Problem Set 4
CMSC 426
Assigned Tuesday, October 25, Due Tuesday, November 1
The goal of this assignment is for you to implement the K Means algorithm to cluster
pixels in an image by their intensity. This algorithm works iteratively. We are given an
image and a number k, which indicates the number of clusters we are to produce. First,
we guess some reasonable values for the central intensity of each cluster. Then we
alternate between performing the following two steps. 1) Every pixel is assigned to a
cluster. A pixel is assigned to the cluster whose central intensity is closest to the pixel’s
own intensity. 2) For every cluster, we recompute the central intensity as the mean
intensity of all pixels that have been assigned to that cluster. We stop this iteration when
the centers of the cluster stop changing.
Here’s an example of how this might work. Suppose the “image” consists of three pixels
with intensities: 0, 100, 255, and we want to form these into two clusters. We might start
out by guessing random intensities between 0 and 255 for the two cluster centers. For
example, we might guess the values 30 and 140. Then we would assign the pixel with
intensity 0 to the cluster centered at 30, and we would assign pixels with intensities 100
and 255 to the cluster centered at 140. Next, we would assign the first cluster a center of
0, and the second cluster a center of 177.5. In the next iteration, none of the cluster
assignments would change, so none of the cluster centers would change, and we would
stop.
1. 25 points Write a function that will take, as input, a vector of cluster centers, and
an image, and that will return a representation showing which pixels are assigned
to which clusters. For example, given input of cluster centers = [17 23] and an
image = [3 19 22 4 17 44 5] the output might look like: [1 1 2 1 1 2 1]. You do
not need to represent your input or output in this fashion, however; just document
your representation (in my code, I find it easier to use a 3D matrix to represent
cluster membership). If a pixel intensity is equidistant from two cluster centers,
you can handle this in any way you choose. Of course, although this example is
1D, your code must work for a 2D image. Hint: Be sure to convert images from
uint8 to double before performing any arithmetic operations.
Turn in your documented code, and a run showing the output of your code on the
example given in the previous paragraph.
2. 25 points Write a function to display your results. This function should take as
input the cluster centers, and a representation that shows which cluster each pixel
is assigned to. Use these to generate a new image, in which each pixel intensity is
replaced by the value of the cluster center it has been assigned to. For example,
with input like: [17 23] for the cluster centers, and [1 1 2 1 1 2 1] for the cluster
assignments, this function will create an image: [17 17 23 17 17 23 17].
