J. Biomedical Science and Engineering, 2009, 2, 336-344
doi: 10.4236/jbise.2009.25049 Published Online September 2009 (http://www.SciRP.org/journal/jbise/
Published Online September 2009 in SciRes.http://www.scirp.org/journal/jbise
Lossless compression of digital mammography using
base switching method
Ravi kumar Mulemajalu1, Shivaprakash Koliwad2
1Corresponding author, Department of IS&E., KVGCE, Sullia, Karnataka, India; 2Department of E&C., MCE, Hassan, Karnataka, India.
Email: 1perajeravi@yahoo.com, 2spksagar2006@yahoo.co.in
Received 31March 2009; revised 15 May 2009; accepted 25 May 2009.
Mammography is a specific type of imaging that
uses low-dose x-ray system to examine breasts.
This is an efficient means of early detection of
breast cancer. Archiving and retaining these
data for at least three years is expensive, diffi-
cult and requires sophisticated data compres-
sion techniques. We propose a lossless com-
pression method that makes use of the
smoothness property of the images. In the first
step, de-correlation of the given image is done
using two efficient predictors. The two residue
images are partitioned into non overlapping
sub-images of size 4x4. At every instant one of
the sub-images is selected and sent for coding.
The sub-images with all zero pixels are identi-
fied using one bit code. The remaining sub-
images are coded by using base switching
method. Special techniques are used to save
the overhead information. Experimental results
indicate an average compression ratio of 6.44
for the selected database.
Keywords: Lossless Compression; Mammography
image; Prediction; Storage Space
Breast cancer is the most frequent cancer in the women
worldwide with 1.05 million new cases every year and
represents over 20% of all malignancies among female.
In India, 80,000 women were affected by breast cancer
in 2002. In the US, alone in 2002, more than 40,000
women died of breast cancer. 98% of women survive
breast cancer if the tumor is smaller than 2 cm [1]. One
of the effective methods of early diagnosis of this type of
cancer is non-palpable, non-invasive mammography.
Through mammogram analysis radiologists have a de-
tection rate of 76% to 94%, which is considerably higher
than 57% to 70% detection rate for a clinical breast ex-
amination [2].
Mammography is a low dose x-ray technique to ac-
quire an image of the breast. Digital image format is
required in computer aided diagnosis (CAD) schemes to
assist the radiologists in the detection of radiological
features that could point to different pathologies. How-
ever, the usefulness of the CAD technique mainly de-
pends on two parameters of importance: the spatial and
grey level resolutions. They must provide a diagnostic
accuracy in digital images equivalent to that of conven-
tional films. Both pixel size and pixel depth are factors
that critically affect the visibility of small low contrast
objects or signals, which often are relevant information
for diagnosis [3]. Therefore, digital image recording
systems for medical imaging must provide high spatial
resolution and high contrast sensitivity. Due to this,
mammography images commonly have a spatial resolu-
tion of 1024x1024, 2048x2048 or 4096x4096 and use 16,
12 or 8 bits/pixel. Figure 1 shows a mammography im-
age of size 1024x1024 which uses 8 bits/pixel.
Nevertheless, this requirement retards the implemen-
tation of digital technologies due to the increment in
processing and transmission time, storage capacity and
cost that good digital image quality implies. A typical
mammogram digitized at a resolution of 4000x5000 pix-
els with 50-µm spot size and 12 bits results in approxi-
mately 40 Mb of digital data. Processing or transmission
time of such digital images could be quite long. An effi-
cient data compression scheme to reduce the digital data
is needed.
The goal of the image compression techniques is to
represent an image with as few bits as possible in such a
way that the original image can be reconstructed from
this representation without or with minimum error or
distortion. Basically image compression techniques have
been classified into two categories namely lossy and
lossless methods. Lossy compression methods cannot
achieve exact recovery of the original image, but
achieves significant compression ratio. Lossless com-
pression techniques, as their name implies, involve no
loss of information. The original data can be recovered
R. K. Mulemajalu et al. / J. Biomedical Science and Engineering 2 (2009) 336-344 337
SciRes Copyright © 2009 JBiSE
Figure 1. A Mammography image of
size 1024x1024 which uses 8 bits/pixel.
exactly from the compressed data. In medical applica-
tions, lossless coding methods are required since loss of
any information is usually unacceptable [4]. Perform-
ance of the lossless compression techniques can be
measured in terms of their compression ratio, bits per
pixels required in the compressed image and the time for
encoding and decoding. On the other hand, since the
lossy compression techniques discard some information,
performance measure includes the mean square error and
peak signal to noise ratio (PSNR) in addition to the
measures used for the lossless compression.
Lossless image compression systems typically func-
tion in two stages [5]. In the first stage, two-dimensional
spatial redundancies are removed by using an image
model which can range from a relatively simple causal
prediction used in the JPEG-LS [6,7] standard to a more
complicated multi-scale segmentation based scheme. In
the second stage, the two-dimensional de-correlated re-
sidual which is obtained from the first stage, along with
any parameters used to generate the residual is coded
with a one-dimensional entropy coder such as the Huff-
man or the Arithmetic coder.
Existing lossless image compression algorithms can
be broadly classified into two kinds: Those based on
prediction and those that are transform based. The pre-
dictive coding system consists of a prediction that at
each pixel of the input image generates the anticipated
value of that pixel based on some of the past pixels and
the prediction error is entropy coded. Various local,
global and adaptive methods can be used to generate
prediction. In most cases, however the prediction is
formed by a linear combination of some previous pixels.
The variance of the prediction error is much smaller than
the variance of the gray levels in the original image.
Moreover, the first order estimate of the entropy of the
error image is much smaller than the corresponding es-
timate for the original image. Thus higher compression
ratio can be achieved by entropy coding the error image.
The past pixels used in the prediction are collectively
referred to as a context. The popular JPEG-LS standard
uses the prediction based coding technique [8]. Trans-
form based algorithms, on the other hand, are often used
to produce a hierarchical or multi-resolution representa-
tion of an image and work in the frequency domain. The
popular JPEG-2000 standard uses the transform based
coding technique [9].
Several techniques have been proposed for the loss-
less compression of the digital Mammography. A.
Neekabadi et al. [10] uses chronological sifting of pre-
diction errors and coding the errors using arithmetic
coding. For the 50 MIAS (Mammography Image Analy-
sis Society) images, CSPE gives better average com-
pression ratio than JPEG-LS and JPEG-2000. Xiaoli Li
et al. [11] uses grammar codes in that the original image
is first transformed into a context free grammar from
which the original data sequence can be fully recon-
structed by performing parallel and recursive substitu-
tions and then using an arithmetic coding algorithm to
compress the context free grammar. Compression ratio
achieved is promising but it involves more complicated
processing and large computation time. Delaunay trian-
gulation method [12] is another approach. It uses geo-
metric predictor based on irregular sampling and the
Delaunay triangulation. The difference between the
original and the predicted is calculated and coded using
the JPEG-LS approach. The method offers lower bit rate
than the JPEG-LS, JPEG-lossless, JPEG2000 and PNG.
A limitation is the slow execution time. Lossless
JPEG2000 and JPEG-LS are considered as the best
methods for the mammography images. Lossless JPEG
2000 methods are preferred due to the wide variety of
features, but are suffered from a slightly longer encoding
and decoding time [13].
Recently, there have been a few instances of using
segmentation for lossless compression. Shen and Ran-
gayyan [14] proposed a simple region growing scheme
which generates an adaptive scanning pattern. A differ-
ence image is then computed and coded using the JBIG
compression scheme. Higher compression ratio is possi-
ble with such a scheme for the high resolution medical
images. But the application of the same scheme to nor-
mal images did not result in significant performance
improvement. Another scheme reported in literature in-
volves using a variable block size segmentation(VBSS)
to obtain a context sensitive encoding of wavelet coeffi-
cients, the residual being coded using a Huffman or
Arithmetic coder [15,16]. The performance of the
method is comparable to that of the lossless JPEG stan-
dard. Mar wan Y. et al. [17] proposed fixed block based
(FBB) lossless compression methods for the digital
mammography. The algorithm codes blocks of pixels
within the image that contain the same intensity value,
thus reducing the size of the image substantially while
encoding the image at the same time. FBB method
alone gives small compression ratio but when used in
conjunction with LZW it provides better compression
338 R. K. Mu lemajalu et al. / J. Biomedical Science and Engineering 2 (2009) 336-344
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We propose a method based on Base switching (BS).
Trees-Juen Chuang et al. [18] have used Base-switching
method to compress the general images. [19] And [20]
also have used the same concept for the compression of
digital images. The algorithm segments the image into
non overlapping fixed blocks of size nn and codes the
pixels of the blocks based on the amount of smoothness.
In the proposed work we have optimized the original BS
method for the compression of mammography images.
Specific characteristics of mammography images are well
suited for the proposed method. These characteristics in-
clude low number of edges and vast smooth regions.
The organization of the paper is as follows. Section 2
describes the basic Base Switching (BS) method. The
proposed algorithm is given in Section 3. Experimental
results and conclusion are given in Sections 4 and 5 re-
The BS method divides the original image (gray-level
data) into non-overlapping sub-images of size nn
Given a sub-image A, whose N gray values are
g0,g1,…gN-1 , define the “minimum” m, “base” b and the
“modified sub-image “AI, whose N gray values are
N-1, by
gm min (1)
1minmax  ii ggb (2)
nn nnnn
AmI (3)
Also, for all i=0 to N -1 (4)
mgg i
where N=and each of the elements of I is 1. The
value of ‘b’ is related to smoothness of the sub-image
where smoothness is measured as the difference between
maximum and minimum pixel values in the sub-image.
The number of bits required to code the gray values gi
I is,
B = (5)
Then, total bits required for the whole sub-image is,
Z = N bits. (6)
For example, for the sub-image of Figure 2, n=4,
N=16, m=95& b=9. Modified sub-image of Figure 3 is
obtained by subtracting 95 from every gray values of A.
For the sub-image in Figure 3, since B=4, =64 bits.
95 96 97 99
96 97 103 103
97 96 96 103
96 96 97 103
Figure 2. A sub-image A with n=4, N=16,
m=95, b=9& B=4.
012 4
128 8
211 8
112 8
Figure 3. Modified sub-image AI.
In order to reconstruct A, value of B and m should be
known. Therefore encoded bit stream consists of m, B
and AI coded using B bits. In the computation of B, If
b is not an integer power of 2, log2 (b) is rounded to the
next higher integer. Thus, in such cases, higher number
of bits is used than absolutely required. BS method uses
the following concept to exploit this redundancy.
It is found that, min gi
I=0 and max gi
I=b-1 (7)
The image AI = ( g0
) can be treated as an
N digit number (g0
N-1) b in the base b number
system. An integer value function f can be defined such
that f (AI,b)= decimal integer equivalent to the base-b
= (8)
N-1 bN-1 (9)
Then, number of bits required to store the integer f (AI,
b) is
Z= (10)
Reconstruction of AI is done by switching the binary
(base 2) number to a base b number. Therefore, recon-
struction of A needs the value of m and b. The format of
representation of a sub-image is as shown below.
Min. value in
the n
n block.
(8 bits)
Value of b
For the nn
(8 bits)
f (AI, b) coded using
Z bits
( bits)
For the example of Figure 3, b=9 and therefore
=51 bits. It is easy to prove that always B
. W
know that, Maximum value of f (AI, b) =b N1. -
Total number of bits required to represent f in binary is
Z== (11)
bN 2
bN 2
N (12)
This verifies that AB ZZ
2.1. Formats Used for Encoding
Original BS algorithm uses a block size of 3x3 for seg-
R. K. Mulemajalu et al. / J. Biomedical Science and Engineering 2 (2009) 336-344 339
SciRes Copyright © 2009 JBiSE
mentation. There are three formats used by the original
algorithm for encoding the sub-images.
If b{1,2 …,11}, then the coding format is
1 bit
7 bits
8 bits
Binary equivalent of f (AI, b)
ZB bits
This format is economical when b<2 3.4
If b (12, 13,…., 128}, then the coding format is
(1 bit)
(7 bits)
(7 bits)
Binary equivalent of
min max
gfor i
ii ii
Here P(min,max) is a pair of two 3 bit numbers in-
dicating the position of minimum and maximum values.
If b>11, writing the positions of minimum and maximum
values is economical than coding them.
Format 3:
If b (129, 130,…., 256}, then the coding format is
(1 bit)
The original nine gray values: g0,g1,…g8
(72 bits)
Here, c stands for the category bit. If c is 0, then the
block is encoded using Formats 1 or 2; otherwise Format
3 is used.
2.2. Hierarchical Use of BS Technique
The encoded result of Subsection 2.1 can be compressed
further in a hierarchical manner. We can imagine that
there is a so-called “base-image”, whose gray values are
b0, b1, b2, …, b255; then, since it is a kind of image
(except that each value is a base value of a sub-image
rather than a gray value of a pixel), we can use the same
BS technique to compress these base values. The details
are omitted. Besides b, the minimal value m of each
block can also be grouped and compressed similarly. We
can repeat the same procedure to encode b and m values
In the proposed method, we made following modifica-
tions to the basic BS method.
1) Prediction
2) Increasing the block size from 3x3 to 4x4
3) All-zero block removal
4) Coding the minimum value and base value
3.1. Prediction
After reviewing the BS method, it is found that number
of bits required for a sub-image is decided by the value
of base ‘b’. If ‘b’ is reduced, the number of bits required
for a sub-image is also reduced. In the proposed method,
prediction is used to reduce the value of ‘b’ significantly.
A predictor generates at each pixel of the input image the
anticipated value of that pixel based on some of the past
inputs. The output of the predictor is then rounded to the
nearest integer, denoted
and used to form the dif-
ference or prediction error
nnn xxe  (14)
This prediction error is coded by the proposed entropy
coder. The decoder reconstructs from received code
words and perform the reverse operation
nnn xex  (15)
The quality of the prediction for each pixel directly
affects how efficiently the prediction error can be en-
coded. The better this prediction is less is the informa-
tion that must be carried by the prediction error signal.
This, in turn, leads to fewer bits. One way to improve the
prediction used for each pixel is to make a number of
predictions then chose the one which comes closest to
the actual value [21]. This method also called as
switched prediction has the major disadvantage that the
choice of prediction for each pixel must be sent as over-
head information. The proposed prediction scheme uses
two predictors and one of them is chosen for every block
of pixels of size 4x4. Thus, the choice of prediction is to
be made only once for the entire 4x4 block. This reduces
the amount of overhead. The two predictions are given
in Eq.16 and 17, in that, Pr1 is the popular MED pre-
dictor used in JPEG-LS standard and Pr2 is the one used
by [5] for the compression of mammography images.
For the entire pixels of a block of size 44, one of the
two predictions is chosen depending on the smoothness
property of the predicted blocks. Here, smoothness is
measured as the difference between maximum and
minimum pixel values in the block. The predictor that
gives the lowest difference value will be selected for that
block. The advantage here is that the overhead re-
quired for each block is only one bit.
otherwise. C-BA
B). (A,min C if B) (A,max Pr
B). (A,max C if B) (A,min
Here, A, B, C, D, E and F are the neighbors of pixel in-
volved in prediction as depicted in Figure 4.
The proposed switched prediction is described in the
equation form in 18 where d1 and d2 are the differ-
340 R. K. Mulemajalu et al. / J. Biomedical Science and Engineering 2 (2009) 336-344
SciRes Copyright © 2009 JBiSE
Figure 4. Neighbors of pixel in-
volved in prediction.
ences between maximum and minimum values for the
two blocks obtained using the two predictors Pr1 and Pr2
Pr = Pr
1 if d1<d2 (18)
= Pr2 otherwise
Figure 5 illustrates the prediction technique. It
shows two error images which are obtained by using
two predictors Pr1 and Pr2 respectively. The BS algo-
rithm divides them into 4x4 sub-images and computes
the difference between maximum and minimum pixel
values for all the four sub-images. For the first
sub-image, difference ‘d1’ is 6 and ‘d2’ is 8, where d1
and d2 are the differences of the sub-images corre-
sponding to the predictors Pr1 and Pr2 respectively.
Now, since d1<d2, the prediction Pr considers 4x4
sub-image of predictor Pr1 for further processing. This
procedure is repeated for all the other sub-images. The
resulting error image is shown in Figure 6. We use a
separate file predict to store the choice of predictor
made at every sub-image.
Figure 5. Prediction technique.
3.2. Increasing the Block Size from 3x3 to 4x4
It is obvious that smaller block size gives lower b value
but at the cost of increased overhead for the total image.
The basic BST algorithm uses a block size of 3x3 to
achieve optimum balance between amount of overhead
and compression efficiency. Since the prediction in-
creases smoothness, a larger block size can be chosen
without significant difference in the smoothness. Cer-
tainly, this will improve the compression ratio. We have
tested the proposed algorithm using different block sizes
and found that block size of 4x4 gives the best result.
This is supported by Table 1 giving the average com-
pression ratios obtained for the 50 mammography im-
ages for various block sizes.
3.3. All-Zero Block Removal
Mammography images are highly correlated so that pix-
els inside most of the sub-images are same. During pre-
diction and subtraction they have the highest chance of
becoming zeros. If a sub-image of the error image has all
its pixel values as zero, then that is marked as an all-zero
block by storing a bit 1 in the encoding format. For each
of the remaining sub-images, bit 0 is stored in the en-
coding format and is retained for further processing.
Mammography images of MIAS data-set shows very
large amount of all-zero blocks. This is supported by
Table 2 showing average number of all-zero blocks pre-
sent in the 50 mammography images of the MIAS dataset.
For these images, total bits required for marking the
presence or absence of all-zero blocks is 65536, since
Figure 6. Resulting error image.
Table 1. Average compression ratio obtained for various block sizes.
Table 2. Average number of all-zero blocks present in the 50
MIAS images.
3x3 4x4 4x8 8x4 8x8
6.18 6.44 6.15 6.18 5.92
Image size No. of blocks
of size 4
Average no. of
all-zero blocks
ing blocks
102465 536 32 282 33 254
R. K. Mulemajalu et al. / J. Biomedical Science and Engineering 2 (2009) 336-344 341
SciRes Copyright © 2009
total sub-images are 65536. The error image will have
both negative and positive pixel values since the predic-
tion has changed the range of the pixel values from [0,
255] to [-255, 255]. Therefore, 9 bits are required to re-
cord the pixel values. The approximate average com-
pression ratio obtained by all-zero block removal for the
50 MIAS images considered in Table 2 can be estimated
by the following formula.
codingfor used pixelper bits block per pixels blocks remaining 65536
8 1024 1024
9 16 33254 65536
8 10241024
into sub-images of size 4x4.The sub-images are then
processed one by one. For each sub-image, we have to
determine whether it belongs to all-zero category and if
so they are removed. The remaining blocks are retained
for further processing.
Here the value 65536 indicates the overhead bits re-
quired for marking the presence or absence of all-zero
blocks. The numerator gives total bits used by the origi-
nal uncompressed image. This computation clearly
shows that removal of all-zero blocks alone gives an
approximate compression ratio of 1.73. The two binary files zero and predict are separately
run length encoded, grouped and Huffman encoded.
Also, the two four bit files min and base are combined to
form an eight bit file and Huffman encoded.
3.4. Coding the Minimum Value and the
Base Value
The error image will have both negative and positive
pixel values. The prediction has changed the range of the
minimum value from [0,255] to [-255,255]. Therefore, 9
bits are required to record the minimum value. By
studying various images, it is found that minimum val-
ues are ranging from -128 to 64. More concentration is
observed between -8 to 0. Similarly, base values are
concentrated in the range 1 to 15. This statistics is sup-
ported by Table 3 of average number of minimum val-
ues and base values for the 50 mammography images.
3.6. Decoding a Sub-Image
Following are the decoding steps:
1) The files min, base, zero and predict are recon-
2) The decoding algorithm first checks whether the
block is an all-zero block or not. If all-zero, then a 4x4
block of zero’s is generated.
3) Otherwise, base value and minimum value are first
obtained by using the files min and base. The modified
image AI is reconstructed as explained in Section 2 and
4x4 error image is obtained by adding min value to it.
To exploit this redundancy, we use a typical categorize
and coding technique. A four bit code is used to identify
the minimum values. Minimum values less than 1 and
greater than -15 are given with codes 0 to 14, whereas
other minimum values are represented by the code 15
followed by their actual 9 bit values. A scheme similar to
this can be used to code the base values also. Base val-
ues between 1 and 15 are identified by using 4 bit codes
whereas values greater than 15 are identified using the
code 15 followed by their actual 9 bit values. The two
four bit codes for each of the sub-images are combined
to get an 8 bit number. Such 8 bit numbers are stored in a
file and Huffman encoded at the end.
4) Type of prediction used is read from the predict file.
The prediction rule is applied to the 4x4 error image and
the original 4x4 sub-image is reconstructed.
We evaluated the performance of the proposed scheme
using the 50 gray-scale images of the MIAS dataset that
include three varieties of images: Normal, Benign and
Malignant. The MIAS is a European Society that re-
searches mammograms and supplies over 11 countries
with real world clinical data. Films taken from the UK
national Breast Screening Program have been digitized
to 50 micron pixel edge and representing each pixel with
an 8 bit word. MATLAB is the tool used for simulation.
All the simulation was conducted on a 1.7GHZ proces-
sor and was supplied with the same set of 50 mammog-
raphy images. Each mammogram has a resolution of
1024x1024 and uses 8 bits/pixel. Results of the proposed
method are compared with that of the popular methods.
Comparison of Compression results for the 50 MIAS
images is shown in Table 4. This set includes all the
three varieties of images namely normal, benign and
3.5. System Overview
As shown in Figure 7, we first divide the error image
Table 3. Average number of minimum and base values in 50
MIAS images.
Average No. of
minimum and
base values
Average no. of mini-
mum values in the
range -14 to 0
Average no. of
base values in
the range 1 to 15
33 253 32 466 33 097
342 R. K. Mulemajalu et al. / J. Biomedical Science and Engineering 2 (2009) 336-344
SciRes Copyright © 2009 JBiSE
Figure 7. System overview.
Table 4. Comparison of compression results for the 50 MIAS
4.30 5.88 6.29 6.39 6.44
Figure 8 and Figure 9 show the two images mdb040.
pgm and mdb025.pgm that gives best and the worst
compression ratio respectively.
Several techniques have been used for the lossless com-
pression of mammography images; none of them have
used the smoothness property of the images. Our study
has shown that there is very large number of zero blocks
present in mammography images. We have picked up the
concept of Base switching transformation and success-
fully optimized and applied it in conjunction with other
existing compression methods to digitized high resolu-
tion mammography images. Comparison with other ap-
proaches is given for a set of 50 high resolution digital
mammograms comprising of normal, benign and malig-
nant images. Compared with the PNG method, one of
the international standards, JBIG, performs better by
36%. Transformation method based JPEG200, another
international compression standard, when used in loss-
less mode, performs slightly better than JBIG by 7%.
Whereas, the latest standard for lossless image compres-
sion JPEG-LS based on prediction based method, per-
forms best among the four international standards of
lossless coding techniques. It gives a compression ratio
of 6.39 which is 1.5% better than the JPEG 2000. Finally,
for these images, the proposed method performs better
than PNG, JBIG, JPEG2000 and JPEG-LS by 50%, 9.5%,
R. K. Mulemajalu et al. / J. Biomedical Science and Engineering 2 (2009) 336-344 343
SciRes Copyright © 2009 JBiSE
Figure 8. Image mdb040. CR=14.16. Figure 9. Image mdb025. CR=4.55.
2.4% and approximately 1% respectively. The success of
our method is primarily due to its zero block removal
procedure, compression of the overheads and the
switched prediction used. It should be also noted that the
speed of the BST method is very much comparable with
the speed of other standard methods as verified by [18].
Further investigation on improvement of the perform-
ance of our method is under way, by developing more
suitable prediction methods. Motivated by the results
obtained here, our next study will carry out the compres-
sion of larger database of natural images and medical
images obtained by other modalities.
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