Chapter 7
Multiscale Shape
Characterization
7.1 MULTISCALE TRANSFORMS
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7.1.1 The Scale-Space
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7.1.2 Time-Frequency Transforms
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7.1.3 Gabor Filters
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7.1.4 Time-Scale Transforms or Wavelets
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7.1.5 A Unified Approach to Linear Multiscale Transforms
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7.1.6 Case Study: Interpreting the Transforms
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7.1.7 Analyzing the Multiscale Transforms
7.2 A FOURIER APPROACH TO MULTISCALE CURVATURE
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7.2.1 Curvature Estimation using a Fourier Property
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7.2.2 Numerical Differentiation using the Fourier Property
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7.2.3 Gaussian Filtering and the Multiscale Approach
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7.2.4 Some Simple Solutions for the Shrinking Problem
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7.2.5 The Curvegram
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7.2.6 Some Experimental Results
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7.2.7 Curvature-Scale Space
7.3 MULTISCALE CONTOUR ANALYSIS USING WAVELETS
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7.3.1 Preliminary Considerations
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7.3.2 The W-Representation
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7.3.3 Choosing the Analyzing Wavelet
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7.3.4 Shape Analysis From the W-Representation
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7.3.5 Dominant Point Detection using the W-Representation
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7.3.6 Local Frequencies and Natural Scales
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7.3.7 Contour Analysis using the Gabor Transform
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7.3.8 Comparing and Integrating the Multiscale Representations
7.4 MULTISCALE ENERGIES
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7.4.1 The Multiscale Bending Energy
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7.4.2 The Multiscale Bending Energy
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7.4.3 Neuromorphometry with Bending Energy
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7.4.4 The Multiscale Wavelet Energy
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7.4.5 Case of Study: Classification of Ganglion Cells
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7.4.6 The Feature Space
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7.4.7 Feature Selection and Dimensionality Reduction
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