Front Cover -- Microscope Image Processing -- Copyright Page -- Contents -- Foreword -- Reference -- Preface -- Acknowledgments -- Chapter 1: Introduction -- 1.1 The Microscope and Image Processing -- 1.2 Scope of This Book -- 1.3 Our Approach -- 1.3.1 The Four Types of Images -- 1.3.1.1 Optical Image -- 1.3.1.2 Continuous Image -- 1.3.1.3 Digital Image -- 1.3.1.4 Displayed Image -- 1.3.2 The Result -- 1.3.2.1 Analytic Functions -- 1.3.3 The Sampling Theorem -- 1.4 The Challenge -- 1.5 Nomenclature -- 1.6 Summary of Important Points -- References -- Chapter 2: Fundamentals of Microscopy -- 2.1 Origins of the Microscope -- 2.2 Optical Imaging -- 2.2.1 Image Formation by a Lens -- 2.2.1.1 Imaging a Point Source -- 2.2.1.2 Focal Length -- 2.2.1.3 Numerical Aperture -- 2.2.1.4 Lens Shape -- 2.3 Diffraction-Limited Optical Systems -- 2.3.1 Linear System Analysis -- 2.4 Incoherent Illumination -- 2.4.1 The Point Spread Function -- 2.4.2 The Optical Transfer Function -- 2.5 Coherent Illumination -- 2.5.1 The Coherent Point Spread Function -- 2.5.2 The Coherent Optical Transfer Function -- 2.6 Resolution -- 2.6.1 Abbe Distance -- 2.6.2 Rayleigh Distance -- 2.6.3 Size Calculations -- 2.7 Aberration -- 2.8 Calibration -- 2.8.1 Spatial Calibration -- 2.8.2 Photometric Calibration -- 2.9 Summary of Important Points -- References -- Chapter 3: Image Digitization -- 3.1 Introduction -- 3.2 Resolution -- 3.3 Sampling -- 3.3.1 Interpolation -- 3.3.2 Aliasing -- 3.4 Noise -- 3.5 Shading -- 3.6 Photometry -- 3.7 Geometric Distortion -- 3.8 Complete System Design -- 3.8.1 Cumulative Resolution -- 3.8.2 Design Rules of Thumb -- 3.8.2.1 Pixel Spacing -- 3.8.2.2 Resolution -- 3.8.2.3 Noise -- 3.8.2.4 Photometry -- 3.8.2.5 Distortion -- 3.9 Summary of Important Points -- References -- Chapter 4: Image Display -- 4.1 Introduction -- 4.2 Display Characteristics.

4.2.1 Displayed Image Size -- 4.2.2 Aspect Ratio -- 4.2.3 Photometric Resolution -- 4.2.4 Grayscale Linearity -- 4.2.5 Low-Frequency Response -- 4.2.5.1 Pixel Polarity -- 4.2.5.2 Pixel Interaction -- 4.2.6 High-Frequency Response -- 4.2.7 The Spot-Spacing Compromise -- 4.2.8 Noise Considerations -- 4.3 Volatile Displays -- 4.4 Sampling for Display Purposes -- 4.4.1 Oversampling -- 4.4.2 Resampling -- 4.5 Display Calibration -- 4.6 Summary of Important Points -- References -- Chapter 5: Geometric Transformations -- 5.1 Introduction -- 5.2 Implementation -- 5.3 Gray-Level Interpolation -- 5.3.1 Nearest-Neighbor Interpolation -- 5.3.2 Bilinear Interpolation -- 5.3.3 Bicubic Interpolation -- 5.3.4 Higher-Order Interpolation -- 5.4 Spatial Transformation -- 5.4.1 Control-Grid Mapping -- 5.5 Applications -- 5.5.1 Distortion Removal -- 5.5.2 Image Registration -- 5.5.3 Stitching -- 5.6 Summary of Important Points -- References -- Chapter 6: Image Enhancement -- 6.1 Introduction -- 6.2 Spatial Domain Methods -- 6.2.1 Contrast Stretching -- 6.2.2 Clipping and Thresholding -- 6.2.3 Image Subtraction and Averaging -- 6.2.4 Histogram Equalization -- 6.2.5 Histogram Specification -- 6.2.6 Spatial Filtering -- 6.2.7 Directional and Steerable Filtering -- 6.2.8 Median Filtering -- 6.3 Fourier Transform Methods -- 6.3.1 Wiener Filtering and Wiener Deconvolution -- 6.3.2 Deconvolution Using a Least-Squares Approach -- 6.3.3 Low-Pass Filtering in the Fourier Domain -- 6.3.4 High-Pass Filtering in the Fourier Domain -- 6.4 Wavelet Transform Methods -- 6.4.1 Wavelet Thresholding -- 6.4.2 Differential Wavelet Transform and Multiscale Pointwise Product -- 6.5 Color Image Enhancement -- 6.5.1 Pseudo-Color Transformations -- 6.5.2 Color Image Smoothing -- 6.5.3 Color Image Sharpening -- 6.6 Summary of Important Points -- References -- Chapter 7: Wavelet Image Processing.

7.1 Introduction -- 7.1.1 Linear Transformations -- 7.1.2 Short-Time Fourier Transform and Wavelet Transform -- 7.2 Wavelet Transforms -- 7.2.1 Continuous Wavelet Transform -- 7.2.2 Wavelet Series Expansion -- 7.2.3 Haar Wavelet Functions -- 7.3 Multiresolution Analysis -- 7.3.1 Multiresolution and Scaling Function -- 7.3.2 Scaling Functions and Wavelets -- 7.4 Discrete Wavelet Transform -- 7.4.1 Decomposition -- 7.4.2 Reconstruction -- 7.4.3 Filter Banks -- 7.4.3.1 Two-Channel Subband Coding -- 7.4.3.2 Orthogonal Filter Design -- 7.4.4 Compact Support -- 7.4.5 Biorthogonal Wavelet Transforms -- 7.4.5.1 Biorthogonal Filter Banks -- 7.4.5.2 Examples of Biorthogonal Wavelets -- 7.4.6 Lifting Schemes -- 7.4.6.1 Biorthogonal Wavelet Design -- 7.4.6.2 Wavelet Transform Using Lifting -- 7.5 Two-Dimensional Discrete Wavelet Transform -- 7.5.1 Two-Dimensional Wavelet Bases -- 7.5.2 Forward Transform -- 7.5.3 Inverse Transform -- 7.5.4 Two-Dimensional Biorthogonal Wavelets -- 7.5.5 Overcomplete Transforms -- 7.6 Examples -- 7.6.1 Image Compression -- 7.6.2 Image Enhancement -- 7.6.3 Extended Depth-of-Field by Wavelet Image Fusion -- 7.7 Summary of Important Points -- References -- Chapter 8: Morphological Image Processing -- 8.1 Introduction -- 8.2 Binary Morphology -- 8.2.1 Binary Erosion and Dilation -- 8.2.2 Binary Opening and Closing -- 8.2.3 Binary Morphological Reconstruction from Markers -- 8.2.3.1 Connectivity -- 8.2.3.2 Markers -- 8.2.3.3 The Edge-Off Operation -- 8.2.4 Reconstruction from Opening -- 8.2.5 Area Opening and Closing -- 8.2.6 Skeletonization -- 8.3 Grayscale Operations -- 8.3.1 Threshold Decomposition -- 8.3.2 Erosion and Dilation -- 8.3.2.1 Gradient -- 8.3.3 Opening and Closing -- 8.3.3.1 Top-Hat Filtering -- 8.3.3.2 Alternating Sequential Filters -- 8.3.4 Component Filters and Grayscale Morphological Reconstruction.

8.3.4.1 Morphological Reconstruction -- 8.3.4.2 Alternating Sequential Component Filters -- 8.3.4.3 Grayscale Area Opening and Closing -- 8.3.4.4 Edge-Off Operator -- 8.3.4.5 h-Maxima and h-Minima Operations -- 8.3.4.6 Regional Maxima and Minima -- 8.3.4.7 Regional Extrema as Markers -- 8.4 Watershed Segmentation -- 8.4.1 Classical Watershed Transform -- 8.4.2 Filtering the Minima -- 8.4.3 Texture Detection -- 8.4.4 Watershed from Markers -- 8.4.5 Segmentation of Overlapped Convex Cells -- 8.4.6 Inner and Outer Markers -- 8.4.7 Hierarchical Watershed -- 8.4.8 Watershed Transform Algorithms -- 8.5 Summary of Important Points -- References -- Chapter 9: Image Segmentation -- 9.1 Introduction -- 9.1.1 Pixel Connectivity -- 9.2 Region-Based Segmentation -- 9.2.1 Thresholding -- 9.2.1.1 Global Thresholding -- 9.2.1.2 Adaptive Thresholding -- 9.2.1.3 Threshold Selection -- 9.2.1.4 Thresholding Circular Spots -- 9.2.1.5 Thresholding Noncircular and Noisy Spots -- 9.2.2 Morphological Processing -- 9.2.2.1 Hole Filling -- 9.2.2.2 Border-Object Removal -- 9.2.2.3 Separation of Touching Objects -- 9.2.2.4 The Watershed Algorithm -- 9.2.3 Region Growing -- 9.2.4 Region Splitting -- 9.3 Boundary-Based Segmentation -- 9.3.1 Boundaries and Edges -- 9.3.2 Boundary Tracking Based on Maximum Gradient Magnitude -- 9.3.3 Boundary Finding Based on Gradient Image Thresholding -- 9.3.4 Boundary Finding Based on Laplacian Image Thresholding -- 9.3.5 Boundary Finding Based on Edge Detection and Linking -- 9.3.5.1 Edge Detection -- 9.3.5.2 Edge Linking and Boundary Refinement -- 9.3.6 Encoding Segmented Images -- 9.3.6.1 Object Label Map -- 9.3.6.2 Boundary Chain Code -- 9.4 Summary of Important Points -- References -- Chapter 10: Object Measurement -- 10.1 Introduction -- 10.2 Measures for Binary Objects -- 10.2.1 Size Measures -- 10.2.1.1 Area -- 10.2.1.2 Perimeter.

10.2.1.3 Area and Perimeter of a Polygon -- 10.2.2 Pose Measures -- 10.2.2.1 Centroid -- 10.2.2.2 Orientation -- 10.2.3 Shape Measures -- 10.2.3.1 Thinness Ratio -- 10.2.3.2 Rectangularity -- 10.2.3.3 Circularity -- 10.2.3.4 Euler Number -- 10.2.3.5 Moments -- 10.2.3.6 Elongation -- 10.2.4 Shape Descriptors -- 10.2.4.1 Differential Chain Code -- 10.2.4.2 Fourier Descriptors -- 10.2.4.3 Medial Axis Transform -- 10.2.4.4 Graph Representations -- 10.3 Distance Measures -- 10.3.1 Euclidean Distance -- 10.3.2 City-Block Distance -- 10.3.3 Chessboard Distance -- 10.4 Gray-Level Object Measures -- 10.4.1 Intensity Measures -- 10.4.1.1 Integrated Optical Intensity -- 10.4.1.2 Average Optical Intensity -- 10.4.1.3 Contrast -- 10.4.2 Histogram Measures -- 10.4.2.1 Mean Gray Level -- 10.4.2.2 Standard Deviation of Gray Levels -- 10.4.2.3 Skew -- 10.4.2.4 Entropy -- 10.4.2.5 Energy -- 10.4.3 Texture Measures -- 10.4.3.1 Statistical Texture Measures -- 10.4.3.2 Power Spectrum Features -- 10.5 Object Measurement Considerations -- 10.6 Summary of Important Points -- References -- Chapter 11: Object Classification -- 11.1 Introduction -- 11.2 The Classification Process -- 11.2.1 Bayes' Rule -- 11.3 The Single-Feature, Two-Class Case -- 11.3.1 A Priori Probabilities -- 11.3.2 Conditional Probabilities -- 11.3.3 Bayes' Theorem -- 11.4 The Three-Feature, Three-Class Case -- 11.4.1 Bayes Classifier -- 11.4.1.1 Prior Probabilities -- 11.4.1.2 Classifier Training -- 11.4.1.3 The Mean Vector -- 11.4.1.4 Covariance -- 11.4.1.5 Variance and Standard Deviation -- 11.4.1.6 Correlation -- 11.4.1.7 The Probability Density Function -- 11.4.1.8 Classification -- 11.4.1.9 Log Likelihoods -- 11.4.1.10 Mahalanobis Distance Classifier -- 11.4.1.11 Uncorrelated Features -- 11.4.2 A Numerical Example -- 11.5 Classifier Performance -- 11.5.1 The Confusion Matrix -- 11.6 Bayes Risk.

11.6.1 Minimum-Risk Classifier.