Comp 665 - Fall 2008 - 1 - Problem Set #1
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Comp 665 Imaging, Graphics, and Vision
Fall 2008
Problem Set #3
Issued Tuesday, 11/4/08; Due Wednesday, 11/18/08
Homework Information: Some of the problems are probably too long to be done the night
before the due date, so plan accordingly. Late homework will penalized as explained on the
course Web site. Feel free to get help from others, but the work you hand in should be your own.
Problem 1. “PCA Compression”
In class we developed a principal component color space for the Mandrill image that was able to
capture more than 95% of the variance using only 2 color components. In this exercise, you are
asked to develop PCA model for each 2 x 2 block of pixels in the Mandrill image. As shown in
lecture 17, each 2 x 2 block of pixels can be considered as a point in a 12-dimensional “image-
block space”.
A) How many principal components are necessary to represent 95% of the variance under
the assumptions of this model?
B) Give the mean “image-block” vector, and the first 2 principal-components (factors) and
their associated eigenvalues.
C) Plot the projection of each “image-block” onto the first two principal-components.
D) How many principal-components are required to match the same MAE metric of the
vector quantization method mentioned in class?
E) Explain how PCA and VQ might be combined to further reduce the overhead of PCA
compression. Make sure that to discuss any additional overheads that this combination
would require.
Problem 2. “Combining Error-Diffusion and VQ”
It is straightforward to combine error-diffusion dithering, as discussed in lecture 16, with vector
quantization, discussed in lecture 17. It entails a small modification to the VQ loop given in class,
where the error introduced by choosing the nearest codebook entry is distributed to pixels that
will be subsequently quantized.
A) Implement a vector quantizer of the MandrillTiny image that uses at least 10 iterations of
the Linde-Buzo-Gray algorithm to establish a codebook with 32 color entries. Use
whatever method you like to generate your initial codebook.
B) Print a list of all 32 r, g, b triples in your final codebook.
C) Compute the MAE using VQ only and print your resulting image.
D) Modify your previous vector quantizer to incorporate error-diffusion dithering. Once
again compute the MAE (relative to the original source image) and print your result.
E) Comment on the relative artifacts seen in the two images. Note any noticeable image
contours introduced by the vector quantization and noise artifacts.