tongue features analyzed through fractal dimensions · tongue features analyzed through fractal...

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



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



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



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



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.



IJCMS

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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



IJCMS

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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



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Graphical Representation of Tongue Images – CBCD

Table 2 - Data Analysis of Tongue Images UsingSobel Improved Box Counting Dimension- SIBCD

Scaling

Image 2 3 4 5 6 7 8 9 10 DB

a 1655 1038 724 538 399 323 252 205 175 1.4

b 1813.5 1197 902.5 717.6 591.5 502.7142 436 358 330 1.1

c 676 447 331 256 215 176 158 145 124 1

d 999 677 493 388 324 261 238 199 177 1.1

e 969 636.6665 450 362.9998 295.6666 254 213.75 191.5556 175.1999 1.1

f 435 286 212 165 144 119 108 95 83 1

g 48 251 193 160 123 110 90 76 76 1.1

h 876 553 390 293 235 187 166 141 117 1.2

i 715 480 340.75 286.5999 237.6666 200 160.625 144.2222 124.8 1.1

j 1781 1135 804 607 457 366 300 252 212 1.3



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Graphical Representation of Tongue Images - SIBCD

Table 3- HarFA Fractal Analysis of Tongue(CBCD)

Image Discrete Continuous

BW B+BW W+BW BW B+BW W+BW

a 0.8847 1.1278 1.9933 0.8424 1.1619 1.994

b 1.0171 1.5049 1.9222 1.1029 1.5159 1.9268

c 1.0378 1.7443 1.9633 0.9807 1.7121 1.9674

d 1.1529 1.6991 1.9163 1.1081 1.6889 1.9167

e 0.8661 1.5976 1.9466 0.8217 1.5821 1.9474

f 0.916 1.7222 1.9213 0.9295 1.7241 1.9245

g 0.9311 1.3868 1.9916 0.8951 1.3659 1.9947

h 0.9729 1.6147 1.9675 1.0294 1.6352 1.9704

i 0.9101 1.713 1.9412 0.8857 1.7224 1.9437

j 1.1025 1.6072 1.9507 1.0487 1.622 1.9528



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Graphical Representation of Tongue Images of CBCD using HARFA

Table 4 - HarFA Fractal Analysis of Tongue-SIBCD

Image Discrete Continuous

BW B+BW W+BW BW B+BW W+BW

a 1.3907 1.2617 1.9843 1.4762 1.312 1.9867

b 1.041 1.0214 1.9826 1.0298 1.0016 1.985

c 1.0222 1.0087 1.9935 0.9215 0.967 1.9952

d 1.0268 1.0486 1.9893 1.0402 1.0197 1.9918

e 0.986 1.0855 1.9883 1.0649 1.1085 1.991

f 0.9827 0.9889 1.9958 1.0261 1.039 1.9977

g 1.0101 1.0486 1.9956 0.9292 1.0468 1.9979

h 1.199 1.1783 1.9906 1.1468 1.1724 1.9932

i 1.0468 1.0531 1.9925 1.0987 1.1042 1.9945

j 1.3136 1.233 1.9815 1.2508 1.1972 1.9844



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Graphical Representation of Tongue Images using HARFA - SIBCD Table 5 Data Analysis of Tongue Images Using Lacunarity

Image Factor Mean SD Var Lacunarity=1+(Var/Mean^2)

a

Original 1 235.6 36.6 1339.56 1.024133016

0 235.6 36.6 1339.56 1.024133016

Histo 1 219.6 65.9 4342.81 1.090054653

0 117.9 35.5 1260.25 1.090662793

b

Original 1 168.7 49.2 2420.64 1.085055037

0 168.7 49.2 2420.64 1.085055037

Histo 1 104.1 84.8 7191.04 1.663575351

0 58.5 47.9 2294.41 1.670439039

j

Original 1 208.9 59.4 3528.36 1.080852976

0 208.9 59.4 3528.36 1.080852976

Histo 1 173.9 100.6 10120.36 1.334654599

0 91.9 53.3 2840.89 1.336374756

Table 6 Data Analysis For Few Tongue Images Using Lacunarity

Images a b c d e f g h i j

Original 1.02 1.08 1.08 1.09 1.08 1.09 1.02 1.06 1.08 1.08

Histo stretched 1.09 1.66 1.2 1.3 1.5 1.4 1.26 1.29 1.35 1.33

Table 7 Sausage Method for tongue images c,e

Scaling Area Radius ks Ds=2-ks Area Radius ks Ds=2-ks

3 792 15.874508

0.4 1.6

850 16.445502

0.6 1.4

5 238 8.7021418 226 8.4799228

7 96 5.5267942 101 5.6688944

9 49 3.9485325 48 3.9080337

11 31 3.1406427 17 2.3257452

13 17 2.3257452 16 2.2563043

15 8 1.5954481 5 1.2613124

17 5 1.2613124 3 0.9770084



IJCMS

ISSN 2347 – 8527

Volume 4, Issue 1

January 2015

Table 8 Data Analysis for Form Factor, Boundary Descriptors

Sca

lin

g

Tongue Image c Tongue Image e T

ota

l A

rea

Fo

rm F

act

or

Inv

asl

og

Co

mp

act

nes

s

Ro

un

dn

ess

To

tal

Are

a

Fo

rm F

act

or

Inv

asl

og

Co

mp

act

nes

s

Ro

un

dn

ess

2 2763 0.048 3.028 529.59 20.65 3106 0.044 3.13 287.42 22.86

3 1372 0.03 3.52 424.75 33.79 1584 0.02 3.92 633.83 50.41

4 827 0.029 3.54 433.42 34.48 1000 0.015 4.21 844.09 67.14

5 568 0.027 3.594 457.56 36.4 702 0.013 4.38 1002.55 79.75

6 422 0.026 3.642 479.61 38.15 530 0.012 4.41 1034.69 82.31

7 320 0.024 3.728 522.67 41.58 418 0.013 4.37 994.94 79.14

8 255 0.028 3.586 453.75 36.09 356 0.008 4.88 1647.29 131.03

9 215 0.022 3.8 562.37 44.73 293 0.01 4.6 1250.52 99.47

10 183 0.023 3.784 553.3 44.01 257 0.006 5.05 1959.26 155.85

Table 9 - Data Analysis of Tongue Images Using Percolation Model

Image a b c d e f g h i j

DB 1.1 1.5 1.7 1.6 1.5 1.6 1.2 1.6 1.6 1.6

p = DB/2 0.55 0.75 0.85 0.8 0.75 0.8 0.6 0.8 0.8 0.8

a b c d e

f g h i j Figure 3 Normal and Affected Tongue Images (a : Normal Tongue; b – j : Affected Tongue)

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IJCMS

ISSN 2347 – 8527

Volume 4, Issue 1

January 2015

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