Image Processing and Computer Vision
2.0
  • Image Processing
    • 1. Images
      • 1.1. Image Formation
      • 1.2. Image Definition
      • 1.3. Image Discretization
        • 1.3.1. Quantization
        • 1.3.2. Sampling
      • 1.4. Image Interpolation
        • 1.4.1. Interpolating 1D functions
        • 1.4.2. Interpolating 2D functions
      • 1.5. Image Extrapolation aka the Border Problem
      • 1.6. Image Representation
        • 1.6.1. Coordinates and Indices
        • 1.6.2. Color Images
        • 1.6.3. Domain Iterators
      • 1.7. Image Histograms
        • 1.7.1. Univariate Histogram
        • 1.7.2. Multivariate Histograms
    • 2. Color
      • 2.1. Colorimetry
        • 2.1.1. The physics of color
        • 2.1.2. The perception of color
        • 2.1.3. Spectral versus Color Space
        • 2.1.4. Chromaticity Coordinates
        • 2.1.5. Color matching experiment
        • 2.1.6. The XYZ color model
      • 2.2. Color Models
        • 2.2.1. RGB Color Model
    • 3. Point Operators
      • 3.1. Image Arithmetic
        • 3.1.1. Definition
        • 3.1.2. Python/Numpy
        • 3.1.3. Practical Use
        • 3.1.4. Exercises
      • 3.2. Histogram Based Image Operations
        • 3.2.1. Contrast Stretching
        • 3.2.2. Histogram Equalization
        • 3.2.3. Thresholding
    • 4. Geometrical Operators
      • 4.1. Forward Transform
      • 4.2. Backward Transform
      • 4.3. Geometrical Transform in Scikit-Image
    • 5. Local Operators
      • 5.1. Local Operators in Python
      • 5.2. Linear Operators: Convolutions
        • 5.2.1. Linearity Definition
        • 5.2.2. Translation Invariance
        • 5.2.3. Linearity + Translation Invariance \(\Rightarrow\) Convolutions
        • 5.2.4. Convolutions and Correlations
        • 5.2.5. Convolutions in the Continuous Domain
        • 5.2.6. Properties of the Convolution Operator
        • 5.2.7. Often Used Convolutions
        • 5.2.8. Exercises
      • 5.3. Morphological Image Operators
        • 5.3.1. Definition
      • 5.4. Percentile Filtering
        • 5.4.1. Definition
        • 5.4.2. Algorithms
      • 5.5. Bilateral Filtering
        • 5.5.1. Definition
        • 5.5.2. Algorithms
        • 5.5.3. Bilateral filtering of color images
        • 5.5.4. Theoretical Considerations
    • 6. Local Structure
      • 6.1. Gaussian Convolutions and Derivatives
        • 6.1.1. Properties of the Gaussian Convolution
        • 6.1.2. Derivatives of Sampled Functions
        • 6.1.3. More about Algorithms for Gaussian Convolutions
      • 6.2. Local Structure
        • 6.2.1. Gradient Gauge Coordinate System
        • 6.2.2. Curvature Gauge Coordinate System
      • 6.3. Subpixel Localization of Local Structure
        • 6.3.1. Isophotes — Contour Lines
        • 6.3.2. Edges
        • 6.3.3. Lines
        • 6.3.4. X-Corners
        • 6.3.5. Concluding (computational) remarks
    • 7. Scale Space
      • 7.1. Linear Scale Space
      • 7.2. Linear Diffusion
      • 7.3. Sampling Linear Scale-Space
        • 7.3.1. Direct versus Incremental Calculation
        • 7.3.2. Pyramids
      • 7.4. Exercises
  • Computer Vision
    • 1. The Pinhole Camera
      • 1.1. Projective Geometry
        • 1.1.1. Projective Geometry in 2D
        • 1.1.2. Projective Geometry in 3D
      • 1.2. The Pinhole Camera Matrix
        • 1.2.1. The Camera Projection Matrix
        • 1.2.2. The Internal and External Camera Matrices
      • 1.3. Camera Calibration
        • 1.3.1. Estimating the Camera Matrix using the DLT
      • 1.4. Projectivities
        • 1.4.1. A plane in 3D
        • 1.4.2. The rotating camera
      • 1.5. Exercises
    • 2. Stereo Vision
      • 2.1. Triangulation
      • 2.2. Epipolar Geometry and the Fundamental Matrix
    • 3. Images in Motion
      • 3.1. Optic Flow
      • 3.2. Motion Tracking
        • 3.2.1. Correlation Tracking
      • 3.3. Exercises
    • 4. Convolutional Neural Networks
      • 4.1. A Brief History of Object Classification and CNN’s
        • 4.1.1. Old AI and CV Paradigm: “Model the world”
        • 4.1.2. Statistics and machine learning: the bag of visual words model
        • 4.1.3. The CNN comes in: “Model the brain”
        • 4.1.4. Success has many fathers
      • 4.2. Recap Machine Learning and Neural Networks
        • 4.2.1. Supervised Machine Learning
        • 4.2.2. Fully Connected Neural Network
      • 4.3. From fully connected network to convolutional network
      • 4.4. Convolutional Neural Network
        • 4.4.1. Back Propagation for the Convolution Module
        • 4.4.2. A Convolutional Layer in a CNN
        • 4.4.3. Max Pooling
      • 4.5. Exercises
  • Mathematical Tools
    • 1. Mean and Median Values
      • 1.1. The mean value
      • 1.2. The weighted mean value
      • 1.3. The median value
      • 1.4. The weighted median value
    • 2. Multivariate Functions
      • 2.1. Plotting a multivariate function
      • 2.2. Differentiating a multivariate function
      • 2.3. Symbolic Math Computations
    • 3. Linear Algebra Recap
      • 3.1. Vectors
      • 3.2. Basis Vectors
      • 3.3. Linear Mappings
      • 3.4. Matrices
      • 3.5. Linear Equations, Determinants and Inverse Matrices
      • 3.6. Vector Norm, Inner Products, Orthogonality and the Cross Product
      • 3.7. Eigenvectors and Eigenvalues
      • 3.8. Singular Value Decomposition
    • 4. Least Squares Estimators
      • 4.1. Fitting a straight line
      • 4.2. Least Squares Estimators
      • 4.3. Examples of least squares estimators
        • 4.3.1. 2nd-order polynomial
        • 4.3.2. Multivariate polynomials
    • 5. Homogeneous Coordinates
      • 5.1. Homogeneous coordinates in 2D space
        • 5.1.1. Rigid Body Transformation
        • 5.1.2. Affine Transformations
        • 5.1.3. Projective Transforms
        • 5.1.4. Overview of 2D Transforms
      • 5.2. Lines in 2D projective space
      • 5.3. Points at infinity
      • 5.4. Coordinate (Frame) Transforms
      • 5.5. Estimating Parameters
        • 5.5.1. Estimating an Affine Transform using LSQ
        • 5.5.2. Estimating a Projective Transform using the DLT
      • 5.6. Exercises
Image Processing and Computer Vision
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© Copyright 2021, Rein van den Boomgaard, Leo Dorst.

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