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UCU-CV-1 (Image Processing ... on two-dimensional signals (Data (hough…

- - - - continious 2d function:
        u = I(x, y)
        
        defined in differential calculus,
        we can calculate derivative on both axes
        
        slope-function of the 2d signal by given axis and point,
        with the help of derivatives of two axes, we can compute the gradient
        (same meaning as in gradient descent algorithm in machine learning)
        Gradient has:
        
        magniture - the "strength" of change
        
        angle - the direction of change (points to the lowest regions)
    - - limited on 2 axes, sampled
        I(x, y) = [[u00, u01, ..., u0n],
        [u10, u11, ..., u1n],
        ...
        [um0, um1, ..., umn]]
        
        ...
        dI/dx = [[u01-u00, ...], ...] = [[u00, ...], ...] * [1, -1]
        dI/dy = [[u10-u00, ...], ...] = [[u00, ...], ...] * [1, -1]^T
        "^T" - matrix transponation
        "*" - is operation of convolution
        
        change between the samples in given axis,
        approximation of derivative function in given point and axis
        Gradient approximation can be calculated:
        
        magnitude - sqrt( (dI/dx)^2 + (dI/dy)^2 ), sqrt - square root
        
        angle - arctan( {dI/dx} / {dI/dy} )
    - - ...
    - - ...
      - to find lines, circle, ellipses or function-described shape
  - - - Simple
        
        I(x, y) > u_threshold
      - Adaptive
        
        not mentioned in the lectures
      - to segment objects / texture elements
    - - Edge detection
        
        Kernels:
        
        Sobel,
        
        Laplacian (3x3),
        
        Roberts Cross,
        
        ...
        
        find the poly-line between the objects / the texture elements
      - Bluring
        
        Kernels
        
        Box blur (all values of the kernel are the same)
        
        Gaussian
        
        to remove high-frequency noise
      - Sharpening
    - - edge detection algorithm with strong and weak thresholds for contours
      - find edges in the image with weak edges
    - - Gaussian
        
        to scale image without image frequency distortion
      - Laplacian
- - - - with global shutter
        CCD
      - with rolling shutter
        CMOS
    - - grayscale
      - color
        
        Bayer pattern
      - has filters to cut wave frequencies
    - - depends on
        
        ISO - sensitivity of the sensor
        
        Aperture - how big is the "hole" in the lens - light throughput
        
        Shutter time - time spent for image capturing
        
        there is exposure triangle to understand how and when to change these parameters
  - - - hole threw which light goes, smaller light - sharpen image
        
        parallel lines in the world stay parallel in the image (affine projection)
      - for mathematical explanation of the world in the image,
        in affine distortion we may have less optical image distortion
    - - lens (or set of lenses) have bigger image throughput - a larger amount of light
        
        parallel lines in the world may not be parallel in the photo
        
        lenses may give optical distortion, color distortion
        
        has focus -> may have focus blur
  - - - because of object or sensor movement
    - - object is not in focus area
    - - high-frequency noise,
        because of sensor electronics
    - - kernel blur (box, gaussian),
        kernel median,
        NLMeans
        mean/median of pixel in time (frames)
        frequency cut
        NNs
- - - - for markup
    - - for explanation where it is used
    - - comment
- - - - find the closed poly-line of the object / texture element
    - - find the correspondence of objects or object elements between frames in the video
    - - Gaussian of Laplacian #
      - ...
      - find the objects that are differ from the surroundings (background)
  - - - algorithms
        
        FAST feature detector
        
        Harris Corner Detector
        
        Good Features to Track
        
        (the fast "approximation" of Harris Corner Detector)
        
        SIFT feature detector # #
      - find the points in the image that can be
      - set of points (x, y) in the image
    - - algorithms
        
        Local Binary Patterns
        
        BRIEF descriptor
        
        rBRIEF (rotated)
        
        used in ORB
        
        HoG (Histogram of Oriented Gradient)
        
        SIFT descriptor
      - data that describes the surroundings of the feature point
      - there is the function to compare two descriptors
        and there is an algorithm to match descriptors from 2 frames
    - - repeatability
      - invariance to photometric and geometric transforms of the
        image
- - - - continious function:
        u = f(x)
        
        defined in differential calculus
        
        slope of the function in givent point
    - - limited and sampled:
        I(x) = [u0, u1, u2, ..., un]
        
        it's possible to use Taylor series expansion to prove
        that derivative of series is computed:
        dI/dx = [x1-x0, x2-x1, ...] = [x0, x1, x2...] * [1, -1]
        "*" - is operation of convolution
        
        change between the samples,
        approximation of derivative function in given point
    - - ...
- - - - Meaning of the 1st derivative