Multimedia University: EMM3126 Digital Image and Video Compression Lab Experiment 2
EMM3126 Digital Image and Video Compression
Lab Experiment 2
Generating a JPEG Encoder and Decoder
Objective
To learn the fundamentals of JPEG encoder and decoder using MATLAB.
Equipment
MATLAB software.
Introduction
JPEG is an image compression standard developed by the Joint Photographic
Experts Group, which was formally accepted as an international standard in 1992.
The JPEG standard allows for both lossy and lossless compression of still images.
The algorithm for lossy coding is a DCT-based coding scheme. This is the baseline
of JPEG and is sufficient for many applications. However, to meet the needs of
applications that cannot tolerate loss, e.g., compression of medical images, a
lossless coding scheme is also provided and is based on predictive coding scheme.
From the algorithm point of view, JPEG includes four distinct modes of operation,
namely, sequential DCT-based mode, progressive DCT-based mode, lossless mode
and hierarchical mode.
In the sequential DCT-based mode, an image if first partitioned into blocks of 8 x 8
pixels. The blocks are processed from left to right and top to bottom. The 8 x 8 twodimensional forward DCT is applied to each block and the 8 x 8 DCT coefficients are
quantized. Finally, the quantized DCT coefficients are entropy encoded and output
as part of the compressed image data.
In this lab experiment, we will carry out a simple experiment based on sequential
DCT-based mode, with the encoder and decoder block diagram of a typical
sequential DCT-based mode JPEG shown in Figure 1 below.
Since the entropy encoder and entropy decoder are complicated, it will not be
implemented in this lab experiment. This experiment will be carried out by using a
gray scale image.
Revised September 2010 by Dr. Chang Yoong Choon
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Multimedia University: EMM3126 Digital Image and Video Compression Lab Experiment 2
Figure 1. Block diagram of a typical sequential mode JPEG encoder and decoder.
Procedures:
Part 1: Importing Image to MATLAB
Type the command below at MATLAB command prompt:
I = imread('cameraman.tif');
Then type
size(I)
What does the size of I corresponds to?
Now type
imfinfo('cameraman.tif')
With the information obtained from iminfo, answer the following questions:
a.
b.
c.
d.
e.
f.
g.
How many bits are used for every pixel intensity?
What is the height of the image?
What is the width of the image?
What is the color type of the image?
What is the minimum value of the pixel intensity?
What is the maximum value of the pixel intensity?
Why do we have these minimum and maximum values?
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Multimedia University: EMM3126 Digital Image and Video Compression Lab Experiment 2
Part 2: Shifting Down Pixel
The first step in this JPEG experiment is you have to shift the pixel value by -2P-1,
where P is the number of bits used. Construct a MALAB to carry out this operation.
Hints: You may use MATLAB command ones().
function h = shift_down(array,bit)
% Write the code yourself
You should be able to execute the command below
I = shift_down(I,8);
Part 3: Forward Discrete Cosine Transform (FDCT)
The next step is to carry out Forward Discrete Cosine Transform (FDCT) 8-by-8
block of matrix I. However, in this part of the experiment, we will be using a simplified
FDCT that is used for an 8-by-8 matrix. The transform matrix T is given by
T pq 
1
8
 0.25 cos
p  0, 0  q  7
 ( 2q  1) p
16
1  p  7, 1  q  7
For an 8-by-* matrix A, T * A is an 8-by-8 matrix whose columns contain the onedimensional DCT of the columns of A. The two dimensional DCT of A can be
computed as B= T * A * T’ ( T Transpose). The inverse two-dimensional DCT of B is
given by T’ * A * T. The matrix T can be invoked with the command
T = dctmtx(8)
To process 8-by-8 block of matrix A, we will use the command blkproc.
C = blkproc(I ,[8 8], fun, P1, P2 .. ) processes the image I by applying the function
fun to each distinct 8-by-8 block of I, padding I with zeros if necessary. fun can be an
inline function, a text string containing the name of a function, or a string containing
an expression. fun should operate on an 8-by-8 block, x, and return a matrix, vector,
or scalar y:
y = fun(x)
P1 and P2 are the additional parameters that are passed to fun. To test blkproc, type
the command below
blkproc(I, [8 8] , 'P1 + x' , ones(8,8))
You are now required to construct a MATLAB program to carry out FDCT on 8-by-8
block of I.
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Multimedia University: EMM3126 Digital Image and Video Compression Lab Experiment 2
function h = FDCT(matrix)
% Write the code yourself
Part 4: Quantization
Before we implement the quantization, we need to implement the quantization table.
The formula to generate the quantization table is given by
Qij  1  (1  i  j ) * quality
where 0  i  7, 0  j  7
The parameter quality specifies the quality factor and the recommended range is
from 1 to 25, where quality =1 gives the best quality but the lowest compression rate.
Notice that the quantization table is an 8-by-8 matrix.
The quantization output is such that
 I ij 
Iˆij  round  
 Qij 
where Qij is the quantization table, and I ij is the FDCT matrix from Part 3. You are
now required to construct a MATLAB code to implement the quantization process.
function h = quantization(matrix, quality)
%write the code yourself
Part 5: Putting the Whole JPEG Encoder
Now, try putting the whole encoder together, starting from shifting down the pixel
intensity value, to FDCT, and then implementing the quantization. You are now
required to construct a MATLAB code to perform this operation.
function h = jpeg_encoder(picture, quality)
%write the code yourself
Part 6: Creating the JPEG Decoder
In order to construct JPEG decoder, first you have to dequantize the encoded matrix.
To dequantize, you can use
Iij  Qij Iˆij
where Qij is the quantization table from Part 4, and Iˆij is the dequantized matrix.
Then, we need to carry out the IFDCT, remember that the 8-by-8 transform matrix T
is given in Part 3. The IFDCT of matrix Iij is J  T  * I * T . The final stage will be
shifting up J by 2P-1 where P = 8 is used for representing an intensity value of a pixel.
Construct a MATLAB code to perform the decoder operation.
Revised September 2010 by Dr. Chang Yoong Choon
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Multimedia University: EMM3126 Digital Image and Video Compression Lab Experiment 2
function h = jpeg_decoder(matrix, quality)
%write the code yourself
Part 7: Creating the Whole JPEG Operation
You are now required to construct a MATLAB code to integrate the JPEG encoder
and decoder you have just constructed.
function h = jpeg_operation(picture,quality)
%write the code yourself
Part 8: Analysis of Reconstructed Image Quality
In the last part of this experiment, you are required to analyse the reconstructed
image quality by changing the quality factor to 2, 5, 7, 20 and 50. Discuss your
observations in the lab report when the quality factor is changed to 2, 5, 7, 20 and
50. Compute also the PSNR value of the reconstructed image when you change the
quality value.
Marking Scheme
Evaluation for this lab experiment is through written lab report. The lab report should
be handwritten (MATLAB code and results can be computer generated) and follow
the standard report format, i.e. begin with Introduction and end with Conclusion.
Students should answer all questions and discuss the observations. Marks will be
given in the scale of 0 to 100, based on the following marking scheme:
i) Lab experiment overview (10 marks)
 Introduction to the experiment
 Summary of the lab experiment
 Procedure
ii) Results and observation (50 marks)
 Explain the results gathered from the experiment
 Answer all questions listed in the experiment
iii) Discussion and conclusion (10 marks)
 Conclusive remarks on the experiment
iv) Written communication skill (30 marks)
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