Image understanding using sparse representations /

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Image understanding has been playing an increasingly crucial role in several inverse problems and computer vision. Sparse models form an important component in image understanding, since they emulate the activity of neural receptors in the primary visual cortex of the human brain. Sparse methods hav...

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Bibliographic Details
Main Authors: Thiagarajan, Jayaraman Jayaraman (Author), Ramamurthy, Karthikeyan Natesan (Author), Spanias, Andreas (Author), Turaga, Pavan (Author)
Format: eBook
Language:English
Published: San Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, 2014.
Series:Synthesis digital library of engineering and computer science.
Synthesis lectures on image, video, and multimedia processing ; # 15.
Subjects:
Computer vision.
Image processing > Digital techniques > Mathematics.
Machine learning.
Sparse matrices.
clustering
compressed sensing
dictionary learning
graph embedding
image classification
image reconstruction
image recovery
kernel methods
natural images
sparse representations
Online Access:Abstract with links to full text
Table of Contents:
  • 1. Introduction
  • 1.1 Modeling natural images
  • 1.2 Natural image statistics
  • 1.3 Sparseness in biological vision
  • 1.4 The generative model for sparse coding
  • 1.5 Sparse models for image reconstruction
  • 1.5.1 Dictionary design
  • 1.5.2 Example applications
  • 1.6 Sparse models for recognition
  • 1.6.1 Discriminative dictionaries
  • 1.6.2 Bag of words and its generalizations
  • 1.6.3 Dictionary design with graph embedding constraints
  • 1.6.4 Kernel sparse methods
  • 2. Sparse representations
  • 2.1 The sparsity regularization
  • 2.1.1 Other sparsity regularizations
  • 2.1.2 Non-negative sparse representations
  • 2.2 Geometrical interpretation
  • 2.3 Uniqueness of l0 and its equivalence to the l1 solution
  • 2.3.1 Phase transitions
  • 2.4 Numerical methods for sparse coding
  • 2.4.1 Optimality conditions
  • 2.4.2 Basis pursuit
  • 2.4.3 Greedy pursuit methods
  • 2.4.4 Feature-sign search
  • 2.4.5 Iterated shrinkage methods
  • 3. Dictionary learning: theory and algorithms
  • 3.1 Dictionary learning and clustering
  • 3.1.1 Clustering procedures
  • 3.1.2 Probabilistic formulation
  • 3.2 Learning algorithms
  • 3.2.1 Method of optimal directions
  • 3.2.2 K-SVD
  • 3.2.3 Multilevel dictionaries
  • 3.2.4 Online dictionary learning
  • 3.2.5 Learning structured sparse models
  • 3.2.6 Sparse coding using examples
  • 3.3 Stability and generalizability of learned dictionaries
  • 3.3.1 Empirical risk minimization
  • 3.3.2 An example case: multilevel dictionary learning
  • 4. Compressed sensing
  • 4.1 Measurement matrix design
  • 4.1.1 The restricted isometry property
  • 4.1.2 Geometric interpretation
  • 4.1.3 Optimized measurements
  • 4.2 Compressive sensing of natural images
  • 4.3 Video compressive sensing
  • 4.3.1 Frame-by-frame compressive recovery
  • 4.3.2 Model-based video compressive sensing
  • 4.3.3 Direct feature extraction from compressed videos
  • 5. Sparse models in recognition
  • 5.1 A simple classification setup
  • 5.2 Discriminative dictionary learning
  • 5.3 Sparse-coding-based subspace identification
  • 5.4 Using unlabeled data in supervised learning
  • 5.5 Generalizing spatial pyramids
  • 5.5.1 Supervised dictionary optimization
  • 5.6 Locality in sparse models
  • 5.6.1 Local sparse coding
  • 5.6.2 Dictionary design
  • 5.7 Incorporating graph embedding constraints
  • 5.7.1 Laplacian sparse coding
  • 5.7.2 Local discriminant sparse coding
  • 5.8 Kernel methods in sparse coding
  • 5.8.1 Kernel sparse representations
  • 5.8.2 Kernel dictionaries in representation and discrimination
  • 5.8.3 Combining diverse features
  • 5.8.4 Application: tumor identification
  • Bibliography
  • Authors' biographies.

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