CS 659 Image Processing
Exam One
Name: Student ID #:
Covering Lectures 1~6. There are 4 questions. Each is 25 points.

1. (a) (10 points) Determine the convolution and correlation of the two sequences shown below.
   Note that, black dots represent value 1 and white dots represent value 0. Underline the pixel at
   the origin. Note that the answers are 4 by 4 matrices.

(b) (15 points) Perform the convolution
f g
and the correlation
f g
. Assume the origin is
located at the lower-left corner. Underline the pixel at the origin. Note that the answers are 3 by 4
matrices.
3 5 1 2 1
: , :
6 2 1 3

2. (a) (10 points) Apply contrast stretching to the image below using
   2, 1, 5, 7. r1 = s1 = r2 = s2 =
   Show your computation and the output image. Note that using rounding to be all integers.
3. 1 0 0 0 0 0 1
4. 1 1 1 0 1 0 1
5. 3 4 4 5 5 0 0
6. 3 4 4 5 5 5 5
7. 4 4 4 4 5 7 0
8. 1 4 5 6 5 6 1
9. 0 4 4 1 5 6 1
10. 0 1 1 1 0 5 0
    (b) (15 points)
    Let the input pixels {y(m)}={2, 3, 8, 4, 2} and the window W = [-1, 0, 1]. What is the median
    filter output {v(m)}? Let W contain an even number of pixels, say W = [-1, 0, 1, 2]. What is the
    median filter output {v(m)}? Note that let the boundary pixels stay the same (i.e., without the
    median computation). Note that using floating-point numbers (i.e., DO NOT round into
    integers).
11. (10 points) (a) Given a template f, find the location of exact match in the image g by using
    Correlation of fg minus Correlation of f'g. Show your calculations and mark the matched
    locations.
    (b) (15 points) Is it possible to perform the matching by using only one correlation (f and g are
    shown below)? If the answer is Yes, show the modified template and your calculations, and
    mark the matched locations. If the answer is No, describe your opinion why it cannot work.
    f:
12. 1 0
13. 0 1
14. 1 0
    g:
15. 0 0 0 0 0 0 0
16. 0 1 0 1 0 0 0
17. 1 0 1 1 1 1 0
18. 0 1 0 1 0 0 0
19. 0 0 0 1 1 1 0
20. 1 1 0 0 0 1 0
21. 1 1 0 0 0 1 0
22. 0 0 0 0 0 0 0
23. (25 points) Apply histogram equalization to the image below. Let the output gray levels are in
    the range of [0, 7]. Show your step-by-step calculations, the input/output pixel mapping, and
    the resulting output image.
24. 1 5 5 0 0 1 0
25. 1 2 2 0 1 0 1
26. 7 6 6 5 5 0 0
27. 7 6 7 5 5 5 5
28. 7 6 7 3 5 7 0
29. 1 4 1 6 5 6 1
30. 2 4 1 1 5 1 1
31. 2 2 0 0 0 0 5

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