CSE190 – Image Processing – Homework #8
Instructor: Prof. Serge Belongie. T.A.: Josh Wills.
http://www-cse.ucsd.edu/~sjb/classes/wi02/cse190
Due (in class) 1:25pm Wed. Mar. 13, 2002.
Written exercises
1. Suppose you are given a set of Nfeature vectors {x1,x2,. . . , xN}and kprototype vectors
{m1,m2, . . . , mk}. Assume all of the vectors are of size n×1. Show that the N×kmatrix
of squared Euclidean distances between the feature vectors and the prototype vectors can be
obtained by computing the following matrix:
T=E1T
k+1NFT−2XTY
where Eis an N×1 vector with entries Ei=kxik2,Fis a k×1 vector with entries Fi=kmik2,
1is a column vector of ones whose length is given by its subscript, Xis an n×Nmatrix of
feature vectors, and Yis an n×kmatrix of prototype vectors.
2. Consider the 2 ×2 matrix
A=a b
c d .
Show that the inverse is given by
A−1=1
det(A)d−b
−c a .
Matlab exercises
1. Clustering in color space using k-means.
(a) Implement the k-means clustering algorithm as described in class. For the stopping
criterion, allow the user to supply a threshold on the change in J(the sum of squared error
over all clusters) on each iteration, as well as a maximum allowed number of iterations
(e.g. 25). Have your program output the value of Jon each iteration. Initialize the cluster
centers by choosing kfeature vectors at random from the data.
(b) Load in Figure 6.30(a) (the bowl of strawberries) and use imresize with the ’bilinear’
option and M=0.25 to reduce its resolution by a factor of 4 in xand y. Display the resized
image. Construct a matrix of 3-dimensional feature vectors for this image using the RGB
values of each pixel.
(c) Use k-means to perform clustering on this image using k= 3 and k= 4. In each case,
run three trials to see the effects of the random initialization. Display each of the six
resulting segmentations as a pseudocolor cluster membership image, like the example
shown in class. (Note: if you don’t have access to a color printer, it’s ok to use shades of
gray.)
Things to turn in:
•Code listing for parts 1a and 1b.
•Program output and parameter settings for part 1c.
2. Lucas-Kanade optical flow.
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