Page 292 -

5.7 Exercises 271

3. Replace the current value with this weighted mean and iterate until either the motion is
below a threshold or a finite number of steps has been taken.
4. Cluster all final values (modes) that are within a threshold, i.e., find the connected
components. Since each pixel is associated with a final mean-shift (mode) value, this
results in an image segmentation, i.e., each pixel is labeled with its final component.
5. (Optional) Use a random subset of the pixels as starting points and find which com-
ponent each unlabeled pixel belongs to, either by finding its nearest neighbor or by
iterating the mean shift until it finds a neighboring track of mean-shift values. Describe
the data structures you use to make this efficient.

6. (Optional) Mean shift divides the kernel density function estimate by the local weight-
ing to obtain a step size that is guaranteed to converge but may be slow. Use an alter-
native step size estimation algorithm from the optimization literature to see if you can
make the algorithm converge faster.