Measuring Shape

Table of contents

1. Cover
2. Half Title
3. Title Page
4. Copyright Page
5. Table of Contents
6. Introduction
7. 1. The Meaning(s) of Shape
   1. Why Shape Matters
      1. Measuring versus Comparing
      2. Shape and Human Vision
   2. Classification and Identification
      1. Hierarchical Classification
      2. The Threshold Logic Unit
      3. Faces and Fingerprints
      4. The General Problem
   3. Correlating Shape with History or Performance
      1. Shape Matching and Morphing
   4. Object Recognition versus Scene Understanding
8. 2. The Role(s) of Computers
   1. Digital Images
      1. Pixel Array Size
      2. Color
      3. Camera Specifications
   2. Image Processing to Correct Limitations
      1. Color Adjustment
      2. Noise Reduction I: Speckle Noise
      3. Noise Reduction II: Periodic Noise
      4. Nonuniform Brightness
      5. Contrast and Brightness Adjustments
      6. Distortion Correction
      7. Blur Removal
   3. Image Processing for Enhancement
      1. Edges
      2. Texture
      3. Cross-Correlation
   4. Thresholding and Binary Images
      1. Automatic Threshold Setting
      2. Morphological Processing I: Erosion and Dilation
      3. Morphological Processing II: Outlines, Holes, and Skeletons
      4. The Euclidean Distance Map and Watershed Segmentation
      5. Boolean Combinations
      6. Encoding Boundary Information
   5. Measurement
      1. Counting
      2. Measuring Size
      3. Measuring Location
      4. Measuring Density
      5. Measuring Shape
   6. Sections and Projections
      1. Stereology and Geometric Probability
      2. Volume
      3. Surface Area and Length
      4. Topology
   7. Voxel Arrays
      1. Three-Dimensional Measurements
   8. Short-Range Photogrammetry
   9. Computer Graphics, Modeling, Statistical Analysis, and More
9. 3. Two-Dimensional Measurements (Part 1)
   1. Template Matching and Optical Character Recognition (OCR)
      1. Syntactical Analysis
      2. Reading License Plates
      3. Universal Product Code (UPC)
      4. Cross-Correlation
   2. Describing Noncircularity
      1. More Dimensionless Ratios to Measure Shape
      2. Example: Leaves
      3. Example: Graphite in Cast Iron
   3. Dimension as a Shape Measurement
      1. Using the Fractal Dimension
   4. Skeletons and Topology
      1. Branching Patterns
   5. Landmarks
      1. Human Faces
   6. Other Methods
      1. Curvature Scale Space
      2. Some Additional Approaches
10. 4. Two-Dimensional Measurements (Part 2)
    1. The Medial Axis Transform (MAT)
       1. Syntactical Analysis with the MAT
       2. The Shock Graph
    2. Fourier Shape Descriptors
       1. Shape Unrolling
       2. Complex Coordinates
       3. Vector Classification
       4. Symmetry Estimation Using the Boundary
       5. Symmetry Estimation Using the Interior Pixels
    3. Wavelet Analysis
    4. Moments
       1. Example: Tiger Footprints
       2. Zernike Moments
    5. Cross-Correlation
    6. Choosing a Technique
       1. Example: Arrow Points
11. 5. Three-Dimensional Shapes
    1. Acquiring Data
       1. Registration and Alignment
    2. Measuring Voxel Arrays
       1. Topology, Skeletons, and Shape Factors
       2. Projections (Silhouettes) of Shapes
       3. Spherical Harmonics
       4. Spherical Wavelets
    3. Imaging Surfaces
       1. Stereoscopy
       2. Shape from Shading
       3. Other Methods
    4. Surface Metrology
       1. Roundness
       2. Straightness
       3. Noncontacting Measurement
    5. Image Representation
    6. Topography
       1. Fractal Dimension
12. 6. Classification, Comparison, and Correlation
    1. Field Guides
       1. Template Matching and Cross-Correlation
       2. A Simple Identification Example
    2. Defining the Task
       1. Decision Thresholds
       2. Covariance
       3. Example: Mixed Nuts
    3. Cluster Analysis
       1. Dendrograms
       2. Using Rank Order Instead of Value
       3. K-Means and K-Neighbors
       4. Spanning Trees and Clusters
    4. Populations
       1. Gaussian (Normal) Distributions
    5. Comparing Normal and Non-Normal Data Sets
       1. Nonparametric Comparison
       2. Nonparametric Estimation of Covariance
       3. Outliers
    6. Bayes’ Rule
    7. Neural Nets
    8. Syntactical Analysis
    9. Correlations
       1. Physical Examples
       2. Biological Examples
    10. Example: Animal Cookies
        1. Additional Measurements
    11. Heuristic Classification
    12. Conclusions
13. References
14. Index