ELG 7173 - Assignment #3
Last Updated $Date: 2007-03-25 19:12:41 -0400 (Sun, 25 Mar 2007) $
The 5×5 image, f(m,n),
is processed by two systems in cascade.
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
The second system produces the output
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
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?
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
(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
X-ray image im_in using a 9×9 Gaussian convolution
kernel with β=0.5.
- Try different values of α and β,
using this chest X-ray.
Comment on the effect of these parameters.
Describe the function of the time gain compensation in an ultrasound
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?
$Date: 2007-03-25 19:12:41 -0400 (Sun, 25 Mar 2007) $