Digital Image Processing

Dept. of Electrical and Computer Engineering Miami University
1
Homework 1 Assignment
Weights: 30pts
Due Date: August 30, 2020.
Turn in Method: Upload your homework to class web-site midnight of August 30.
Due Date: August 31, 2020
Weight: 30 points

1. (6pts) Textbook (4th edition) problems: 2.16(b)(c).
   Consider the two image subsets S1 and S2 in the following figure. With the reference to
   Section 2.5 and assuming V = {1}, determine whether there two subsets are (a) 4-adjacent (b)
   8-adjacent (c) m-adjacent (Note: you can find solution of 2.16(a) in the textbook website)
2. (9pts) Textbook (4th edition) problems: 2.20 (b).
   Consider the image segment shown in the figure that follows. (Note: you can find solution of
   2.20 (a) in the textbook website)
3. (15 pts) In the lecture note #3 slide 32 and 36, we define the affine transformation of
   coordinate as
   ECE 429/529 Digital Image Processing
   Fall 2020
   Dept. of Electrical and Computer Engineering Miami University
   2
   [? ? 1] = [? ? 1]? = [? ? 1][
   ?11 ?12 0
   ?21 ?22 0
   ?31 ?32 1
   ]
   where (x, y) are the transformed coordinates, (v, w) is the original coordinate and the element
   of T for various types of transformation are given below:
   The inverse transformation T-1, to go from the transformed back to the original coordinates
   is just as important for performing inverse mapping
   (a) Find the inverse scaling transformation
   (b) Find the inverse translation transformation
   (c) Find the inverse vertical and horizontal shearing transformation
   (d) Fine the inverse rotation transformation
   (e) Show a composite inverse translation/rotation transformation
   (Note: The affine transformation matrices are defined differently in the 3rd and 4th edition of
   textbook. Both are correct. We follow the definition used in the 3rd edition because Matlab
   uses the same definition).

Sample Solution