ScaleSpace Theory in Computer Vision

Tony Lindeberg
KTH (Royal Institute of Technology)

Stockholm, Sweden
Contents
 Introduction and overview (1)
 Theory of a visual frontend
 Goal
 The nature of the problem
 Scalespace representation
 Philosophies and ideas behind the approach
 Relations to traditional numerical analysis
 Organization of this book
Part I: Basic scalespace theory

Linear scalespace and related multiscale representations (31)
 Early multiscale representations
 Quadtree
 Pyramid representations
 Scalespace representation and scalespace properties
 Uniqueness of scalespace representation
 Summary and retrospective
 Wavelets
 Regularization
 Relations between different multiscale representations

Scalespace for 1D discrete signals (61)
 Scalespace axioms in one dimension
 Properties of scalespace kernels
 Kernel classification
 Axiomatic construction of discrete scalespace
 Axiomatic construction of continuous scalespace
 Numerical approximations of continuous scalespace
 Summary and discussion
 Conclusion: Scalespace for 1D discrete signals

Scalespace for ND discrete signals (101)
 Scalespace axioms in higher dimensions
 Axiomatic discrete scalespace formulation
 Parameter determination
 Summary and discussion
 Possible extensions

Discrete derivative approximations with scalespace properties (123)
 Numerical approximation of derivatives
 Scalespace derivatives
 Discrete approximation of scalespace derivatives
 Computational implications
 Kernel graphs
 Summary and discussion

Feature detection in scalespace (149)
 Differential geometry and differential invariants
 Experimental results: Lowlevel feature extraction
 Feature detection from differential singularities
 Selective mechanisms
Part II: The scalespace primal sketch: Theory

The scalespace primal sketch (165)
 Greylevel blob
 Greylevel blob tree
 Motivation for introducing a multiscale hierarchy
 Scalespace blob
 Scalespace blob tree
 Greylevel blob extraction: Experimental results
 Measuring blob significance
 Resulting representation

Behaviour of image structures in scalespace: Deep structure (187)
 Trajectories of critical points in scalespace
 Scalespace blobs
 Bifurcation events for critical points: Classification
 Bifurcation events for greylevel blobs and scalespace blobs
 Behaviour near singularities: Examples
 Relating differential singularities across scales
 Density of local extrema as function of scale
 Summary

Algorithm for computing the scalespace primal sketch (227)
 Greylevel blob detection
 Linking greylevel blobs into scalespace blobs
 Basic blob linking algorithm
 Computing scalespace blob volumes
 Potential improvements of the algorithm
 Data structure
Part III: The scalespace primal sketch: Applications

Detecting salient bloblike image structures and their scales (249)
 Motivations for the assumptions
 Basic method for extracting blob structures
 Experimental results
 Further treatment of generated blob hypotheses
 Properties of the scale selection method
 Additional experiments

Guiding early visual processing with qualitative scale and region information (271)
 Guiding edge detection with blob information
 Automatic peak detection in histograms
 Junction classification: Focusofattention
 Example: Analysis of aerosol images
 Other potential applications

Summary and discussion (307)
 Scalespace experiences
 Relations to previous work
 Greylevel blobs
 Laplacian sign blobs
 Invariance properties
 Alternative approaches and further work
 Conclusions
Part IV: Scale selection and shape computation
in a visual frontend
 Scale selection for differential operators (317)
 Basic idea for scale selection
 Proposed method for scale selection
 Blob detection
 Junction detection
 Edge detection
 Discrete implementation of normalized derivatives
 Interpretation in terms of selfsimilar Fourier spectrum
 Summary and discussion

Direct computation of shape cues by scalespace operations (349)
 Shapefromtexture: Review
 Definition of an image texture descriptor
 Deriving shape cues from the second moment matrix
 Scale problems in texture analysis
 Computational methodology and experiments
 Spatial selection and blob detection
 Estimating surface orientation
 Experiments
 Summary and discussion

Nonuniform smoothing (383)
 Nonlinear diffusion: Review
 Linear shapeadapted smoothing
 Affine scalespace
 Definition of an affine invariant image texture descriptor
 Outlook
Appendix:

Technical details (395)
 Implementing scalespace smoothing
 Polynomials satisfying the diffusion equation

Bibliography (399)

Index (415)
Responsible for this page:
Tony Lindeberg
