.1 Entropy -- 1.2 Relative entropy and mutual information -- 1.3 Decomposition of mutual information -- 1.4 Inequalities -- 1.4.1 Jensen's inequality -- 1.4.2 Log-sum inequality -- 1.4.3 Jensen-Shannon inequality -- 1.4.4 Data processing inequality -- 1.5 Entropy rate -- 1.6 Entropy and coding -- 1.7 Continuous channel -- 1.8 Information bottleneck method -- 1.9 f-divergences -- 1.10 Generalized entropies -- 1.11 The similarity metric. 2. Image registration -- 2.1 The registration pipeline -- 2.1.1 Spatial transform -- 2.1.2 Interpolation -- 2.1.3 Metric -- 2.1.4 Optimization -- 2.2 Similarity metrics based on Shannon's information measures -- 2.2.1 Information channel -- 2.2.2 Joint entropy -- 2.2.3 Mutual information -- 2.2.4 Normalized measures -- 2.3 Probability density function estimation -- 2.3.1 Histogram estimation -- 2.3.2 Parzen window estimation -- 2.3.3 Entropic spanning graphs -- 2.4 High-dimensional information measures including spatial information -- 2.5 Image registration based on f -divergences -- 2.6 Similarity measures based on generalized entropies -- 2.7 Measures based on the similarity metric -- 2.8 Image fusion -- 2.8.1 Communication channel -- 2.8.2 Specific information -- 2.8.3 Fusion criteria -- 2.8.4 Visualization. 3. Image segmentation -- 3.1 Maximum entropy thresholding -- 3.1.1 Entropy -- 3.1.2 Relative entropy -- 3.2 Thresholding considering spatial information -- 3.2.1 Grey-level co-occurrence matrix -- 3.2.2 Minimum spatial entropy thresholding -- 3.2.3 Excess entropy -- 3.3 Evolving curves -- 3.4 Information bottleneck method for image segmentation -- 3.4.1 Split-and-merge algorithm -- 3.4.2 Histogram clustering -- 3.4.3 Registration-based segmentation. 4. Video key frame selection -- 4.1 Related work and first IT-based approaches -- 4.2 Key frame selection based on Jensen-Shannon divergence and Jensen-Renyi divergence -- 4.2.1 Jensen-Renyi divergence -- 4.2.2 The core computational mechanism -- 4.2.3 Locating shots, subshots, and key frames -- [4.3] Key frame selection techniques using Tsallis mutual information and Jensen-Tsallis divergence for shots with hard cuts -- 4.3.1 Mutual information-based similarity between frames -- 4.3.2 Jensen-Tsallis-based similarity between frames -- 4.3.3 Keyframe selection -- 4.4 Experimental results -- 4.4.1 Results on JS and JR-based methods -- 4.4.2 Results on JT and TMI driven techniques -- 4.5 Conclusion. 5. Informational aesthetics measures -- 5.1 Introduction -- 5.2 Origins and related work -- 5.3 Global aesthetic measures -- 5.3.1 Shannon's perspective -- 5.3.2 Kolmogorov's perspective -- 5.3.3 Zurek's perspective -- 5.4 Compositional aesthetic measures -- 5.4.1 Order as self-similarity -- 5.4.2 Interpreting Bense's channel -- 5.5 Informational analysis of Van Gogh's periods -- 5.6 Towards Auvers period: evolution of Van Gogh's style -- 5.6.1 Randomness -- 5.6.2 Structural complexity -- 5.6.3 Artistic analysis -- 5.7 Color and regional information. A. Digital-image-palette -- Bibliography -- Authors' biographies.