Computer Vision: Statistical Models for Marr's Paradigm

978-3-030-96530-3
1
	Preface
		Story of David Marr
		Beyond David Marr's Paradigm
		Introducing the Book Series
	Contents
	About the Authors
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	1 Introduction
		1.1 Goal of Vision
		1.2 Seeing as Bayesian Inference
		1.3 Knowledge Representation
		1.4 Pursuit of Probabilistic Models
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	2 Statistics of Natural Images
		2.1 Image Space and Distribution
		2.2 Information and Encoding
		2.3 Image Statistics and Power Law
		2.4 Kurtosis and Sparsity
		2.5 Scale Invariance
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	3 Textures
		3.1 Julesz Quest
		3.2 Markov Random Fields
			Markov Random Field (MRF)
			Ising and Potts Models
			Gaussian Markov Random Field (GMRF)
			Advanced Models: Hierarchical MRF and Mumford–Shah Model
			Selecting Filters and Learning Potential Functions
		3.3 Filters for Early Vision
			Correlation and Convolution
			Edge Detection Filters
			Gaussian Filters
			Derivative of Gaussian and Laplacian of Gaussian Filters
			Gabor Filters
		3.4 FRAME Model
			Intuition and the Big Picture
			Deriving the FRAME Model
				Learning Potential Functions
				Filter Selection
		3.5 Texture Ensemble
			Ensembles in Statistical Physics
			Texture Ensemble
			Type Theory and Entropy Rate Functions
				A Simple Independent Model
				From FRAME Model to Julesz Ensemble on Infinite Lattice
				From Julesz Ensemble to FRAME Model on Finite Lattice
			Equivalence of FRAME and Julesz Ensemble
				From Julesz Ensemble to FRAME Model
				From FRAME Model to Julesz Ensemble
		3.6 Reaction and Diffusion Equations
			Turing Diffusion-Reaction
			Heat Diffusion
			Anisotropic Diffusion
			GRADE: Gibbs Reaction and Diffusion Equations
			Properties of GRADE
				Property 1: A General Statistical Framework
				Property 2: Diffusion
				Property 3: Reaction
		3.7 Conclusion
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	4 Textons
		4.1 Textons and Textures
			Julesz's Discovery
			Neural Coding Schemes
		4.2 Sparse Coding
			Image Representation
			Basis and Frame
			Olshausen–Field Model
			A Three-Level Generative Model
		4.3 Active Basis Model
			Olshausen–Field Model for Sparse Coding
			Active Basis Model for Shared Sparse Coding of Aligned Image Patches
			Prototype Algorithm
			Statistical Modeling
			Shared Matching Pursuit
		4.4 Sparse FRAME Model
			Dense FRAME
			Sparse Representation
			Maximum Likelihood Learning
			Generative Boosting
			Sparse Model
		4.5 Compositional Sparse Coding
			Sparsity and Composition
			Compositional Sparse Coding Model
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	5 Gestalt Laws and Perceptual Organization
		5.1 Gestalt Laws for Perceptual Organization
		5.2 Texton Process Embedding Gestalt Laws
			Introduction
			Background on Descriptive and Generative Learning
			A Multi-layered Generative Model for Images
			A Descriptive Model of Texton Processes
				Background: Physics Foundation for Visual Modeling
				Gestalt Ensemble
			An Integrated Learning Framework
				Integrated Learning
				Mathematical Definitions of Visual Patterns
			Effective Inference by Simplified Likelihood
				Initialization by Likelihood Simplification and Clustering
				Experiment I: Texton Clustering
				Experiment II: Integrated Learning and Synthesis
			Discussion
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	6 Primal Sketch: Integrating Textures and Textons
		6.1 Marr's Conjecture on Primal Sketch
		6.2 The Two-Layer Model
			Structure Domain
			The Dictionary of Image Primitives
			Texture Domain
			Integrated Model
			The Sketch Pursuit Algorithm
		6.3 Hybrid Image Templates
			Representation
			Prototypes, ε-Balls, and Saturation Function
			Projecting Image Patches to 1D Responses
			Template Pursuit by Information Projection
			Example: Vector Fields for Human Hair Analysis and Synthesis
		6.4 HoG and SIFT Representations
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	7 2.1D Sketch and Layered Representation
		7.1 Problem Formulation
		7.2 Variational Formulation by Nitzberg and Mumford
			The Energy Functional
			The Euler Elastica for Completing Occluded Curves
		7.3 Mixed Markov Random Field Formulation
			Definition of W2D and W2.1D
			The Mixed MRF and Its Graphical Representation
			Bayesian Formulation
		7.4 2.1D Sketch with Layered Regions and Curves
			Generative Models and Bayesian Formulation
				Generative Models of Curves
				Generative Models of Regions
			Bayesian Formulation for Probabilistic Inference
			Experiments
				Experiment A: Computing Regions and Free Curves
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	8 2.5D Sketch and Depth Maps
		8.1 Marr's Definition
		8.2 Shape from Stereo
			The Image Formation Model
			Two-Layer Representation
			The Inference Algorithm
			Example Results
		8.3 Shape from Shading
			Overview of Two-Layer Generation Model
			Results
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	9 Learning by Information Projection
		9.1 Information Projection
			Orthogonality and Duality
			Maximum Likelihood Implementation
		9.2 Minimax Learning Framework
			Model Pursuit Strategies
			2D Toy Example
			Learning Shape Patterns
			Relation to Discriminative Learning
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	10 Information Scaling
		10.1 Image Scaling
			Model and Assumptions
			Image Formation and Scaling
			Empirical Observations on Information Scaling
			Change of Compression Rate
			Variance Normalization
			Basic Information Theoretical Concepts
			Change of Entropy Rate
		10.2 Perceptual Entropy
			A Continuous Spectrum
		10.3 Perceptual Scale Space
		10.4 Energy Landscape
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	11 Deep Image Models
		11.1 Deep FRAME and Deep Energy-Based Model
			ConvNet Filters
			FRAME with ConvNet Filters
			Learning and Sampling
			Learning a New Layer of Filters
			Deep Convolutional Energy-Based Model
			Hopfield Auto-Encoder
			Multi-grid Sampling and Modeling
			Adversarial Interpretation
		11.2 Generator Network
			Factor Analysis
			Nonlinear Factor Analysis
			Learning by Alternating Back-Propagation
			Nonlinear Generalization of AAM Model
			Dynamic Generator Model
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	12 A Tale of Three Families: Discriminative, Descriptive, and Generative Models
		12.1 Introduction
			Three Families of Probabilistic Models
			Supervised, Unsupervised, and Self-supervised Learning
			MCMC for Synthesis and Inference
			Deep Networks as Function Approximators
			Learned Computation
			Amortized Computation for Synthesis and InferenceSampling
			Distributed Representation and Embedding
			Perturbations of Kullback–Leibler Divergence
			Kullback–Leibler Divergence in Two Directions
		12.2 Descriptive Energy-Based Model
			Model and Origin
			Gradient-Based Sampling
			Maximum Likelihood Estimation (MLE)
			Objective Function and Estimating Equation of MLE
			Perturbation of KL-divergence
			Self-adversarial Interpretation
			Short-Run MCMC for Synthesis
			Objective Function and Estimating Equation with Short-Run MCMC
			Flow-Based Model
			Flow-Based Reference and Latent Space Sampling
			Diffusion Recovery Likelihood
			Diffusion-Based Model
		12.3 Equivalence Between Discriminative and DescriptiveModels
			Discriminative Model
			Descriptive Model as Exponential Tilting of a Reference Distribution
			Discriminative Model via Bayes Rule
			Noise Contrastive Estimation
			Flow Contrastive Estimation
		12.4 Generative Latent Variable Model
			Model and Origin
			Generative Model with Multi-layer Latent Variables
			MLE Learning and Posterior Inference
			Posterior Sampling
			Perturbation of KL-divergence
			Short-Run MCMC for Approximate Inference
			Objective Function and Estimating Equation
		12.5 Descriptive Model in Latent Space of Generative Model
			Top-Down and Bottom-Up
			Descriptive Energy-Based Model in Latent Space
			Maximum Likelihood Learning
			Short-Run MCMC for Synthesis and Inference
			Divergence Perturbation
		12.6 Variational and Adversarial Learning
			From Short-Run MCMC to Learned Sampling Computations
			VAE: Learned Computation for Inference Sampling
			GAN: Joint Learning of Generator and Discriminator
			Joint Learning of Descriptive and Generative Models
			Divergence Triangle: Integrating VAE and ACD
		12.7 Cooperative Learning via MCMC Teaching
			Joint Training of Descriptive and Generative Models
			Conditional Learning via Fast Thinking Initializer and Slow Thinking Solver
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	Bibliography