Lossless Compression of Dithered Images
Basar Koc #1, Ziya Arnavut *2, Huseyin Kocak #
1 Department of Computer Science, University of Miami, Miami, FL 33146 USA
(Email id: b.koc@ umiami.edu)
2 Department of Computer Science, SUNY Fredonia, Fredonia, NY 14063, USA
Abstract- In order to display high-bit resolution images on
low-bit resolution displays, bit resolution needs to be
reduced. This problem is vital especially for low-cost or
small (mobile) devices. To untangle the bit reduction
problem, special color quantization algorithms, called
dithering, are employed on high-bit resolution images. The
dithering process helps to provide solution the problem,
but it does not help much in terms of storage and
transmission of images. To reduce storage and to lower
data transmission, numerous special compression
techniques have been proposed in the last several decades.
While the well-known compression algorithms, such as
gzip, help lower image file sizes, they are not usually
adequate. To improve the compression gain, special
compression techniques that take into account structure of
image data must be developed. We propose to implement
the pseudo-distance technique (PDT) for dithered images
which has been reported in the literature earlier [6].The
compression result of this approach will be compared with
result of graphic interchange format (GIF) and portable
network format (PNG).
Keywords— Color palette, lossless image compression, dithering,
pseudo-distance metric, GIF, PNG
I. INTRODUCTION
For long term storage and efficient transmission of data,
data compression is critical. Over the past decade,
several compression techniques have been proposed.
Few of the researchers [1,2] focused on general data
compression, while others [3,4] designed more specific
file compression techniques for movies, sound, and
image files. When a file type is known, better
compression results can be attained with less effort
because better prediction models can be designed.
Usually, this set of available colors, called a color
palette, may be selected by a user from a wide variety of
available colors. Such device restrictions make it
particularly difficult to display natural color images
since these images usually contain a wide range of
colors which must then be quantized by a palette with
limited size. This color quantization problem is
considered in two parts: the selection of an optimal color
palette and the optimal mapping of each pixel of the
image to a color from the palette.
Color quantization proposed by M.T.Orchard and
C.A.Bouman [2] of images develops algorithms for
the design of hierarchical tree structured color
palettes in cooperating performance criteria which
reflect subjective evaluations of image quality.
Tree structured color palettes greatly reduce the
computational requirements of the palette design
and pixel mapping tasks, while allowing colors to
be properly allocated to densely populated areas of
the color space. The algorithms produce higher
quality images and require less computation than
earlier non-hierarchical method. A color image
quantization is a three-step process: the first step is
designing a suitable palette to reduce the number of
colors, the second step is coding, and the final step
is decoding.
A low-cost display device (e.g.
mobile) has limited ability for true colors. For
example, there are 16.8 million (2^24) possible
color combinations in an RGB color image. Since
an RGB color image consists of three bytes for each
pixel; one byte for each color (red, blue, and green),
a color image quantization is applied to map 24 bits
to 16, 8, or 4 bits per pixel. For each RGB image,
by generating a set of representative colors, a
palette is formed. Later, the palette is used in image
encoding and decoding. In the encoding process,
each color pixel in the RGB image is replaced with
the index of the closest color in the palette. In
effect, each RGB color pixel is represented by an
index, which is mapped to the color palette. If the
palette size is 256 or less, each index can be
represented with a byte. Hence, effectively, image
size is reduced from 3 bytes per color to one byte
per index value by applying the quantization. In
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quantization process, we may have quantization
errors, e.g., distortion. To overcome quantization
errors, dithering algorithms are used. In a dithered
image, colors not available in the palette are
approximated by a diffusion of colored pixels from
within the available palette.
In recent years, several dithering algorithms were
proposed. The most well-known algorithm was
developed in 1976 by Floyd–Steinberg [4], which is
known as the Floyd–Steinberg dithering technique.
It uses error-diffusion algorithms instead of basic
dithering algorithms, such as average, ordered, or
random, and produces images which look closer to
original form. Error diffusion techniques are
commonly used for displaying images which have
been quantized to very few levels. The application
of error diffusion techniques to the display of color
images. A modified error diffusion technique is
proposed for resolving the quantized images. The
new error diffusion technique has been reported
easy for implementation using the tree structured
color palettes developed.
A re-ordering and re-indexing method
utilizes a new context model along with pseudo
distance technique in compression of color mapped
images. Graphic Interchange Format (GIF) and
Portable Network Format (PNG) are two of the
well-known and frequently used techniques for the
compression of color mapped images. There are
several techniques (JPEG) that achieve better
compression results than GIF and PNG; however,
most of these techniques need two passes on the
images data, while others do not run in linear time.
The pseudo distance technique runs in linear time
and requires only one pass. It has been reported by
[10] the proposed context model along with the
pseudo distance technique yields better results for
compression gain than both GIF and PNG.




Sampling the original image for
color statistics.
Choosing a color map based on
those statistics.
Mapping the colors to their
representative in the color map.
Quantizing the image.
The quantized image obtained is
given as input image to the previous block which
implements pseudo distance transformation and
encodes the transformed image using Run Length
Encoder.
Most of the color-mapped image
compression techniques, which require two passes,
the pseudo-distance compression technique requires
one pass and runs in linear time. There are several
techniques that yield better compression results
than GIF and PNG. Run length encoder is used for
them to compress the data. On run length encoded
data, arithmetic coding can be done to obtain an
output is in the form of binary file and decoded on
it.
Quantized Images
PDT
RLE
Decoder
BAC
Original Image
II. BLOCK DIAGRAM AND DESCRIPTION
The original RGB color image is
quantized by using the steps given below.
Reconstruction
Image
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1) Level 1: Quantization:-Sampling the
original image, choosing the color and
mapping the color and output is in the
form of quantized image.
2) Level
2:
Pseudo
Distance
Transformation (PDT):-Pseudo-distance
transformation used for calculating (by
calculating Euclidean distance) distance
between every pair of indices from a
color palette or by applying suitable
algorithm in further.
3) Level 3: Run Length Encoder:-The use
of run length is vital in entropy coder
phase since the output of the PDT on
dithered images contains a significant
number of zeros.RLE detects long run
sequences and regroup the repetitive
sequences.RLE along with binary
arithmetic coder gives compression
output.
4) Level 4 : Decoder:-The encoder output
is converted into original form.
III. ALGORITHMS
A.
Encoding Algorithm
the error matrix E. Then, this index value,
along with the right neighbouring index
value (3), is used to determine the error
value 0 from the pseudo-distance matrix (P
(3, 3) = 0). After that, the error value (0) is
written next to the top-left corner element
(3) of the matrix E. In each row, this process
is repeated similarly, except the error value
of the left most element of each row in E is
predicted using the pixel immediately above
that element in I.
B. Decoding Algorithm
The decoder part of the
application uses a procedure similar to that
used by the encoding algorithm. The
encoded image file consists of the index
table of the original image and the error
signals. Hence, the decoder can easily
construct the Euclidean distance and the
pseudo-distance matrices.
The original image is
reconstructed as follows: First, the pseudodistance matrix is reconstructed from the
index table. Then the index number of the
first pixel at the top-left corner, call it a, is
encoded with the original index value. Later
the process is applied as follows:
Receive the error signal e of
the next pixel of the encoded image E.In
row a of the pseudo-distance matrix, search
for the error signal value e. Emit the
corresponding column value x as the
original index value of the reconstructed
image, as shown in Figure 6. Let x be a and
repeat the process from 1 until we reach the
end of the file. Clearly, in the decoding
process, we obtain the original index values
without any loss.
First, the top-left corner index
value (3) is copied to the top-left corner of
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Lossless compression of heading,
dithered
paragraph
images with the pseudo-distance techniqueauthor
[11],the
pseudo distance technique (PDT) is used toaffiliation
achieve
better compression
11 author gain
namethan the any well-known
image 24compression
schemes (GIF,PNG &
title
JPEG2000).The compression gain reported by
research is 46.8% for GIF and 14.2% for PNG. It
has been reported that further improvement 3.9%
was obtained by using PDT technique. This
indicates promising feature of PDT for image
Images
Compression Ratio
Lenna
1.09
Man
1.09
Lossless compression of images [1],
Chall
1.17
the compression ratio is the size of original image
Coral
1.16
to the size of the compressed image and bit rate is
the number of bits per pixel required by the
Shuttle
1.18
compressed image. For example, a 256*256, 8 bits
Sphere
1.25
per pixel image requires 256*256*8 bits=65536*8
bits=65536 bytes form. If the compressed image
Brain
1.60
requires 32768 bytes then compression ratio is 2.0.
Since the image has 256*256=65,536 pixels, the compression.
A survey on palette recording
compressed file needs 32768*8/65536=4 bits per
methods for improving the compression of color
pixel on average bit rate is 4.
indexed image [12], the entropy values for original
The compression ratio reported by image and recorded image are reported as 7.62.
It has been reported that further
research on any images by using compression
entropy
values
7.41 for the original image and 5.21
algorithm such as gizp.It has been reported that
further improvement was obtained by using for recorded image was obtained by using Zeng’s
Huffman coding method. The compression ratios of method. The compression was 4%-5% worse for
JPEG-LS and 3%-5% worse for lossless JPEG2000
any images are given in table as follows:
by using Zeng’s method.
The following Table gives the quality
Color quantization of images [2],
PSNR
and
quantization
error by using LBG
the PSNR and quantization error reported by
algorithm.
research as follows: For girl image PSNR is 30.6
dB and quantization error is 15.13 by using Linde Buzo –Gray (LBG) algorithm. For Lena image
PSNR is 30.15 dB and quantization error is 5.37 by
using LBG algorithm.
An
efficient
re-indexing
algorithm for color mapped images [8], the entropy
value for 2 to 32 color palette reported as 2.1 and
33 to 256 color palette reported as 3.3. It has been
reported that further entropy was decreased; the
entropy value 2.0 for 2 to 32 color palette and 2.5
for 33 to 256 was obtained by using Zeng’s method.
Images-
Girl
Lena
Pepper
PSNR (dB)
30.6
15.13
28.92
Quantization
30.15
5.37
8.72
Error
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IV. CONCLUSIONS
The PDT is an efficient lossless image
compression method for color-palette images since
the PDT runs in linear time and requires only onepass [11]. In our previous work [11], we have
shown that, when the PDT is used in conjunction
with a context-model BAC, we obtained better
compression results than the well-known image
compressors such as GIF, PNG, JPEG-LS, and
JPEG2000 on dithered images. In this paper, we
have shown that further compression gains are
possible when we update one more neighbor of the
predicted pixel in PDT matrix. Indeed, with this
modification, on three sets of dithered images, we
have achieved on average 3.9% improvement over
our previous work resulting in total gains of 46.8%
over GIF and 14.2% over PNG.
REFERENCES
[1] Lossless compression of dithered images, June 2013.
[2] M. T. Orchard and C. A. Bouman, “Color quantization of
images”,[ IEEE Trans. Signal Process., vol. 39, no. 12,pp.
2677–2690, Dec. 1991.
[3][Online].Available:“http://www.visgraf.impa.br/Courses/ip
00/proj/Dithering1/”
[4] R. W. Floyd and L. Steinberg, “An adaptive algorithm for
spatial grey scale”,[ in Proc. Soc. Inf. Display, 1976, vol.
17,pp. 75–77.
[6] C. Alasseur, A. G. Constantinides, and L. Husson,
BColour quantisation through dithering techniques,[ in Proc.
ICIP, Sep. 14–17, 2003, vol. 1, pp. I-469–I-472.
[7] Z. Yao and Y. Wan, “A high performance dithering method
for gray and color image quantization”,[ in Proc. 6th Int.
Conf. WiCOM, Sep. 23–25, 2010, pp. 1–4.
[8] S. Battiato, G. Gallo, G. Impoco, and F. Stanco, “An
efficient re-indexing algorithm for color-mapped images”,[
IEEE . Image Process., vol. 13, no. 11, pp. 1419–1423, Nov.
2004.
[9] B. Koc and Z. Arnavut, “Gradient adjusted predictor with
pseudo-distance technique for lossless compression of color
mapped” images,[ in Proc. FIT, Dec. 19–21, 2011, pp. 275–
280.
[10] B. Koc and Z. Arnavut, “A new context-model for the
pseudo-distance technique in lossless compression of color
mapped Images”,[ in Proc. SPIE Opt. Eng.þ Appl., Appl.
Digit. Image Process. XXXV, Aug. 12–16, 2012, p. 84 991O.
[11] B. Koc, Z. Arnavut, and H. Kocak, “Lossless
compression of dithered images with the pseudo-distance
technique”,[ in Proc. 9th Int. Conf. HONET, Dec. 12–14,
2012, pp. 147–151.
[12] A. J. Pinho and A. J. R. Neves, BA survey on palette
reordering methods for improving the compression of colorindexed images,[ IEEE Trans. Image Process., vol. 13, no.
11, pp. 1411–1418, Nov. 2004.
[5] L. Akarun, Y. Yardunci, and A. E. Cetin, “Adaptive
methods for dithering color images”,[ IEEE Trans. Image
Process.,vol. 6, no. 7, pp. 950–955, Jul. 1997.
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