Homework 4
16-311 Introduction to Robotics
Prof. Howie Choset

• (70%) Group: Dead Reckoning

• (30%) Individual: Convolution.

  Individual Work (but learning from each other is encouraged)
  • Write a C or MATLAB program to perform convolution (if you want to use another language, ask me but it is probably fine).

    If written in MATLAB you should use only very basic functions and operators. The ''conv'' function is right out. If in doubt, write your own version of the function in question, or ask the head TA.
    Your program should input two pgm file names from the keyboard: one for the image and one for the mask. It should save the result as "output.pgm".
    Write a function that convolves the mask with the image.
    The size of the input and output images should be the same. To make things easier, you will not have to worry about padding the edges of the input image, as discussed in class. Instead, we will just accept that the right-most and bottom-most pixels in the output image will be "wrong."
    In other words, if the input image has r rows and c columns and the mask has m rows and n columns, the output image will have r rows and c columns but the first r-m+1 rows and c-n+1 columns will have the output. Simply put zeros in the remaining rows and columns.

  • Use your program to perform convolution on these two images with each of the three masks provided for a total of six output images. Make a web page which shows these six images.
    Be sure to do a contrast operation after the convolution, so that the values range from 0-255!

  The masks:
  mask1.pgm
  mask2.pgm
  mask3.pgm
  
  The images:
  image1.pgm
  image2.pgm
  
  
  • Also answer the following questions.
    • (a) What do these masks do to the input image?

    • (b) What are the advantages of using a small mask? Why would you want to use a large mask?

    • (c) Suppose you wanted to identify the horizon in images at sea. What mask might you use to do this?

  • Some sample code based on last week's code is here.
    A note:
    There may be some confusion about the FlipMask routine in the code provided for homework 4. Basically, this routine takes the input mask and rotates it about the origin by 180 degrees. Why? Well, as you might remember from class, convolution technically requires the mask to be flipped. If you don't flip the mask, the operation is called correlation. Many members of the vision community use the two interchangeably, which is why we told you not to worry about flipping the mask. In the starter code provided, we flipped the mask. You can opt to simply comment this out or you can use the convensional/signal processing version of convolution and flip the mask -- it is your choice. However, for the masks and images provided, it really doesn't make much difference--do you know why? Please be careful; it is easy to get confused, but resolving this confusion will have a nice payoff!

Turn in:

Email the head TA with:
• A link to your web page (which has your images and a POINTER to your source code)
• A link to an AFS path with your executable or matlab script. The andrew unix machines have matlab installed, so you can test your code there using X-frowarding, or by running "matlab -nodesktop" which will give you a matlab command prompt and you can type the name of your executable there. As usual make sure I have permissions. If you use matlab, I'll need read permissions for your scripts and also write permissions in your folder so I can save the output image.
• Answers to the above questions (in the e-mail and/or on your webpage. Use a .pdf if you want anything other than text).