Image PreProcessing - PowerPoint PPT Presentation

1 / 15
About This Presentation
Title:

Image PreProcessing

Description:

Filter in spatial domain (filtr v prostorov dom ne) ... Low-pass filter (n zkofrekvencn filtr) ... Linear filter (line rn filtr) ... – PowerPoint PPT presentation

Number of Views:345
Avg rating:3.0/5.0
Slides: 16
Provided by: michalk8
Category:

less

Transcript and Presenter's Notes

Title: Image PreProcessing


1
Image Pre-Processing
  • Image pre-processing (predzpracování obrazu)
  • transformations of the input image leading to
    noise reduction, image improvement or preparation
    of the image for subsequent image analysis
  • Image pre-processing operations
  • Spatial domain
  • Point transforms
  • Linear filters
  • Non-linear filters
  • Frequency domain
  • Filters in frequency domain

2
Point Transforms
  • Point transform (bodová transformace)
  • a pixel by pixel transformation of the image
    array in spatial domain
  • Position-dependent point transform
  • g(x,y) t ( f(x,y), x, y)
  • t lt 0, NI gt ? lt 0, Nx gt ? lt 0, Ny gt ? lt 0, NI
    gt
  • Compensation for uneven illumination
  • Compensation for uneven dark charge of CCD pixels
  • Position-independent point transform
  • g(x,y) t ( f(x,y))
  • t lt 0, NI gt ? lt 0, NI gt
  • Change of image brightness t (x) x k
  • Change of image contrast t (x) any function
    of x, for example
  • t (x) k x, t (x) k xn, t (x) k
    log(x), t (x) k exp(x)

3
Position-independent Point Transforms
  • Look-up table (LUT)
  • Usually t (x) is pre-computed, the table of its
    values is called look-up-table (LUT). The LUT is
    1D array of values. The size of this array is
    determined by the bit depth of the image (256
    values for 8-bit image, 4096 values for 12-bit
    image, etc.).
  • Intensity histogram
  • The best way to choose t (x) is to look at the
    intensity histogram of the given image. Intensity
    histogram is a 2D plot where x-axis represents
    intensity (e.g. 0-255 for 8-bit image) and y-axis
    represents the number of pixels in the image
    having the corresponding intensity.

4
Position-independent Point Transforms
  • Example of the influence of point transform
    (contrast change) on the intensity histogram for
    t (x) 4 x

5
Other Intensity Histogram Examples
  • Under- and over-exposed image (pod- a
    pre-exponovaný obraz)

6
Filters
  • Filter (filtr)
  • a position-independent operator that transforms
    the image
  • Filter in spatial domain (filtr v prostorové
    doméne)
  • spatial operator that produces the output image
    array g(x,y)from the input image array f(x,y)
  • Filter in frequency domain (filtr ve frekvencní
    doméne)
  • frequency operator that produces the output image
    spectrum ?(x,y) from the input image spectrum
    F(x,y)
  • Low-pass filter (nízkofrekvencní filtr)
  • a filter that keeps low frequencies and
    suppresses the high ones
  • High-pass filter (vysokofrekvencní filtr)
  • a filter that keeps high frequencies and
    suppresses the low ones

7
Linear Filters
  • Linear filter (lineární filtr)
  • spatial linear operator that produces the output
    image array g(x,y) from the input image array
    f(x,y) in the following way g(x0,y0) is obtained
    by a linear combination of pixels of the input
    image array f(x,y) within a neighbourhood of
    pixel (x0,y0).
  • nm1 3x3 neighbourhood
  • nm2 5x5 neighbourhood
  • nm3 7x7 neighbourhood

8
Linear Filters
  • Convolution kernel (konvolucní jádro)
  • The function h(a,b) is called convolution kernel.
  • The function h(a,b) is usually symmetric
    h(a,b) h(-a,b) h(a,-b) h(-a,-b).
  • The values of the function h(a,b) usually depend
    on radius
  • The function h(a,b) is specified as a matrix H.
  • If nm then the matrix H is square.
  • g(x,y) F(x,y) H
  • F(x,y) matrix of neighbours of pixel (x,y)
  • H convolution kernel
  • scalar matrix multiplication
    (defined in the same way as scalar vector
    multiplication)

9
Linear Filters
  • Principle of linear filtering using a 3x3
    convolution kernel
  • The intensity value at position (m,n) is replaced
    by the sum of nine numbers, where each number is
    obtained by multiplication of the number in
    matrix with the intensity value behind this
    number.
  • This process (nine multiplications plus eight
    additions) must be performed for each position in
    the image, i.e. all values of m and n.

10
Linear Filters
  • Problem with linear image filtering
  • Image convolution can be realised by scanning the
    convolution mask line by line over the image. At
    the shaded pixels the intensity value has already
    been replaced by the convolution sum. Thus the
    intensity values at the shaded pixels falling
    within the filter mask need to be stored in an
    extra buffer!

11
Smoothing Linear Filters
  • Smoothing (vyhlazování)
  • elimination of high frequencies
  • usually performed using averaging (either
    weighted or non-weighted)
  • Example Smoothing using average 3x3 filters
  • non-weighted weighted
    weighted

12
Smoothing Linear Filters
  • Gaussian filter (Gaussuv filtr)
  • the best smoothing filter

13
Smoothing Linear Filters
  • Example of Gaussian filtering with different
    values of s
  • Original s 1
  • s 2 s 4

14
Edge Detection Linear Filters
  • Edge detection (detekce hran)
  • usually performed using linear filters simulating
    1st or 2nd derivative
  • can be used for edge enhancement or object
    boundaries reconstruction
  • Sobel filter
  • approximates the first derivative of the image
  • the basic kernels are (1,-1) or (1,0,-1)
  • mostly 3x3 kernel is used with the sum of
    coefficients equal to 0
  • results for several 3x3 kernels can be averaged
  • there are 8 possibilities of the following type
  • often used after Gaussian filter(so called
    derivative of Gaussian DroG)

15
Edge Detection Linear Filters
  • Laplacian filter
  • approximates the second derivative of the image
  • the basic kernel is (1,-2,1)
  • mostly 3x3 kernel is used with the sum of
    coefficients equal to 0
  • two basic types of 3x3 kernel are used, others
    are possible
  • often used after Gaussian filter(so called
    Laplacian of Gaussian LoG Mexican hat filter)
Write a Comment
User Comments (0)
About PowerShow.com