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ELG 7173 - Assignment #3

Last Updated $Date: 2007-03-25 19:12:41 -0400 (Sun, 25 Mar 2007) $

  1. Image Filters

    The 5×5 image, f(m,n), is processed by two systems in cascade.
    f(m,n) =
    0 0 0 0 0
    0 9 8 7 0
    0 9 8 7 0
    0 9 8 7 0
    0 0 0 0 0

    The first system produces the output g1(m,n) = f(m,n) − f(m−1,n).
    The second system produces the output g2(m,n) = g1(m,n) − g1(m,n−1).
    1. i) Compute images g1 and g2 ii) Does the sequence of application of the two operators affect the result? Why or why not? iii) Explain the effects of the two operators

    2. An image is processed by applying the 3×3 mean filter mask twice in series. i) Show a single filter which implements the combined effect ii) What is the effect of applying a 3×3 median filter twice in series? Can this be represended by a single filter?

  2. Image Filtering

      In this section we develop the unsharp mask. This is classic (and still widely used) technique for image enhancement. It was originally implemented entirely with photographic techniques in the development process.

    1. Develop an Octave or Matlab™ function:
      function kernel= Gaussian_kernel(beta, kernel_size)
      This function calculates a Gaussian blur convolution kernel, in which the amplitude of each pixel is exp(−βr²), where r is the radial distance (in pixels) from the convolution kernel centre. kernel_size can be assumed to be an odd, positive integer.
      For example, k=Gaussian_kernel(0.2,9), will calculate a 9x9 matrix, in which the centre pixel (5,5) will have a value of
      exp(−0.2×0²) = 1
      Pixel (3,2) will have a value of
      exp(−0.2×( (3−5)²+(2−5)²)) = 0.074.
      Subsequently, the Gaussian kernel will need to be normalized, such that sum(sum(Gaussian_kernel(beta,kernel_size))=1.

    2. Derive the expression for the unsharp mask based on the Gaussian filter in the previous question, using a parameter α as given in class. Write a function to calculate the unsharp mask filtered image of the X-ray image im_in using a 9×9 Gaussian convolution kernel with β=0.5.

    3. Try different values of α and β, using this chest X-ray. Comment on the effect of these parameters.

  3. Ultrasound Imaging

    1. Describe the function of the time gain compensation in an ultrasound amplifier?
    2. Improved focus may be achieved using various techniques. In class we discussed mechanical focusing (acoustic lens), and electronic focusing (transducer arrays). Describe one of the techniques. How does it work, and how does it focus the ultrasound beam?

Last Updated: $Date: 2007-03-25 19:12:41 -0400 (Sun, 25 Mar 2007) $