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Dr. Chittaranjan Verma delivered this lecture for Digital Image Processing course at B R Ambedkar National Institute of Technology. It includes: Basic, Compression, Methods, Huffman, Coding, Symbol, Based, Predictive
Typology: Slides
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^
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Decompose a multilevel image (grayscale or color) into aseries of binary images ^
Apply any binary image compression encoding schemee.g. run length encoding, symbol based coding
^
^
Gray level r of an m-bit image can be represented in polynomialform
1
1
2
1
0
1
2
1
0
0
2
2
2
2
2
where
= 0 or 1
m
m^
m^
i
m^
m^
i i
i
a^
a^
a^
a^
a
a
^
^
^
^
^
^
^
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^
^
^
127 (01111111) = 01000000 (gray code) ^
128 (10000000) = 11000000 (gray code)
1
1
1
0
2
i^
i^
i
m^
m
g^
a^
a
i^
m
g^
a
^
Exclusive OR
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Binary code
Gray code
Binary code
Gray code
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Block Transform Encoding^ 1. Input MxN image is subdivided into sub images of size nxn2. nxn sub images are converted into transform arrays. This
tends
to
decorrelate
pixel
values
and
pack
as
much
information as possible in the smallest number of coefficients
selectively
eliminates
or
coarsely
quantizes the
coefficients with least information
quantized coefficients NOTE: Any of the above steps can be adapted to each subimage:
(adaptive transform coding), based on local image information
Encoder Decoder
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Choice of transformation function depends on ^
Acceptable amount of reconstruction error ^
Computational resources
^
Consider an
n x n
subimage
g(x,y)
whose generalized
discrete forward transform
T(u,v)
(transform coefficients) can
be given as: ^
The generalized inverse transform is given as: ^
r(x,y,u,v)
and
s(x,y,u,v)
are called forward and inverse
transformation kernels or basis functions or basis images
1
1 0
0
( , )
( ,
) ( ,
,^
, )
for
,^
0,1, 2,...,
1
n^
n x^
y
T u v
g x y r x y u v
u v
n
^
^
^
1
1 0
0
n^
n u^
v
^
^
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Transform selection: Example Three
approximations
of
the
512x
gray
scale
image.
These
pictures
were
obtained by dividing the original image into subimages of size 8x8, representingeach
subimage
using
one
of
the
transform,
truncating
50%
of
the
resulting
coefficients and taking the inverse transform of the truncated coefficient array. Thedifference between original and reconstructed image is also shown
DFT Transformrms error =2.32 gray levels
WHT Transform
rms error = 1.78 gray levels
DCT Transformrms error =1.13 gray levels
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^
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^
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Zonal coding
: Transform coefficients with large variance
are retained. Same set of coefficients retained in allsubimages ^
Threshold coding
: Transform coefficients with large
magnitude in each subimage are retained. Different set ofcoefficients retained in different subimages
^
^
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A typical zonal mask. Retained coefficients are
shown in shaded
Zonal bit allocation
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^
^
^
A single global threshold for all subimages ^
A different threshold for each subimage ^
Threshold as a function of location of coefficient
^
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Thresholding schemes and Coding ^
A single global threshold for all subimagesThe level of compression differs from image to image dependingupon the number of coefficients that exceeds the global threshold ^
A different threshold for each subimageSame number of coefficients are discarded for each subimage
coding rate is constant and known in advance ^
Threshold as a function of location of coefficientIt results in a variable code rate. In this case, the quantizationand thresholding can be combined
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^
^
^
Encoder Decoder
