Description
1 Overview
The goal of this lab is to provide some hands-on experience with fundamental image compression concepts
and techniques. Due to the exponential growth in usage and storage of digital graphic media, image compression has been very important in helping reduce storage and transmission bandwidth problems. Many
real-world applications depend heavily on image compression, such s digital photography, video games,
digital movie archival/streaming, and medical imaging. For this lab, we will study some fundamental image
compression techniques such as chroma subsampling, image transform, and quantization.
The following images will be used for testing purposes:
• lena.tif
• peppers.png
These images can be found on the course website.
2 Chroma Subsampling
First, we will study the effects of chroma subsampling on image quality and how it can be used to provide
image compression. For this study, we will use the peppers image. First, let us convert the image from
the RGB colorspace into the YCbCr colorspace using the rgb2ycbcr function. Plot each of the image
channels (Y, Cb, and Cr) separately.
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1. Describe the Cb and Cr channel images. Why do they appear this way?
2. Compare the level of image detail in the Cb and Cr images with the Y channel image. Which contains
more fine details? What does that say about the luma (Y) and chroma (Cb and Cr) channels?
Now, reduce the resolution of the chroma channels by a factor of 2 in both the horizontal and vertical directions and then upsample them back to the original resolution using bilinear interpolation. The imresize
function will come in handy. Also, you will need to separate the color image into three separate images so
you can operate on them independently. Recombine the original Y channel image and the two upsampled
Cb and Cr images to create a new color image. This can be considered a simple way of reducing network
bandwidth for image/video transfer – that is, downscaling the chroma images on the server, sending them
over a network to a client, and rescaling on the client.
1. Compare the resulting image from chroma sub-sampling with the original image. How large are the
visual differences?
2. Based on the resulting image, what can you say about chroma sub-sampling and its effect on image
quality?
Let us study the effects of luma sub-sampling. Reduce the resolution of the luma (Y) channel by a factor
of 2 in both the horizontal and vertical directions and then upsample it back to the original resolution using
bilinear interpolation. Recombine the upsampled Y channel image and the original Cb and Cr images to
create a new color image.
1. Compare the resulting image from luma sub-sampling with the original image. How large are the
visual differences?
2. Based on the resulting image, what can you say about luma sub-sampling and its effect on image
quality?
3. Compare the resulting image from luma sub-sampling with the image produced using chroma subsampling. Which method performs better? Which is better for reducing network bandwidth while
preserving visual acuity? Why?
3 Colour Segmentation
Image segmentation is useful in identifying regions of interest in an image to gain a more meaningful representation of the image. In this section, colour segmentation is explored using k-means classification to
segment various colours in an image using the RGB and L
∗a
∗
b
∗
colour spaces. The L
∗a
∗
b
∗
colour space
consists of a luminosity dimension (L
∗
) and two colour dimensions called a
∗
and b
∗
. The a
∗
channel indicates colour which falls along the red-green axis while the b
∗
channel indicates colours which fall along the
blue-yellow axis.
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Load the peppers.png image in Matlab and convert the image to the L
∗a
∗
b
∗
colour space. (Hint:
applycform is useful here.)
Then, classify the colours in the a
∗
and b
∗
colour spaces using k-means clustering for k = 2 and k = 4.
Use kmeans() to do colour segmentation with squared Euclidean distance and the following starting point
matrix, µ.
% K = 2;
% row = [55 200];
% col = [155 400];
K = 4;
row = [55 130 200 280];
col = [155 110 400 470];
% Convert (r,c) indexing to 1D linear indexing.
idx = sub2ind([size(f,1) size(f,2)], row, col);
% Vectorize starting coordinates
for k = 1:K
mu(k,:) = ab(idx(k),:);
end
First reshape the a
∗
and b
∗
channels:
ab = double(im_lab(:,:,2:3)); % NOT im2double
m = size(ab,1);
n = size(ab,2);
ab = reshape(ab,m*n,2);
Output the cluster indices and show the resulting classification for a given k, using the following code, where
cluster idx are the cluster indices. This should show in one image, each cluster with its own unique
colour.
% Label each pixel according to k-means
pixel_labels = reshape(cluster_idx, m, n);
h = figure,imshow(pixel_labels, [])
title(’Image labeled by cluster index’);
colormap(’jet’)
1. For the various values of k, how did the clustering change? Explain.
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2. What is the effect of the initial points on the final clusters? Does this impose any limitations? Why?
Next, output each cluster/segmented region using the original colours of the image using the pixel labels
found for k = 4. (Hint: repmat is useful here. When showing the segmented regions for a particular pixel
label, other pixels should be set to zero.)
3. Include an image of each cluster and comment on the segmentation performance.
4 Image Transform
Let us now study the discrete cosine transform (DCT) and the characteristics of an image in the transform
domain. The DCT decomposes an image into a series of sinusoids with different amplitudes and frequencies.
In block transform coding algorithms, the image is divided into smaller sub-images and each sub-image is
transformed using an image transform separately. Perhaps the most popular image transform for block
transform coding is the DCT. One efficient method for computing the DCT of a sub-image is to use the DCT
transform matrix. The DCT transform matrix can be constructed using dctmtx function. For this study,
we will use the 8×8 DCT transform matrix T and use grayscale Lena image f as the test image. Plot the
8×8 DCT transform matrix.
1. What does each row of the DCT transform matrix represent? Look at the pattern for each row. If you
still don’t see it, try plotting each of the rows as a 1-D function.
Now apply the DCT transformation matrix on each 8×8 sub-image. This can be performed as follows:
F trans = floor(blockproc(f-128, [8 8], @(x) T*x.data*T’));
Plot the DCT of the 8×8 sub-image with top-left corner at (row, col) = (297, 81) and the DCT of the
sub-image with top-left corner at (row, col) = (1, 1).
1. Describe the energy distribution of the DCT of the sub-images. What does each pixel represent? Explain why DCT would be useful for image compression in the context of the DCT energy distribution.
2. Compare the DCT of the two sub-images. How are they different? Why? Explain in the context of
the image characteristics at those locations and the DCT energy distribution.
Now let’s try discarding all but 6 of the DCT coefficients in each sub-image and then reconstructing the
image. This can be done by first applying a threshold to the sub-images,
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mask = [1 1 1 0 0 0 0 0;
1 1 0 0 0 0 0 0;
1 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0];
F_thresh = blockproc(F_trans, [8 8], @(x) mask.*x.data);
and then performing an inverse DCT on the sub-images
f_thresh = floor(blockproc(F_thresh, [8 8], @(x) T’*x.data*T)) + 128;
Plot the reconstructed image and the corresponding PSNR.
1. Describe how the reconstructed image looks compared to the original image. Why does it look this
way?
2. What artifact is most prominent in the image? Why does this artifact appear?
3. What conclusions can you draw about the DCT in terms of image compression? Does it work well?
If yes, why does it work well?
5 Quantization
One of the most important steps in lossy image compression stage is the quantization step. It is highly
desired that the transform coefficients of a sub-image is quantized in such a way that the amount of data
needed to represent the image is greatly reduced without causing undesirable artifacts. Let us now study the
effects of different levels of quantization on image quality. For this study, the grayscale Lena image will be
used as the test image. First, we will construct the quantization matrix used in the JPEG standard:
Z = [16 11 10 16 24 40 51 61;
12 12 14 19 26 58 60 55;
14 13 16 24 40 57 69 56;
14 17 22 29 51 87 80 62;
18 22 37 56 68 109 103 77;
24 35 55 64 81 104 113 92;
49 64 78 87 103 121 120 101;
72 92 95 98 112 100 103 99];
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Now perform the 8×8 DCT transform on the Lena sub-images (remember to subtract 128). To perform
quantization on the sub-images, divide the sub-images by Z, and then round the resulting quantized DCT.
To reconstruct the image, multiply the quantized DCT sub-images by Z and then perform the inverse DCT
transform on the sub-images (remember to add 128). Plot the resconstructed image and the corresponding
PSNR. Now perform the above quantization process again on the image, but this time using 3Z, 5Z, and
10Z. Plot the reconstructed images and the corresponding PSNR.
1. What happens to the DCT coefficients when quantization is performed? What effect does it have on
image quality?
2. Compare the reconstructed image produced using 3Z with the original image. Why does the reconstructed image look this way?
3. Compare the reconstructed images produced by the different levels of quantization, as well as the
PSNR for each reconstructed image. What happens as the level of quantization increases?
4. Which artefact becomes more prominent as the level of quantization increases? Why?
5. What conclusions can you draw about the quantization process? Explain in the context of the trade-off
between compression performance and image quality.
6 Report
Include in your report:
• A brief introduction.
• Pertinent graphs and images (properly labelled).
• Include code (can be included in appendix).
• Include responses to all questions.
• A brief summary of your results with conclusions.
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