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Scale-Space Theory in Computer Vision

Tony Lindeberg

KTH Royal Institute of Technology
Stockholm, Sweden

Contents

  1. Introduction and overview (1)
    1. Theory of a visual front-end
    2. Goal
    3. The nature of the problem
    4. Scale-space representation
    5. Philosophies and ideas behind the approach
    6. Relations to traditional numerical analysis
    7. Organization of this book

    Part I: Basic scale-space theory

  2. Linear scale-space and related multi-scale representations (31)
    1. Early multi-scale representations
    2. Quad-tree
    3. Pyramid representations
    4. Scale-space representation and scale-space properties
    5. Uniqueness of scale-space representation
    6. Summary and retrospective
    7. Wavelets
    8. Regularization
    9. Relations between different multi-scale representations

  3. Scale-space for 1-D discrete signals (61)
    1. Scale-space axioms in one dimension
    2. Properties of scale-space kernels
    3. Kernel classification
    4. Axiomatic construction of discrete scale-space
    5. Axiomatic construction of continuous scale-space
    6. Numerical approximations of continuous scale-space
    7. Summary and discussion
    8. Conclusion: Scale-space for 1-D discrete signals

  4. Scale-space for N-D discrete signals (101)
    1. Scale-space axioms in higher dimensions
    2. Axiomatic discrete scale-space formulation
    3. Parameter determination
    4. Summary and discussion
    5. Possible extensions

  5. Discrete derivative approximations with scale-space properties (123)
    1. Numerical approximation of derivatives
    2. Scale-space derivatives
    3. Discrete approximation of scale-space derivatives
    4. Computational implications
    5. Kernel graphs
    6. Summary and discussion

  6. Feature detection in scale-space (149)
    1. Differential geometry and differential invariants
    2. Experimental results: Low-level feature extraction
    3. Feature detection from differential singularities
    4. Selective mechanisms

    Part II: The scale-space primal sketch: Theory

  7. The scale-space primal sketch (165)
    1. Grey-level blob
    2. Grey-level blob tree
    3. Motivation for introducing a multi-scale hierarchy
    4. Scale-space blob
    5. Scale-space blob tree
    6. Grey-level blob extraction: Experimental results
    7. Measuring blob significance
    8. Resulting representation

  8. Behaviour of image structures in scale-space: Deep structure (187)
    1. Trajectories of critical points in scale-space
    2. Scale-space blobs
    3. Bifurcation events for critical points: Classification
    4. Bifurcation events for grey-level blobs and scale-space blobs
    5. Behaviour near singularities: Examples
    6. Relating differential singularities across scales
    7. Density of local extrema as function of scale
    8. Summary

  9. Algorithm for computing the scale-space primal sketch (227)
    1. Grey-level blob detection
    2. Linking grey-level blobs into scale-space blobs
    3. Basic blob linking algorithm
    4. Computing scale-space blob volumes
    5. Potential improvements of the algorithm
    6. Data structure

    Part III: The scale-space primal sketch: Applications

  10. Detecting salient blob-like image structures and their scales (249)
    1. Motivations for the assumptions
    2. Basic method for extracting blob structures
    3. Experimental results
    4. Further treatment of generated blob hypotheses
    5. Properties of the scale selection method
    6. Additional experiments

  11. Guiding early visual processing with qualitative scale and region information (271)
    1. Guiding edge detection with blob information
    2. Automatic peak detection in histograms
    3. Junction classification: Focus-of-attention
    4. Example: Analysis of aerosol images
    5. Other potential applications

  12. Summary and discussion (307)
    1. Scale-space experiences
    2. Relations to previous work
    3. Grey-level blobs
    4. Laplacian sign blobs
    5. Invariance properties
    6. Alternative approaches and further work
    7. Conclusions

    Part IV: Scale selection and shape computation in a visual front-end

  13. Scale selection for differential operators (317)
    1. Basic idea for scale selection
    2. Proposed method for scale selection
    3. Blob detection
    4. Junction detection
    5. Edge detection
    6. Discrete implementation of normalized derivatives
    7. Interpretation in terms of self-similar Fourier spectrum
    8. Summary and discussion

  14. Direct computation of shape cues by scale-space operations (349)
    1. Shape-from-texture: Review
    2. Definition of an image texture descriptor
    3. Deriving shape cues from the second moment matrix
    4. Scale problems in texture analysis
    5. Computational methodology and experiments
    6. Spatial selection and blob detection
    7. Estimating surface orientation
    8. Experiments
    9. Summary and discussion

  15. Non-uniform smoothing (383)
    1. Non-linear diffusion: Review
    2. Linear shape-adapted smoothing
    3. Affine scale-space
    4. Definition of an affine invariant image texture descriptor
    5. Outlook

    Appendix:

  • Technical details (395)
    1. Implementing scale-space smoothing
    2. Polynomials satisfying the diffusion equation

  • Bibliography (399)
  • Index (415)
Responsible for this page: Tony Lindeberg