Content

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   Abstract
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   Zusammenfassung
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   Acknowledgements
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   Contents
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   List of Tables
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   List of Figures
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  Chapter 1. Introduction
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   1.1 Motivation and Objectives
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  1.2 Input and Output of the Proposed Inverse Lighting
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   1.2.1 Input Image
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   1.2.2 Approaching the Problem and Overview of the Algorithm
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   1.3 Contributions
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   1.4 Publications
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  Chapter 2. Background and Related Work
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  2.1 Previous Work
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   2.1.1 Data-Driven Approaches
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   2.1.2 Single-Image Approaches
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   2.1.3 Lighting Design
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   2.2 The Appearance of Human Faces
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  2.3 Face Model Extraction with 3DMM from a 2D Image
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   2.3.1 The 3D Morphable Model (3DMM) of Faces
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   2.3.2 3DMM Fitting Algorithm and Joint Lighting Estimation
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   2.3.3 Model-Based Texture Extraction from 2D Image
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   2.4 Illumination Cone
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   2.4.1 Lighting Models
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   2.4.2 Light Sources
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   2.4.3 Light Stage
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   2.4.4 Formalizing the Superposition Principle
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   2.4.5 Estimation of RGB Parameters of Light Sources
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  2.5 Image Formation
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   2.5.1 Rendering
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   2.5.2 Phong Model
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   2.5.3 Torrance-Sparrow and Dipol Functions
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   2.5.4 Soft Cast Shadow Mapping
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   2.5.5 Color Correction
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   2.6 Cast Shadow Detection and Segmentation
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  2.7 Image Compression
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   2.7.1 Downsampling Filters
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   2.7.2 Compressive Sensing Matrix
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   2.7.3 Superpixel Segmentation
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   2.7.4 Texture Patches
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  Chapter 3. Inverse Lighting and Relighting
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  3.1 The Inverse Lighting Framework
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   3.1.1 The Use Case Diagrams for the Proposed Inverse Lighting
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   3.1.2 An Activity Diagram for the Inverse Lighting Algorithm
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   3.2 To Span a Synthetic Illumination Cone
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   3.2.1 Virtual Light Stage (VLS)
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   3.2.2 Adopting a Measurement-Based Reflectance
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   3.2.3 Color Correction
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   3.2.4 3DMM Masks
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   3.3 Cast Shadow Detection and Segmentation
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   3.4 Image Compression
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   3.4.1 Masked Gaussian Downscaling
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   3.4.2 Geometric Superpixels
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   3.5 Inverse Lighting Algorithm with Superpixels
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  3.6 Relighting
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   3.6.1 Intrinsic Texture Decomposition
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   3.6.2 Lighting Design
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   3.7 An Effort to Improve the Estimated Shape after Inverse Lighting
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  Chapter 4. Estimation by Optimization
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   4.1 Linear Model
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   4.2 Cost Function from the Generative Model
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   4.2.1 Least Squares
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   4.3 Maximum A-Posteriori (MAP)
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   4.4 Joint Maximum A-Posteriori (JMAP) for Hyperparameter Optimization
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   4.4.1 Expected Values of the Priors
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   4.5 Optimization with Newton-Raphson
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   4.5.1 Enforcing Nonnegativity and Light-Weight Sparsity
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   4.5.2 The Hyperparameter Optimization Mechanism
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   4.5.3 Handling Occlusions and Areas of Misalignment
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   4.5.4 The Challenge of Cast Shadows
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   4.6 Implementation Tricks and Magic Numbers
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  4.7 Alternative Methods
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   4.7.1 Nonlinear Model ~x = e~
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   4.7.2 Richardson-Lucy (RL)
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   4.7.3 Full Hessian Inverse
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  Chapter 5. Evaluation and Results
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   5.1 Mean Illumination SIMilarity (MISIM)
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   5.2 Results
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   5.2.1 Results of MAP
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   5.2.2 Ambiguity of the Estimated Lighting
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   5.2.3 The JMAP Results
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   5.2.4 Experiments with Different Number of Light Sources n
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   5.2.5 Experiments with Different Number of Superpixels ms
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   5.2.6 Cast Shadows
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   5.3 Relighting Results
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   5.3.1 Lighting Design
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   Chapter 6. Conclusion
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   6.1 Summary of Attempts and Achievements
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   6.2 Unanswered Questions or Future Work
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   Index
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   Bibliography