Assignment 5: Probability and Image Understanding
CSE 415: Introduction to Artificial Intelligence
The University of Washington, Seattle, Autumn 2009
There is no assigned reading for the probabilty part of this assignment, but the lecture notes are the main reference. You are welcome to use any online resources in addition. The reading for the image understanding part of the assignment is linked from the textbook page.
Due Monday, December 7 via Catalyst CollectIt at 11:00 AM.

You should turn in a file in any of the following formats: plain text (.txt), Portable Document Format (.pdf), Microsoft Word (.doc or .docx), or Open Office Text (.odt).
 

  • Recall the fact that the probabilities of a set of mutually exclusive outcomes that represent all the possibilites for a given event must sum to 1. Use it to fill in the gap in the following set of four probability values.

    A: It is snowing at 7 AM on a December morning in Slalom Pass.

    B: It is below 20 degrees Farenheit at 7 AM on a December morning in Slalom Pass.

    P(A^B)=0.4, P(A^~B)=0.2, P(~A^B)=0.3, P(~A^~B)=?.

    Now determine:

    P(A):

    P(B):

    P(A|B):

    P(B|A):

    Finally, show how Bayes' rule expresses P(B|A) in terms of the other values and check your value for P(B|A) by computing it that way.

  • In the Monty Hall problem, determine (a) the probability of winning the car given that you don't (ever) switch your guess. (b) the probability of winning the car given that you do (always) switch your guess. (c) which strategy is more likely to win.
  • An inspection robot for Bloeing airplane wings has the simple job of making sure all 256 rivets are in place along the leading edge of the wing. It will use one digital image to capture the region containing the rivets. Assume that the rivets are 2 cm in diameter and are evenly spaced 2 cm apart, all in a straight line, and that the rivets are dark on a light background. What is the minimum number of pixels theoretically necessary in order to "see" all the rivets and spaces between them? Is this number a safe number for representing this scene? Explain.
  • Consider the following binary images. Compute A eroded by B. Assume that the origin for B is at its center. 
    1  0  1  0  1  1
1  1  1  1  1  1
1  1  1  1  1  1    0  1  0
0  1  0  1  0  1    1  1  1
1  1  1  1  1  1    0  1  0
0  1  1  1  1  1
       (A)            (B)
  • The Hough transform is most commonly used to find straight lines in an image. Modify the formula given in the lecture slides so that it could be used to find circles.
    • Updates and Corrections If necessary, updates and corrections will be posted here and mentioned in class or on the mailing list. (Last updated Nov. 30.)