Color is a sensation generated both by the interaction of the visual sensors in the eyes with the natural environment and by the elaboration of visual information by higher brain functions. This book presents the mathematical framework needed to deal with several models of color processing of digital images. The book starts with a short yet exhaustive introduction to the basic phenomenological features of color vision, which are constantly used throughout the book. The discussion of computational issues starts with color constancy, which is dealt with in a rigorous and self-contained mathematical setting. Then, the original Retinex model and its numerous variants are introduced and analyzed with direct discrete equations. The remainder of the book is dedicated to the variational analysis of Retinex-like models, contextualizing their action with respect to contrast enhancement.  

Table of Contents:
Preface ix Chapter 1. Rudiments of Human Visual System (HVS) Features 1 1.1. The retina 1 1.1.1. Photoreceptors: rods and cones 2 1.2. Adaptation and photo-electrical response of receptors 4 1.3. Spatial locality of vision 5 1.4. Local contrast enhancement 6 1.5. Physical vs. perceived light intensity contrast: Weber- Fechner’s law 9 Chapter 2. Computational Color Constancy Algorithms 13 2.1. The dichromatic and Lambertian image formation models 14 2.2. Classical hypotheses for illuminant and reflectance estimation 17 2.2.1. White-patch assumption and related models 18 2.2.2. Gray-world assumption and related models 20 2.2.3. Shades of gray and multi-scale max-RGB assumptions to mix white-patch and gray-world hypotheses 22 2.2.4. Gray-edge assumption and related models 24 2.2.5. Multi-scale n-th order shades of gray-edge assumption: a general hypothesis 26 Chapter 3. Retinex-like Algorithms for Color Image Processing 29 3.1. Mathematical description of the original ratio-threshold-reset Retinex algorithm 30 3.2. Analysis of the ratio-reset Retinex formula: the limit ε → 0 33 3.2.1. Retinex: “a melody that everyone plays differently” 37 3.3. From paths to pixel sprays: RSR 41 3.3.1. LRSR and SMRSR 43 3.4. A psychophysical method to measure (achromatic) induction 45 3.5. Automatic Color Equalization: ACE 50 3.6. RACE: a model with mixed features between RSR and ACE 52 3.6.1. Regularization of RACE formula: attachment to original image 54 3.7. An alternative fusion between RSR and ACE: STRESS 56 Chapter 4. Variational Formulation of Histogram Equalization 59 4.1. The Caselles–Sapiro model 59 4.2. Interpretation of Caselles–Sapiro’s functional for histogram equalization 65 4.3. Application of histogram equalization techniques to color images 67 Chapter 5. Perceptually-inspired Variational Models for Color Enhancement in the RGB Space 69 5.1. Beyond the Caselles–Sapiro model: modification of the histogram equalization functional to approach visual properties 70 5.1.1. A contrast term coherent with HVS properties 70 5.1.2. Entropic adjustment term 73 5.2. Minimization of perceptual functionals 75 5.2.1. Stability of the iterative semi-implicit gradient descent scheme 80 5.2.2. A general strategy for the reduction of computational complexity 81 5.2.3. Results 83 5.3. Embedding existing perceptually inspired color correction models in the variational framework 85 5.3.1. Alternative variational and EDP formalizations of Retinex-like algorithms 89 5.4. Variational interpretation of the Rudd-Zemach model of achromatic induction 92 5.5. Perceptual enhancement in the wavelet domain 95 5.5.1. Adjustment to the average value in the wavelet domain 98 5.5.2. Local contrast enhancement in the wavelet domain 99 5.6. High-dynamic-range (HDR) imaging 101 5.6.1. A two-stage tone mapping 105 Appendix 111 Bibliography 117 Index 125