
ELG 7173  Assignment #3
Last Updated $Date: 20070325 19:12:41 0400 (Sun, 25 Mar 2007) $

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
g_{1}(m,n) =
f(m,n) −
f(m−1,n).
The second system produces the output
g_{2}(m,n) =
g_{1}(m,n) −
g_{1}(m,n−1).

i) Compute images g_{1} and g_{2}
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

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?

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.
 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.
 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
Xray image im_in using a 9×9 Gaussian convolution
kernel with β=0.5.
 Try different values of α and β,
using this chest Xray.
Comment on the effect of these parameters.

Ultrasound Imaging

Describe the function of the time gain compensation in an ultrasound
amplifier?

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: 20070325 19:12:41 0400 (Sun, 25 Mar 2007) $
