An orthogonal matrix is a square matrix whose columns are orthogonal (dot product with other columns is 0) and have unit norm (dot product with self is 1). From this, it can be shown that its inverse is equal to its transpose (if A is an orthogonal matrix and A^{T} its transpose, then A * A^{T} is the identity matrix).
Do the following:
Deliverables: A text file named p1.txt
containing your matrix, its transpose, and the output from your
program.
Meet Waldo.
Waldo, as you may be aware, frequently hides, and we need to find him. Your job is to create a program which will automatically locate Waldo (and his doppelgangers) in images such as this:
Each image contains the following kinds of Waldos:
Your program must read the input image from findWaldo.png
and write the results to a file called waldo.txt
. This file
must contain one line for each Waldo identified. Each line must contain
the first index (the x coordinate) of the image, a space, and then the
second index (the y coordinate), followed by a newline.
For example:
13 47 78 13 107 33Your numbers need to be within 2 pixels of the center of the Waldo for the normal size Waldos and 4 pixels for the 2x size Waldos. You can output decimal numbers if you'd like. Note that in our convention, images are indexed (x,y) starting from the upper-left corner, with x increasing to the right, and y increasing downward. Be careful, as this is different from matrices, which are indexed (y,x)!
Grading:
Your assignment will be graded as follows:
./findWaldo.png
(./ means the current directory). You may
hardcode this into your program. Your code will be run on three
different maps and your grade will be the average score of the three
runs. Here are several sample pictures to test your code on, and an
image of Waldo himself:
Note: please do not utilize library functions that trivialize the problem. Specifically, the image processing functions, ie. imrotate, imresize, etc. should not be used.
Matlab starter code that reads PNGs is available here: WheresWaldo.m.
Deliverables:
p2.m
Collect ONLY your deliverables into a tar archive named
[AndrewID]_hw1.tar
, where [AndrewID] is replaced by
your Andrew ID, minus the brackets. For example, user with AndrewID
odb
would submit odb_hw1.tar
.
Instructions to submit the tar file TBA.
Failure to follow instructions on this homework will result in an
automatic zero.