2. Image Quality and Information Content
2.1 Difficulties in Image Acquisition and Analysis
2.2 Characterization of Image Quality
2.3 Digitization of Images
2.3.1 Sampling
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2.3.2 Quantization
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2.3.3 Array and matrix representation of images
2.4 Optical Density
2.5 Dynamic Range
2.6 Contrast
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2.7 Histogram
2.8 Entropy
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2.8 Entropy (cont.)
2.9 Blur and Spread Functions
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2.9 Blur and Spread Functions (cont.)
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2.10 Resolution
2.11 The Fourier Transform and Spectral Content
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2.11 The Fourier Transform and Spectral Content
2.11.1 Important properties of the Fourier transform (FT)
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2.11.1 Important properties of the Fourier transform (FT) (cont.)
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2.11.1 Important properties of the Fourier transform (FT) (cont.)
2.1.2 Modulation Transfer Function (MTF)
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2.12 Modulation Transfer Function (MTF)
2.13 Signal-to-Noise Ratio
2.14 Error-based Measures
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2.15 Application: Image Sharpness and Acutance
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3 Removal of Artifacts
3.1 Characterization of Artifacts
3.1.1 Random noise
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3.1.2 Examples of noise PDFs
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3.1.3 Structured noise
3.1.4 Physical Interference
3.1.5 Other types pf noise and artifact
3.1.6 Stationary versus nonstationary processes
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3.1.7 Covariance and cross-correlation
3.1.8 Signal-dependant noise
3.2 Synchronized or Multiframe Averaging
3.3 Space-domain Local-statistics-based Filters
3.3.1 The mean filter
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3.3.1 The mean filter (cont.)
3.3.2 The median filter
3.4.2 Removal of periodic artifacts
3.5 Matrix Representation of Image Processing
3.5.1 Matrix representation of images
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3.5.2 Matrix representation of transforms
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3.5.3 Matrix representation of convolution
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3.5.4 Illustration of convolution
3.5.5 Diagonalization of a circulant matrix
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3.5.6 Block-circulant matrix representation of a 2D filter
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3.6 Optimal filtering
3.6.1 The Wiener filter
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3.7 Adaptive filters
3.7.1 The local LMMSE filter
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3.7.1 The local LMMSE filter (cont.)
3.7.2 The noise-updating repeated Wiener filter
3.7.3 The adaptive 2D LMS filter
3.7.4 The adaptive rectangular window LMS filter
3.7.5 The adaptive-neighborhood filter
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3.7.5 The adaptive-neighborhood filter (cont.)
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3.8 Application: Multiframe Averaging in Confocal Microscopy
3.9 Application: Noise Reduction in Nuclear Medicine Imaging
5 Detection of Regions of Interest
5.1 Thresholding and Binarization
5.2 Detection of Isolated Points and Lines
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5.3 Edge Detection
5.3.1 Convolution mask operators for edge detection
5.3.2 The Laplacian of Gaussian
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5.3.3 Scale-space methods for multiscale edge detection
5.3.4 Canny's method for edge detection
5.3.5 Fourier-domain methods for edge detection
5.3.6 Edge linking
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5.4 Segmentation and Region Growing
5.4.1 Optimal thresholding
5.4.2 Region-oriented segmentation of images
5.4.3 Splitting and merging of regions
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5.4.4 Region growing using an additive tolerance
5.4.5 Region growing using a multiplicative tolerance
5.4.6 Analysis of region growing in the presence of noise
5.4.7 Iterative region growing with multiplicative tolerance
5.4.8 Region growing based upon the human visual system
5.4.9 Detection of calcifications by multitolerance region growing
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5.4.9 Detection of calcifications by multitolerance region growing (cont.)
5.4.10 Application: Detection of calcifications by linear prediction error
5.5 Fuzzy-set-based Region Growing to Detect Breast Tumors
5.6 Detection of Objects of Known Geometry
5.6.1 The Hough transform
5.6.2 Detection of straight lines
5.6.3 Detection of circles
5.7 Methods for the Improvements of Contour or Region Estimates
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5.8 Application: Detection of the Spinal Canal
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5.5 Fuzzy-set-based Region Growing to Detect Breast Tumors
5.5.1 Preprocessing based upon fuzzy sets
5.5.2 Fuzzy segmentation based upon region growing
5.5.3 Fuzzy region growing
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5.10 Application: Detections of the Pectoral Muscle in Mammograms
5.10.1 Detection using the Hough transform