1.  Suppose that an image of dimensions 4กม6 inches has detail to the frequency of 300 dots per inch in each direction.
(a) How many samples are required to preserve the information in the image?
(b) How many values are contained in the DFT F(a, b) of the image?
(c) Suppose that the image is sampled at a frequency that corresponds to detail up to 600 dots per inch (but in reality the detail only goes to 300 dots per inch). What is the effect on the DFT?

2.  Explain how does image Histogram equalization work.

3.  Please explain why MRI scan uses different magnetic fields.

4.  Summarize the general Snakes method for segmentation.

5.  A binary array that represents a portion of a black and white image is given below. Perform the operations listed below on this piece of image. Assume that all of the pixels that surround this segment contain black background.
0 0 0 0 0 0 0
0 0 1 1 0 0 0
0 0 0 1 0 0 0
0 0 0 1 1 0 0
0 0 1 1 1 1 0
0 0 1 1 1 0 0
0 1 0 1 0 1 0
0 0 0 0 0 0 0
(a) Dilation with the structuring element (1) 1 1. The origin is the '1' in bracket.
(b) Erosion with the structuring element (1) 1 1. 
(c) Dilation with the structuring element
1 (1)
0  1
(d) Erosion with the structuring element
1 (1)
0  1
(e) Opening with each of the above structuring elements.
(f) Closing with each of the above structuring elements.