28 G. Jayalalitha, T. G. Grace Elizabeth Rani International Journal of Computer & Mathematical Sciences IJCMS ISSN 2347 – 8527 Volume 4, Issue 1 January 2015 TONGUE FEATURES ANALYZED THROUGH FRACTAL DIMENSIONS G. Jayalalitha, Associate Professor, Department of Mathematics R.V.S. College of Engineering and Technology, Dindigul -624 005, Tamil Nadu, India. T. G. Grace Elizabeth Rani, Research Scholar, Research and Development Center Bharathiar University, Coimbatore - 641046, Tamil Nadu, India. ABSTRACT This paper introduces the applications of "fractals" in the diagnosis of tongue diseases. Fractal Dimension methods and SOBEL Edge Detection methods have been employed in identifying the intensity of the disease and affected regions taking into consideration the reflex zones of tongue. Lacunarity, a measure of "gaps" is investigated. Percolation Method has been studied to understand the invasiveness of the disease. A concise demarcation could be observed between the normal and abnormal tongue, with higher dimension values for abnormal tongue. Analysis of the shape of tongue and evaluation of its dimension using fractal Mathematical techniques saves time and increases the quality of diagnosis in Traditional Chinese Medicine (TCM). Keywords: Fractals, Traditional Chinese Medicine (TCM), Box Counting Method, Lacunarity. 1 INTRODUCTION Diagnosis is the process of identifying a disease through some evaluation procedure. There are various procedures. Examination of tongue to draw conclusions about an individual's health is termed "Tongue Diagnosis", which is widely practiced in Traditional Chinese Medicine. Tongue is one of the most important peripheral sense organs and is the best indicator of various diseases in the body. The symptoms on the surface of the tongue will clearly indicate the root cause. Various parts of the tongue correspond to different organs, referred to as reflex zones [Fig.1 (a)]. It implies that if lung is affected the corresponding area in the tongue will show an abnormality. This is the reason for prevalence of tongue diagnosis in almost all forms of nature cure. Bayesian network has been used to model the relation between chromatic and textural metrics of tongue. These metrics are computed from true color tongue images by using appropriate techniques of image processing. 1 In another paper a unique segmentation method based on the combination of the watershed transform and active contour model has been proposed. The watershed transform is used to get the initial contour, and an active contour model, or "snakes", is used to converge to the precise edge. 2 Support vector machines together with hyper-spectral medical tongue images has been investigated. 3 Our paper focuses on the analysis of tongue images through "fractal" techniques. Fractal geometry developed in the last twenty years is one of the most scintillating and useful scientific discoveries of the century, owing its credit to Mandelbrot. 4 Fractals exhibit some similarity. Most fractals are self - similar i.e., the magnification of any part resembles the original object in a specific manner. Fractals are those beyond the comprehension of Euclidean geometry. They are irregular. Therefore, fractals have many applications in the field of biology. Fractal dimension was found useful in analyzing the structure of blood vessel trees. 5 Fractal dimension analysis has been performed for skin cancer and cervical cancer. 6,7 Analyzing the complex structure of any system is easily effected through fractal theory, which shows beyond doubt that it has applications in osteoporosis. 8
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28 G. Jayalalitha, T. G. Grace Elizabeth Rani
International Journal of Computer & Mathematical Sciences
IJCMS
ISSN 2347 – 8527
Volume 4, Issue 1
January 2015
TONGUE FEATURES ANALYZED THROUGH FRACTAL
DIMENSIONS
G. Jayalalitha, Associate Professor, Department of
Mathematics
R.V.S. College of Engineering and Technology,
Dindigul -624 005, Tamil Nadu, India.
T. G. Grace Elizabeth Rani, Research Scholar,
Research and Development Center
Bharathiar University, Coimbatore - 641046, Tamil
Nadu, India.
ABSTRACT
This paper introduces the applications of "fractals"
in the diagnosis of tongue diseases. Fractal
Dimension methods and SOBEL Edge Detection
methods have been employed in identifying the
intensity of the disease and affected regions taking
into consideration the reflex zones of tongue.
Lacunarity, a measure of "gaps" is investigated.
Percolation Method has been studied to understand
the invasiveness of the disease. A concise
demarcation could be observed between the
normal and abnormal tongue, with higher
dimension values for abnormal tongue. Analysis of
the shape of tongue and evaluation of its
dimension using fractal Mathematical techniques
saves time and increases the quality of diagnosis in
Traditional Chinese Medicine (TCM).
Keywords: Fractals, Traditional Chinese Medicine
(TCM), Box Counting Method, Lacunarity.
1 INTRODUCTION
Diagnosis is the process of identifying a
disease through some evaluation procedure. There
are various procedures. Examination of tongue to
draw conclusions about an individual's health is
termed "Tongue Diagnosis", which is widely
practiced in Traditional Chinese Medicine. Tongue
is one of the most important peripheral sense
organs and is the best indicator of various diseases
in the body. The symptoms on the surface of the
tongue will clearly indicate the root cause. Various
parts of the tongue correspond to different organs,
referred to as reflex zones [Fig.1 (a)]. It implies
that if lung is affected the corresponding area in
the tongue will show an abnormality. This is the
reason for prevalence of tongue diagnosis in
almost all forms of nature cure.
Bayesian network has been used to model
the relation between chromatic and textural
metrics of tongue. These metrics are computed
from true color tongue images by using
appropriate techniques of image processing.1 In
another paper a unique segmentation method based
on the combination of the watershed transform and
active contour model has been proposed. The
watershed transform is used to get the initial
contour, and an active contour model, or "snakes",
is used to converge to the precise edge.2 Support
vector machines together with hyper-spectral
medical tongue images has been investigated.3
Our paper focuses on the analysis of
tongue images through "fractal" techniques.
Fractal geometry developed in the last twenty
years is one of the most scintillating and useful
scientific discoveries of the century, owing its
credit to Mandelbrot.4
Fractals exhibit some
similarity. Most fractals are self - similar i.e., the
magnification of any part resembles the original
object in a specific manner. Fractals are those
beyond the comprehension of Euclidean geometry.
They are irregular. Therefore, fractals have many
applications in the field of biology. Fractal
dimension was found useful in analyzing the
structure of blood vessel trees.5 Fractal dimension
analysis has been performed for skin cancer and
cervical cancer.6,7
Analyzing the complex structure
of any system is easily effected through fractal
theory, which shows beyond doubt that it has
applications in osteoporosis.8
29 G. Jayalalitha, T. G. Grace Elizabeth Rani
International Journal of Computer & Mathematical Sciences
IJCMS
ISSN 2347 – 8527
Volume 4, Issue 1
January 2015
2 METHODS In this paper, the efficiency of fractals in
tongue diagnosis is explored. In Traditional
Chinese Medicine, tongue diagnosis is an essential
procedure. Fractal Dimension, a measure of
irregularity is evaluated. Lacunarity, which deals
with "gaps", has been studied to analyze the
texture of tongue. Sausage and Boundary
Descriptor methods have been investigated to
know the impact of a disease on the boundary of
tongue. Once a particular area of the tongue is
affected, there are chances that neighboring areas
also get affected. In this context, Percolation
Method has been studied.
2.1 Box Counting Dimension Using MATLAB
Box Counting Dimension or just Box
Dimension is a commonly used fractal dimension.
It is also called Minkowski’s Dimension, which is
the slope of log - log plot. Consider a non-empty
bounded subset T of the n - dimensional Euclidean
space. Cover T by boxes, usually squares of size
say R. Let N(R) be the smallest number of boxes
required to cover the subset T. By varying R we
get different values of N (R). The logarithmic
values of N (R) are plotted against the logarithmic
value of 1/ R. The lower and upper box
dimensions of the set T is then given respectively
as
R
RNT
RB
log
loglimdim
0
(1)
R
RNT
RB
log
loglimdim
0
(2)
When the upper and the lower values coincide i.e.,
TT BB dimdim it is called the box dimension
denoted by TBdim and is given as
R
RNT
RB
log
loglimdim
0
(3)
The method of least squares linear
regression is employed here.9
This procedure is
presented in the form of an algorithm.
Algorithm 1
Step 1: Divide the image into regular meshes of
size R.
Step 2: Calculate the number of square boxes that
intersect the image and denote it by N(R).
Step 3: N(R) is purely dependent on the choice of
R.
Step 4: Find N(R) for varying R.
Step 5: Plot (log (1/ R), log N(R)) and find the
slope. This slope is the dimension D.
Straight line is fitted to the plotted points by
./1logloglog RDCRN (4)
In this equation D indicates the fractal dimension,
the degree of complexity and C is a constant. This
algorithm has been applied to the tongue images
[Fig.3] of few patients and the corresponding
dimension has been evaluated using MATLAB.
2.2 Box Counting Dimension Using HARFA
Nezadal et al and Buchnicek et al 10,11
implemented Box Counting procedure in the
software called HARFA, which was developed by
the Institute of Physical and Applied Chemistry,
Techincal University of Bino in the Czech
Republic. Dimension determined by this method is
called Box Counting Dimension (DBBW).The
principle is as follows: square meshes of various
sizes 1/ε is laid over the image. The counts of
mesh boxes NBBW (ε) that contain any part of the
fractal is counted. The fractal properties of cervical
cancer cells were explored using Box Counting
Method. This method is often used to determine
the fractal Box dimension of digitized images of
fractal structures. HARFA analyzes black and
white images. Box Counting Method utilizes the
covering of fractal pattern with raster of boxes and
then evaluating how many boxes NBW, NBBW = NB
+ NBW or NWBW = NW + NBW of the raster are
needed to cover the fractal completely where
NB- number of black squares,
NW- number of white squares,
NBW-number of black and white squares,
NBBW- number of black and white and black
squares,
NWBW-number of black and white and white
squares.
Repeating this measurement with different sizes of
boxes r = 1/ε results in logarithmical function of
box size r and the number of boxes N(r) needed to
cover the fractal completely. The slopes of linear
functions
rDKrN BWBWBW lnlnln (5)
rDKrN BBWBBWBBW lnlnln (6)
rDKrN WBWWBWWBW lnlnln (7)
give DBW, DBBW, DWBW , the fractal dimensions.
DBW characterizes properties of border of fractal
pattern, DBBW characterizes fractal pattern on the
30 G. Jayalalitha, T. G. Grace Elizabeth Rani
International Journal of Computer & Mathematical Sciences
IJCMS
ISSN 2347 – 8527
Volume 4, Issue 1
January 2015
black background and, DWBW characterizes fractal
pattern on the white background. From the above
said program we found out the fractal dimension
of tongue in Discrete and Continuous process
(Fig.3, Tables3,4).This gives the intensity of the
disease on the tongue and also helps in finding the
exact affected organ.
2.3 Sausage Method
Infections on the tongue have an impact on its
shape. The boundary may not be a perfect "U"
shape. It may even have cracks. The surface might
have bumps of various sizes. So evaluation of
perimeter is needed. For this purpose Sausage
method is used, which estimates the boundary
using the parametric equation given below.
(8)
This method is also known as boundary dilation
method. The images were dilated with circles of
increasing diameter. The circles are best
approximated with pixels of sizes 1x1, 3x3 …
17x17. Correspondingly, the approximate radius in
pixels was calculated by
2/1/Ar (9)
where A denotes the area in pixel. The slope of the
regression line kS of the double logarithmic plot of
the counted pixels with respect to the radii give
Ss kD 2 (10)
called the fractal capacity dimension. The diameter
of the tongue can thus be calculated. Sausage
method also helps to evaluate quantitative
parameters such as Area, Perimeter, Form Factor,
and Invaslog.
FormFactor=4πArea/Perimeter2 (11)
Invaslog = – log (Form Factor) (12)
Computation of Invaslog helps in analyzing the
invasions of disease on the surface of the tongue.
Radial distance the distance from the centre of
mass to the perimeter point (x i , y i) is defined as
(13)
where is a vector obtained by the distance
measure of the boundary pixels.
2.4 Boundary Descriptors
For irregularly shaped object, the boundary
direction is the best representation. Consecutive points
on the boundary of a shape give relative position or
direction. A four or eight-connected chain code is used
to represent the boundary of an object by a connected
sequence of line segments. Eight-connected number
schemes are used to represent the direction in this
case. Each direction provides a compact representation
of all the information in a boundary. The direction also
shows the slope of the boundary. Compactness is a
dimensionless quantity, which defined as
Area
Perimeter 2
. We can find Roundness from this by
Roundness = Compactness / 4π, which is minimal
for an irregularly shaped region. It is a simple
measure and used to find the invasiveness of the
patches. It is used as region descriptors including
the mean and median of binary levels, the
minimum and maximum binary level values and
the number of pixels with values above and below
the mean. It is a simple region descriptor. The
pathological cells in the tissue can be refined by
normalizing it with respect to population numbers,
land mass per region and so on. From the
compactness, we can find if the region of interest
is invariant and also find the shape of the irregular
border.
2.5 SOBEL Improved Box Counting Dimension SOBEL operator is a discrete
differentiation operator, which computes an
approximation of the gradient of the image
intensity function. At each point in the image, the
result of the SOBEL operator is either the
corresponding gradient vector or norm of this
vector, which is given by
101
1
2
1
8
1
101
202
101
8
1
xS (14)
121
1
0
1
8
1
121
000
121
8
1
yS (15)
22
yxxy SSS (16)
These kernels are convolved with the
original image to calculate approximations of the
derivatives. The horizontal changes are calculated
by and the vertical changes are calculated by
.
Initially the edges were detected using the
SOBEL filter in HARFA software. Later these
images were subject to box counting dimension
31 G. Jayalalitha, T. G. Grace Elizabeth Rani
International Journal of Computer & Mathematical Sciences
IJCMS
ISSN 2347 – 8527
Volume 4, Issue 1
January 2015
using both MATLAB and HARFA. The dimension
thus obtained is referred to as SOBEL Improved
Box Counting Dimension (SIBCD).
2.6 Texture Analysis - Lacunarity
Mandelbrot introduced the term
“lacunarity” which means gaps. It is a special
property of fractals. Gaps determine the texture of
an object. Texture in one sense can be considered
as the appearance of an object. If there are
minimum numbers of gaps in an object then it
appears smooth (homogeneous). On the other
hand, more number of gaps gives the object a
rough appearance (heterogeneous). Concisely
large gaps imply high lacunarity and small gaps
imply low lacunarity. It is possible to construct
fractals with similar dimensions but with varying
lacunarity. This throws much light on the texture
of an object. Variations on the surface of the
tongue are thus quantified by the presence of gaps.
Lacunarity has its applications in medicine, image
processing, geology, ecology and more.
Lacunarity, related to the distribution of
gap sizes is a measure of lack of rotational and
translational invariance or symmetry in an image.
It is also a scale dependent measure. As stated by
Plotnick et al,12
“Lacunarity” L(r) can be defined in
terms of the local first and second moments (mean,
variance) measured for neighborhood sizes r about
every pixel in an image.
(17)
Here mean (r) and var (r) are the mean
and variance respectively. This is calculated from
Histo Stretched Software (Histo). Lacunarity is
notion distinct and independent from the fractal
dimension D. It is not related to the topology of
the fractal and needs more than one numerical
variable to be fully determined. Lacunarity is
strongly related with the size distribution of holes
on the fractal and with its deviation from
translational invariance. Roughly speaking a
fractal is very lacunar if its holes tend to be large.
Lacunarity and fractal dimensions work together to
characterize patterns extracted from digital images.
2.7 Analysis of Invasiveness - Percolation Model
Percolation in the general sense is the flow of
fluids through porous media. Mathematically speaking
it refers to a simplified lattice model of random
systems or networks and the nature of connectivity in
them. As the disease advances in the internal organ,
the respective area on the tongue also shows increase
in abnormality. The invasiveness of the disease thus
can be thought of as the neighboring cells in the
tongue getting infected in a random manner [Fig. 2 ].
In a square lattice, each site represents an
individual which can be infected with probability
(p) and which is immune with probability (1- p).
At an initial time t = 0, the individual at the center
of the lattice (cell) is infected. We assume now
that in one unit of time this infected site infects all
non-immune nearest neighbor sites. In the second
unit of time, these infected sites will infect all their
non-immune nearest neighbor sites, and so on. In
this way, after ' t ' time steps non-immune sites of
the square grid around the cells are infected, i.e.
the maximum length of the shortest path between
the infected sites and the cell is l ≈ t.13
Algorithm 2
Step 1: Start from the center of empty site (square
lattice) which is the origin.
Step 2:The nearest neighbor sites from the origin
are either occupied with probability p or
blocked with probability 1 − p.
Step 3:The empty nearest neighbor sites proceed
as in Step 2, with probability p, blocked
with probability 1 − p.
The above method is particularly useful for
studying the structure and physical properties of
single percolation cluster.
3 Results and Discussion
Fractal Dimension analysis has been
applied to demarcate the infected tongue from
normal one and the intensity of disease. We have
used the Box Counting Method to analyze tongue
disease. We found that a significantly higher
architecture complexity was noted for normal and
infected tongue. The dimension increases as the
patches increase on the tongue. For Conventional
Box Counting Dimension (CBCD), (Table 1,
Fig.3), we see that the normal tongue shows a
lower dimension of 1.1, where as the infected
tongue shows higher dimension. This dimension
has been evaluated using MATLAB. In the
graphical representation, we observe that
dimension is the same for some images, while the
32 G. Jayalalitha, T. G. Grace Elizabeth Rani
International Journal of Computer & Mathematical Sciences
IJCMS
ISSN 2347 – 8527
Volume 4, Issue 1
January 2015
constant varies, implying that the intensity of the
disease is more.
SOBEL Edge Detection identifies the
boundaries correctly. In the case of infected
tongue, the boundary is not clear and SIBCD
shows lesser dimension. Therefore, we observe
that (Table 2, Fig.3) the dimension is presented in
a reverse order in comparison to CBCD. From the
regression equations on the graphs presented
below we see that though the dimension is the
same for some tongue images, a variation is found
in the constant value emphasizing the intensity of
the disease.
Intensity of the disease was found using
HARFA - Fractal Analysis. The Box Counting
Method utilizes covering the fractal pattern with a
raster of boxes (squares) and then evaluates how
many NBW, NBBW and NWBW of the raster are
needed to cover the fractal completely. This has
been done for various tongue images. From Table
3(Fig.3), for CBCD, the normal tongue shows a
lesser dimension, while the infected ones show
higher dimension given by B + BW. When the
patches are in discrete pattern i.e., in a scattered
manner, the value given by B+BW (Discrete) is
considered. Otherwise values given by
B+BW(Continuous) is considered. This illustration
is evident from the graphical representation.
As in the previous case SIBCD shows
higher fractal dimension for normal tongue than
the infected ones in HARFA (Table 4, Fig.3) too.
Thus, a concise distinction is obtained for infected
and non – infected tongue. The SOBEL Edge
Detection method helps in identifying the
boundary of the tongue. For discrete patches, the
values under B+BW (Discrete) are taken and for
continuously spread patches, the values under
B+BW(Continuous) are taken. Thus, CBCD helps
in analyzing the interior of the tongue and SIBCD
helps in analyzing the boundary of the tongue.
Lacunarity analysis (Tables 5, 6)
performed, reveals that the Histo stretched tongue
image (Fig.3 a) has the least value and while
image (Fig.3 b) has the highest value. Higher
lacunarity value indicates high degree of
heterogeneity, which is the case with image (Fig.3
b). Lacunarity is important for texture pattern. The
variation in the constant values in the regression
equation corresponding to Fractal Dimension
shows more gaps, thus indicating high lacunarity.
The histo stretched tongue image "a" shows a
minimal increase in variance in comparison to
tongue images ( Fig.3 b and j ), for a factor of 1.
This indicates the fact that a high degree of
lacunarity is exhibited for abnormal tongue.
The Sausage method helps in finding the
area and hence the radius. The slope of the
regression line of the double linear logarithmic
plot of the counted pixels versus radius gives ks.
From this the Dimension is found as 1.6 for the
tongue image (Fig.3 c) and 1.4 for tongue image
(Fig.3 e) (Table 7), which is very much in
agreement with the Box Counting Dimension.
Perimeter of the tongue varies from person
to person, thus distinguishing infectious tongue
from normal one. The bumps on the surface of the
tongue give a variation in perimeter. In this study,
too Sausage method comes in handy. Averaging
over the perimeter values obtained for various
scaling from 2 to 10, for the ten tongue images, we
found that the tongue image "b" has the highest
value followed by tongue image (Fig.3 f) with
numerical values 650.56 and 567.78 respectively.
This indicates that the boundary is more infected
for the corresponding tongue images which is
visually evident (Fig.3 - b , d). In addition to this
Sausage Method also helps in finding Form Factor
and Invaslog. Computation of Invaslog helps in
finding the invasiveness of the disease. Averaging
over the Form Factor and Invaslog values obtained
for various scaling from 2 to 10, for the ten tongue
images, we found that the tongue image (Fig.3 c)
has the highest value of Form Factor while the
tongue image (Fig.3 b) has the least Form Factor.
Hence the Invaslog value is the highest for the
tongue image (Fig.3 b) and least for tongue image
(Fig.3 c), with values 5.55 and 3.55 respectively.
This is an indication that for tongue image (Fig.3
b) , the invasiveness of the disease is more and
much attention has to be paid.
33 G. Jayalalitha, T. G. Grace Elizabeth Rani
International Journal of Computer & Mathematical Sciences
IJCMS
ISSN 2347 – 8527
Volume 4, Issue 1
January 2015
Boundary Descriptors have been studied,
as boundary direction is the best representation for
irregularly shaped region. Compactness is a
dimensionless quantity that takes a value 1 for
circular objects and greater than 1 for oblong
objects. This was calculated for all ten tongue
images, two of which are shown in Table 8.
Considering the average of these values for scaling
2 through 10, we infer that high compactness is
obtained for tongue image (Fig.3 b) with
numerical value 5773.14. This indicates the oblong
or rather the irregularity of the border. Roundness
was evaluated using Compactness, which in case
of tongue image (Fig.3 b) is 459.23.
The percolation threshold for the infected
region is given as a ratio of BD to 2D .14
It is
observed that (Table 9, Fig.3) as the fractal
Dimension BD increases, the probability of
threshold increases. The increase in intensity of the
disease is thus visualized with the increase in
texture pattern of the tongue through Percolation
Model.
The MATLAB Fractal Dimension analysis
gives a value of 1.6 for image (Fig.3 e). When
comparing this with reflex zones of the tongue
(Fig.1 a), we infer that spleen or stomach is most
affected. Liver or Gall Bladder is the most affected
organ for the tongue image (Fig.3 c), when
comparing with reflex zones. The Fractal
Dimension is 1.7 in this case. In this manner for
every tongue image the infected organ and the
intensity of the disease can be easily identified.
4 Conclusion
Box Counting Method has been used to
analyze the diseases on the tongue and hence the
diseases in the body. This has been done using
MATLAB. This we have termed as Conventional
Box Counting Method (CBCD). In addition we
have used SOBEL Edge Detection Method to find
the edges exactly and then applied Box Counting
Method. This is termed as SOBEL Improved Box
Counting Method(SIBCD), which has also proven
to be an efficient method.The patches on the
tongue varies for normal and abnormal tongue,
which has been analysed with HARFA, Fractal
Analysis software. The dimension shows the
intensity of the disease. Lacunarity asseses the
texture pattern of the tongue i.e., the size and
distribution of the empty domain. From these
methods the intensity of the disease can be found.
The higher the dimension, the higher is the intensity
of the disease. Tongue with more dark patches show
higher dimension. The fractal dimension DB is
likely to be the most promising tool for the
effectiveness of therapies in various clinical
contexts. It will be very helpful for the doctors in
diagnosing the disease and hence the appropriate
treatment.
Using Euclidean geometry it is not
possible to find the dimension of the irregular
border . SOBEL Edge Detection together with
Boundary Descriptors is found to be effective in
the analysis. So we found the complexity of
tongue using fractal concepts. Abnormality in
tongue shows stress in blood flow which in turn
reflects the health of the internal organ. In
modelling physical features such as tongue,
surface treatment is crucial. This takes care of not
only smooth flowing curves but also sharp edges.
Good surface representations are obtained through
topology. We have employed the idea of
dimension which can be thought of as a measure
of how an object fills space. More high bumps on
the surface , spread of patches cover the tongue in
various forms thus differentiating normal tongue
from abnormal one. In this line application of
Mathematical concepts and analysis of tongue
diseases using dimension proves to be an efficient
tool when compared to the existing methods.
(a) (b) (c)
Figure 1 (a) Reflex Zones of Tongue. (b), (c) Actual tongue
34 G. Jayalalitha, T. G. Grace Elizabeth Rani
International Journal of Computer & Mathematical Sciences
IJCMS
ISSN 2347 – 8527
Volume 4, Issue 1
January 2015
Figure 2 The first four steps of the percolation model
Table 1 Data Analysis of Tongue Images Using Conventional Box Counting Dimension(CBCD)
Scaling
Image 2 3 4 5 6 7 8 9 10 DB
a 336 207 145 116 95 87 71 63 56 1.1
b 3081 1645 1073 765 589 476 394 334 285 1.5
c 2673 1372 827 568 422 320 255 215 183 1.7
d 3357 1724 1092 765 573 443 349 289 262 1.6
e 3106 1584 1000 702 530 418 356 293 257 1.5
f 2331 1187 749 526 393 310 251 211 176 1.6
g 308 179 122 102 83 70 54 44 46 1.2
h 1541 784 493 345 259 203 171 147 122 1.6
i 1996 1000 642 435 325 262 217 182 148 1.6
j 2321 1179 727 509 371 284 232 194 166 1.6
35 G. Jayalalitha, T. G. Grace Elizabeth Rani
International Journal of Computer & Mathematical Sciences
IJCMS
ISSN 2347 – 8527
Volume 4, Issue 1
January 2015
Graphical Representation of Tongue Images – CBCD
Table 2 - Data Analysis of Tongue Images UsingSobel Improved Box Counting Dimension- SIBCD