CS3851 -- Homework

Overview

You are encouraged to work on the homework in groups; however, each student is required to submit solutions to each homework assignment. During the lecture period immediately after the homework assignment has been announced, the class may select one problem to be removed from the assignment (provided at least half of the class can summarize the problem statement for the problem being removed).

Each problem will be graded on the following scale:

  • -3 points: substantially incorrect
  • 0 points: minor mistakes, unorganized, or unclear
  • 3 points: Clearly presented and correct
When calculating your final grade, I will add your average homework problem score to your lab/exam grade. For example, suppose your grade for all exams and lab assignments is 86.3%. If you do not turn in any homework, your final grade will be 83.3% (BC). If you submit correct and clearly presented solutions to all of the problems, your final grade will be 89.3% (AB).

Homework is due at the beginning of the class period indicated. (The one hour grace period does not apply.)

Specific Assignments

Due: 4pm, Friday Week 1

Support forum sign-up:

Create an account, login, and post at least one message to my support forums. You may post just a test message in the test forum, but you may post a "real" message if you prefer. Be sure to indicate who you are in your post (or by using an obvious login name) in order to receive credit for this homework assignment. This assignment must be done individually. Please note that you must click the link contained in the welcome email before you will be able to post messages on the forum.

Week 2 Lecture 3

1.1-1, 1.1-2, 1.2-2, 2.1-1, 2.2-1, 2.3-1, 2-1, and 3.1-1

Week 3 Lecture 2

A.1-1, A.2-1, 4.1-1, 4.3-1, 4.3-2, 4-2, and 4-3

Week 4 Lecture 2

6.1-1, 6.1-5, 6.2-1, 6.2-3, 6.2-4, 6.3-2, 6.4-3, 7.1-1, 7.1-2a, 7.1-4, 7.2-2, and 7.3-2

Week 5 Lecture 3

9.1-1, 9.2-4, 9-1, 16.3-2, 16.3-4 (this need not be a formal proof)

Week 7 Lecture 1

22.1-1, 22.1-2, 22.2-1, 22.2-3, 22.3-2, 24.3-1 and 24.3-2

Week 9 Lecture 3

15.2-1, 15-2, 16.2-2, 16-1a&c, 34.1-1, 34.1-4, and the segmentation problem given below:

An important problem in image processing is called segmentation. You are given image, which can be thought of as a matrix of pixels A[1..m, 1..n]. The pixel at i, j is white if A[i, j] = 1 and black if A[i, j] = 0. The segmentation problem is to partition the image into a set of rectangles, such that each rectangle is either all black or all white. Here is an example:

To simplify the problem, we will assume that the partition is constructed in a very particular way, called a guillotine decomposition. Given any rectangle, you can partition it into two smaller rectangles by cutting completely through the rectangle by either a horizontal or vertical cutting line. In particular, once you start cutting, you cannot change directions or stop part way through cutting.

The resulting rectangles may be decomposed further by repeating this operation. The cost of a guillotine decomposition is the total number of cuts that are made.

Devise a dynamic programming algorithm to determine the minimum cost guillotine segmentation for an image. Hint: Let C[i0,i1,j0,j1] denote the minimum cost of decomposing the rectangular subarray A[i0,i1,j0,j1].

Instead of pseudocode, just give the recursive rule for computing C[i0,i1,j0,j1]. Which entry of the C array is the final answer?

  • © 2001-2009 Dr. Christopher C. Taylor •
  • Office: L-343 •
  • Phone: 277-7339 •
  • npǝ˙ǝosɯ@ɹolʎɐʇ