Irregularity and Asymmetry Analysis of Skin Lesions Based on Multi-scale Local Fractal

Distributions Ma Li* Guo Anzhe Zou Shaofang Xu Weidong

School of automation, Hangzhou Dianzi University, Hangzhou, 310018, China E-mail:*mali@hdu.edu.cn

Abstract—To tackle the problems of detecting structural

irregularity and asymmetry of skin lesion boundaries in the

early CAD diagnosis of melanomas, a multiscaled local

fractal algorithm is proposed in the paper where sequent

removing textural irregularity from skin lesion boundaries is

performed and features of boundary irregularity under

multiscale are extracted. Meanwhile, a novel method of

structural irregularity measurements, as a key diagnostic

factor, is given and boundary asymmetry measurements

using local fractals are also presented. Experiments show

that features extracted by the proposed scheme have

advantages over global fractal and geometric measures in

enlarging inter-differences between tumor and benign lesions

using multiscaled contour irregular information. The local

fractal based asymmetry measures obviously strengthen

asymmetric degrees of melanoma lesions to provide

multi-source irregularity descriptors and enhance the

capability of discriminating skin tumors on characteristics of

boundary irregularity and asymmetry.

Keywords: skin lesion; border irregularity; contour

asymmetry; local fractal distribution

I. INTRODUCTION

Melanoma is known as one of the most malignant and metastatic skin tumors probably appearing on any parts of human bodies. According to statistics, the curability of skin cancer could reach nearly 100% if it is recognized early enough and treated surgically. So melanoma detections using CAD techniques are highly needed to implement clinical diagnosis rules in image processing systems. From characteristics of skin surfaces, there are four well-known ABCD rules for melanoma detections:

A(Asymmetry), B(border irregularity), C(color) and D(Diameter). Although there are lots of literatures involved in melanoma recognitions or detections, the objective of this paper is to pursue another ways of describing melanoma features by Rule A and Rule B to extract important features valuable for skin tumor diagnosis.

Asymmetry of skin lesion surfaces and boundary irregularity are two important determination criterions in melanoma diagnosis. As for asymmetry, take two lines through the major and minor axes respectively on a tumor surface, the divided boundary pairs appear some asymmetry; and there are two types of boundary irregularities with respect to border roughness [2,6]: textural and structural irregularity. Finer variants on borders are called textural irregularity while large convexity and concavity along tumor boundaries represent structure irregularity that is the most important indicator for melanoma diagnosis in clinics.

In the past decade, there are many researches on boundary asymmetry and irregularity analysis of skin lesions. In 1993, Vincent and Andrew analyze boundary irregularity using contour fractals, but the discrimination power is poor as smaller differences of fractal values for visually larger differences of object shapes[2]. Later in 2003 wavelet tree scheme is used to strengthen inter-class differences [4]. As for boundary asymmetry, Michele d’Amico et. al proposed a size function to present a qualitative measure of contour asymmetry with limitation of classification accuracy[5]. There are other researches on feature extractions from geometric measure and curvature analysis for asymmetry in recent years[7,8].

This work is supported by Natural Scientific Fund of China (60775016)

978-1-4244-4131-0/09/$25.00 ©2009 IEEE

Motivation of this paper is to combine the local fractal distributions and multiscale analysis for enhancing inter-class feature differences. Conventional fractal analysis takes a contour as a whole without finer information while local fractals could indicate local roughness. Furthermore, mutiscale analysis would provide much layered information for classification problems and choose proper scale for structurally irregular measures as well (textural irregularity will be removed at larger scale). The novelty of the paper on analysis of contour irregularity and asymmetry lies on: (1) multiscaled local fractals are taken for extraction of boundary roughness features for irregularity and asymmetry analysis; (2) structural irregularity is described in a fractal space to measure the key component with respect to melanoma diagnosis in clinic. (3) A criterion on boundary asymmetry measures is proposed using local fractals at given scale to enhance feature differences between melanomas and benign moles.

II. LOCAL FRACTAL DISTRIBUTION(LFD)

Fractal geometry was first proposed by Mandelbrot to explain object surface roughness in natural world using fractal dimension [1]. Any fractal objects have the property of anisotropies and self-similarity at different scales for describing object surface complexities. In practice, box dimension method is used to calculate the value of fractal dimension of an object. Suppose F is any non-empty bounded subset in

nR ,where ),( δFN refers

to a minimum counting number of grids with maximum diameterδ covering F, then the box dimension on F is defined as:

)/1ln(

),(lnlimdim0 δ

δδ

FNFB →= (1)

For a set in 2D plane, choose a sequence of δ and get a set of date ( )/1ln( δ , ),(ln δFN ), then the slope

of fitted line using LSM in the space of )/1ln( δ ~ ),(ln δFN is the box counting number D.

As mentioned above, D is a global measure of contour complexity of an object with weaker discrimination power. A local fractal dimension is proposed in the paper to calculate the complexity of any given point on a

contour. Suppose A is a point located on a contour, choose a sequence of grids centered at point A with different size ir and calculate the number of contour pixels iN within the grid of size ir . Then local fractal

dimension is derived by LSM fitting data log(1/ ir )~log iN ( similar to Eq.(1)) at point A. this

procedure is carried out to all pixels on the contour and form a local fractal distribution. The local fractals have natural anti-noise characteristics as they are fitted on different grid scales. They represent the relationship between roughness and space positions where smaller value indicates smoother and larger one coarser (large variants on curvatures) at any points of the contour.

Local fractals are sensitive to boundary variations and easy to distinguish normal or malign skin lesion. Fig.1 gives comparison results of local fractal distributions. A fractal distribution of a melanoma shown in Figure1 (a) appears larger variants and higher magnitudes, while that of benign one in Figure1 (b) shows finer waves and lower values.

(a) LFD of a melanoma (b)LFD of a mole

Figure 1. Local fractal distributions

III. CONTOUR IRREGULARITY

A. Features from Multi-scale Local Fractals

Boundary irregularity of malignant melanomas is mainly presented as structural irregularity while larger curvature changes in geometric space correspond to lower frequency components in frequency domain and minor variants to higher frequency components respectively. Original lesion contours are in form of a mixed textural and structural irregularity and in visual system textural irregularity (finer variants) would disappear and structural one be retained with the decrease of resolutions.

In the paper, Gaussian kernels are firstly used to form a set of smoothed contours at different scales. LFDs of a

set of smoothed contours are then calculated. Finally features extracted from the LFDs are illustrated (see the following).

1) Statistics The LFDs of Gaussian smoothed contours at different

scales are computed by local fractal calculation on a sequence of smoothed contours. Based on local fractal distribution at each scale, min, max and mean of the LFD are chosen as good indicators of contour irregularity as the mean represents general smoothness of the contour at given scale. Experiments show that max and mean values of melanoma’ LFD would gradually decrease with the scale increases while that of benign moles nearly unchanged.

2) Counting of Irregularity Measure When setting a threshold value for a LFD(generally

equal to the maximum of mole’s LFD), the counting value S is defined as the number of points in LFD whose values larger than the preset threshold.

=

=N

iiDS

1

))((δ

≤−>−

=0)(00)(D1

))((riDri

iDδ (2)

Where )(iD , local fractal at point i and r , preset

threshold, N, number of points on a contour. S values decrease with the scale increase in case of skin tumor while the S values approach to zeros for benign moles.

B. Measure of Structural Irregularity

1) Structural Irregularity on Geometry It is shown in our experiments that variances of

contour LFD gradually decrease with the scale increases while variance change appears out of order after certain scale value. Later this value is considered as turning point of smoothed contours only with structural irregularity from mixed ones. As for measuring structural irregularity, there are two contours needed: one is a Gaussian smoothed contour L1(only with structural irregularity) at the turning scale, the other is a contour L2 (a reference model)derived from an inverse FFT transform of the first m components of Fourier coefficients of an original contour. So the measure of contour irregularity is

calculated as an accumulated sum of XOR operation of regions covering by L1 and L2.

= =⊕=

N

i

M

jjiLjiL

AstructS1 1

)),(2),(1(1 (3)

2) LFD Based Contour Irregularity A LFD based measure of contour irregularity defined

as

=+

=A

ii

AG

0)(

)1(1 δ

≤−>−

=0)(,00)(,1

)(RiDRiD

iδ (4)

G, LFD based contour irregularity measurement, A, the total number of contour points. R, a preset threshold.

IV. FEATURES OF CONTOUR ASYMMETRY

A. Selection of Symmetric Regions

The symmetric-axis generation is the key step for asymmetry measure of object contours where the symmetry axes called major/minor axis are drawn from the second order moments 02m , 11m ,

20m in the paper[3].

The major and minor axes are mutually perpendicular lines partitioning a skin lesion into four parts. The asymmetry measure of a contour is taken by calculating normalized asymmetry degrees kΔ of a pair of contour segments with respect to central, major and minor axis symmetry. kΔ is related to features selected when approaching zero means absolutely symmetry.

B. Feature Extraction for Asymmetry Measures

After determining symmetry axes, degrees of contour asymmetry depend on features extracted in each contour segment. Besides conventional area A used for shape geometric features, others are illustrated in the following:

1) Averaged Difference of Local Fractals This feature describes an averaged variant of points on

contour segment with respect to their neighbors.

4,3,2,1,))((1

1

2 =−==

imkDN

VIi

i

N

ki

ii (5)

Where )( ikD , the local fractal at the kth point in the ith segment. bm , averaged local fractals of neighbors at

point k.

2) Relative Radial Distance (RD) Suppose the length of each segment

as 4,3,2,1, =iLi . Calculate radial distances along

contour points, ilΔ refers to arc increment in an

interval ]2/,0[ iL . The averaged absolute differences

irΔ of radial distances between a pair of contour points

with arc increment ilΔ are defined on segment i .then

the relative averaged difference of radial distances on segment i .

0

1 ( ) ( ) , 1,2,3,4iL

i i i i i ii

r r l l r l dl iL

Δ = +Δ − =

4,3,2,1,

)(1

)()(1

0

0 =

−Δ+

=Δ

= i

dllrL

dllrllrL

rrRD

i

i

L

iii

L

iiiiii

i

ii

(6)

3) Normalized Zero-cross Rate ρSuppose n is the number of times of local fractal plot

passing a circle whose radius equals to the mean value of the LFD. Then ρ is a ratio of n to N. N, number of

points on a contour.

V. EXPERIMENTAL RESULTS

A set of images containing melanomas or benign moles are selected to testify the effectiveness of proposed features and compare the inter-class differences.

A. Contour Irregularity

Figure2 gives experimental results related to Eq. (3) to calculate contour structural irregularity of a melanoma image. There are two contours in Figure2 (a): contour 1 refers to a reference from inverse transform of Fourier descriptors, and contour 2 smoothed contour from original one at threshold scale. Figure2 (b) is the map showing results (black area) after XOR operation of the above contours. The result of Eq.(3) is 8%.

Table 1 presents comparing results of features extracted from multiscaled LFDs with respect to sample

images of melanomas and moles. Structural irregularity comparisons are given as well.

(a) Contour comparing (b) Structural irregularity

Figure 2. Structural irregularity measure

TABLE I. FEATURE COMPARISONS OF CONTOUR IRREGULARITY

Scale Malign Benign

1 3 5 1 3 5

Multi-

scale

LFD

Max 1.10 1.00 .958 .907 .901 .897

Min .680 .680 .680 .690 .700 .703

Mean .830 .820 .810 .784 .784 .784

Rd

Max 162 162 162 157 157 156

Min 111 111 112 115 115 116

Mean 137 137 137 137 137 137

S 56 50 38 0 0 0

Struct

-irreg

Sample M1 M2 M3 N1 N2 N3

Ss(%) 8.0 8.3 7.8 0 0 0

G(%) 3.9 4.4 4.2 0 0 0

In TABLE I, scale 1,3,5 corresponds to Gaussian deviation 1=δ , 3=δ , 5=δ . It is indicated from table 1 that LFD based multiscale feature values reflect larger differences between skin tumors and moles than conventional geometric features (the Rd here means radial distance of boundaries). Among proposed features, LFD based feature max, mean and counting S of irregularity are selected as contour irregularity descriptors in fractal domain. Two types of measures for structural irregularity all highlight the inter-class differences.

B. Contour Asymmetry

In asymmetry analysis, the partition of symmetric axes is first carried out followed by feature computation of each segments and asymmetry measures. The local fractal distributions (LFD) of divided contour segments on a melanoma and a mole are shown in Figure3.

(a) A malenoma’s map (b) A mole’s map

Figure 3. Local fractal distribution and symmetric axes

TABLE II. ASYMMETRY ANALYSIS

kΔFeature

Melanoma Mole

M.A. m.A C.A M.A m.A C.A.

ρ .1272 .1499 .1625 .0005 .0014 .0012

VI .1929 .3139 .5370 .0478 .0698 .1024

RD .1264 .1749 .3075 .0065 .0123 .0354

A .0183 .0289 .05699 .0017 .0035 .0065

In Table II, M.A, m.A and C.A in the second line represent asymmetry on Major axis, minor axis and central asymmetry respectively. There are 10 images involved, each set has 5 images. From the table, it is indicated that the four features proposed in the paper have strong capability of discriminating skin tumors from moles on asymmetry measures in case of each symmetric axis. Among them, the relative radial distance RD performs well and normalized zero-cross rate ρ has the

largest discriminating power as its inter-class rate of asymmetry measure reaches 245.

VI. CONCLUSION

Algorithms of Contour irregularity and asymmetry measures for skin lesion diagnosis are proposed based on multi-scaled local fractal distributions. In terms of contour irregularity measure, multi-scaled Gaussian filtering is implemented to remove textural irregularity on contours and two types of structural irregularity measure are proposed. Furthermore, some irregularity features derived from LFD at multiscales are given. On the other hand, asymmetry analysis is discussed by presenting partition of symmetric axes and features on asymmetry measures that benefit the inter-class discriminating power from skin tumors.

Experimental results show that proposed features have stronger capability of enhancing inter-class differences for contour irregularity and asymmetry measures. The proposed approach provides a novel way, multiscaled local fractal distributions, of describing contour irregularity and asymmetry. The method overcomes the difficulty in weaker discrimination power of global fractals and integrates layered information to strengthen further classifications.

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