A Edge Detection Method for Microcalfication Clusters in Mammograms

Yu Guang Zhang, Wen Lu, Fu Yun Cheng, Li Song Taishan Medical University, Taian, Shandong, China,271016

Abstract—Edge is one of the most important characteristics of microcalcifications, edge detection of microcalcification clusters has a great significance in computer-aided diagnosis system for the automatic detection of clustered microcalcifications in digitized mammograms. A lot of algorithms have been suggested for extracting medical image edges, however, few of them are well suited for edge extraction of microcalcifications due to obtaining discontinuous edges, or continuous edges with more over-detection points. In this paper, we propose a new method for clustered microcalcifications edge detection by integrating Kirsch edge operator, edge linking with Markov model. First, initial edges are extracted by employing kirsch edge operator. Then, we thin the initial edges and fill many gaps in the edge image using edge linking technique. Finally, closed boundaries of microcalcifications are obtained based on Markov model. The experiments demonstrate that our algorithm can obtain closed boundaries with less over-detection points.

Keywords-edge detection; kirsch edge operator; markov model; mammogram

I. INTRODUCTION

Clear evidence shows that early diagnosis and treatment of breast cancer can significantly increase the chance of survival for patients. One of the most important radiological signs for early detection of breast cancer is the presence and appearance of microcalcifications [1]. Hence, many investigators have developed computer-aided diagnosis (CAD) schemes for identifying regions of potential microcalcification clusters in mammograms [2]. Edges are important characteristic of microcalcifications, therefore, edge extraction of microcalcification clusters has a great significance in computer-aided diagnosis system for the automatic detection of clustered microcalcifications in digitized mammograms.

There exist many methods for medical image edge detection. The following is a brief review of some main methods for detection of medical image edges. Eichel et al. [3]]

described a novel algorithm, known as sequential edge linking (SEL), for the automatic definition of coronary arterial edges in cineangiograms. Wang et al. [4] developed an improved multiresolution sequential edge linking method for medical image edge detection. In [5], a novel mathematical morphological edge detection algorithm is proposed to detect the edge of lung CT image with salt-and-pepper noise. A detection scheme [6] is proposed for the automatic detection of medical image edges using multifractal spectrum theory. Chang [7] applied contextual-based Hopfield neural network for finding the edges of CT and MRI images. Gudmundsson et al. [8] developed an algorithm that detected well-localized, unfragmented, thin edges in medical images based on

optimization of edge configurations using a genetic algorithm. Few of these algorithms are suitable for edge extraction of microcalcifications due to obtaining discontinuous edges, or continuous edges with more over-detection points.

In fact, obtaining closed microcalcification boundaries with less over-detection points is very difficult only using one kind of method. The main reasons [9] can be described as follows. First, microcalcifications are often very small. On mammograms, they appear as tiny objects which can be described as granular, linear, or irregular. According to the literature, the size of microcalcifivations are from 0.1-1.0 mm, and the average diameter is about 0.3 mm. Small ones(ranging 0.1-0.2 mm)can hardly be seen on the mammogram due to their superimposition on the breast parenchymal textures and noise. This reason makes it be very difficult to extract continuous edges with less noise points. Second, microcalcifications often appear in an inhomogeneous background describing the structure of the breast tissue. Some parts of the background, such as dense tissue, may be brighter than the microcalcifications in the fatty part of the breast. In this situation, a lot of edge detection algorithms can hardly extract the edges of microcalcification clusters. Finally, some microcalcifications have low contrast to the background. In other words, the intensity and size of the microcalcifications can be very close to noise or the inhomogeneous background. Hence, many edges of noise and background tissue can often be found in the edge images of microcalcification clusters.

In this paper, we investigate many methods of edge extraction, and propose a novel approach for edge detection of microcalfication clusters by integrating Kirsch operator, edge linking with Markov model. First, we take advantage of kirsch operator to extract initial edges of microcalcification clusters. There exist some gaps in the initial edge images of microcalcifications, in order to obtain closed boundaries of microcalcifications, we fill gaps by employing edge linking technique. Finally, we remove the edges of background tissue and noise using Markov model.

II. INITIAL EDGE EXTRACTION

If a pixel falls on the boundary of an object in an image, then its neighborhood will be a zone of gray-level transition. The two characteristics of principal interest are the slope and direction of that transition. These are the magnitude and direction, respectively, of the gradient vector. Edge detection operators examine each pixel neighborhood and quantify the slope, and often the direction as well, of the gray-level transition. There are several ways to do this, most of which are based upon convolution with a set of directional derivative

Science and Technology Development Project of Taishan Medical University (No.1240)

978-1-4244-4134-1/09/$25.00 ©2009 IEEE

masks [10]. The kirsch edge operator is one of the most important edge operators, which achieves the good tradeoff between keeping edge details and suppressing the noise components. Eight convolution kernels make up the kirsch edge operator. Each point in the image is convolved with all eight masks. Each mask responds maximally to an edge oriented in a particular general direction. The maximum value over all eight orientations is the output value for the edge magnitude image. Details of Kirsch edge detection are described as follows.

Each point in the original medical image oI is convolved

with all eight masks. Let ( ),mF n k denote the value of

convolution at point ( ),n k using the mth mask, then,

( ),mF n k is given by

( ) ( ) ( )1 1

1 1, , ,m o m

j iF n k G n j k i M j i

+ +

=− =−

= + + (1)

where ( ),oG n j k i+ + denotes the gray value at

point ( ),n j k i+ + in the image oI , 1,0,1i = −1,0,1j = − 0, , 1n H= − 0, , 1k W= − W and

H denote the height and width of the image oI , respectively.

( ),mM j i is the coefficient at point ( ),j i in the mth mask.

The maximum convolution ( )max ,F n k is defined as

( )( ) ( )

( )1 2

max8

, , , ,, max

, ,

F n k F n kF n k

F n k= (2)

where ( )max ,F n k can be viewed as filter value, thus the filter

image FI consisting of ( )max ,F n k is written as

( ) ( )

( ) ( )

max max

max max

0,0 0, 1

1,0 1, 1

F F WFI

F H F H W

−=

− − − (3)

We examine three neighborhood points line by line, if the gray of the middle point is the local maximum value, then, which is the extremum point, in this way, the extremum image wMI in the horizontal direction can be obtained, that is,

wMI is defined as

( ) ( )

( ) ( )

0,0 0, 1

1,0 1, 1

w w

w

w w

MI MI WMI

MI H MI H W

−=

− − − (4)

where ( ),wMI n k is the gray value at point, ( ),n k ,in the

image wMI ( ),wMI n k is given by

( ) ( )max 1 2,,

0wF n k F F F

MI n kothers< >

= (5)

where ( )1 max , 1F F n k= − , ( )max ,F F n k= ,

( )2 max , 1F F n k= + , Similarly, the extremum image hMIin the vertical direction can be defined as

( ) ( )

( ) ( )

0,0 0, 1

1,0 1, 1

h h

h

h h

MI MI WMI

MI H MI H W

−=

− − − (6)

where ( ),hMI n k is the gray value at point, ( ),n k ,in the

image hMI ( ),hMI n k is given by

( ) ( )max 3 4,,

0hF n k F F F

MI n kothers< >

= (7)

where ( )3 max 1,F F n k= − , ( )4 max 1,F F n k= + , thus, the

final extremum image MI can be written as

( ) ( )

( ) ( )

0,0 0, 1

1,0 1, 1

MI MI WMI

MI H MI H W

−=

− − − (8)

where ( ),MI n k denotes the gray value at point, ( ),n k , in

the imageMI and is define as

( ) ( ) ( ){ }, max , , ,w hMI n k MI n k MI n k= (10)

We examine each point in the imageMI , if the gray value is larger than the preset thresholdT , then, the corresponding

point is labeled as edge point, in this way, the initial edge image EI is written as

( ) ( )

( ) ( )

0,0 0, 1

1,0 1, 1

EI EI WEI

EI H EI H W

−=

− − − (11)

where ( ),EI n k is the gray value at point, ( ),n k , in the

image EI and is defined by

( ) ( )( )

255 ,,

0 ,MI n k T

EI n kMI n k T

>=

≤ (12)

III. NOISE REMOVING AND EDGE THINNING

The presence of noise in the initial edge image, however, imposes a requirement for noise removing. For each edge point in the initial edge image, the three-by-three neighborhood centered on that point is examined, if the total edge point number is more than two, then, these edge points will be reserved, otherwise, all edge points in that neighborhood are taken as noise.

In order to obtain single pixel edge, the removed noise edge image need to be thinned, the thinning method is described as follows. Firstly, we define sixteen kinds of edge modes and corresponding pattern codes [11] showed in Fig.1.

(a) (b)

Figure 1. (a) Image edge modes, (b) the codes of image edge patterns

Secondly, we examine each point in the edge image, For each edge point, ( )i, j , the three-by-three neighborhood

ijEB centered on that point is examined, if the total edge point

number in the neighborhood ijEB is more than 3, then, we

obtain a three-by-three neighborhood ijCB corresponding

to ijEB in the filter image FI . Let nVEP denote the value of edge pattern n , and be defined by

( )3

1n n

kVEP VP k

=

= (13)

where 1 2 16n , , ,= denotes the codes of edge patterns, ( )nVP k denotes the kth pixel value of edge pattern n in the

filter image FI . Let { }1 2 16maxVEP Max VEP ,VEP , ,VEP= denote the

maximum value of nVEP , and the 1N , 2N and 3N are the pixels in the neighborhood ijCB corresponding to maxVEP ,

then, in the neighborhood ijEB , those pixels which have the

same positions as 1N , 2N and 3N in the neighborhood

ijCB are labeled as edge points. Finally, in this way, we can obtain the thinned edge image. In the thinned edge image, there are still a lot of discontinuous edges. Hence, edge point linking is the process of associating nearby edge points so as to create a closed, connected boundary. This process is executed by employing edge connection algorithm [11].

IV. BACKGROUND EDGE REMOVING

In the continuous edge image, there exit a lot of edges of background tissue, in order to eliminate these edges, we propose an algorithm based on the Markov model shown in Fig.2.

ir1ir +

iθ1iθ +

( )0,0o ( )00 0,A n k

( ),i i iA n k( )11 1,i iiA n k+ ++

0rB

Figure 2. Markov model of microcalcification boundary

In Fig.2, the point, ( )0,0 denotes the middle point

between B and oA which are boundary points of

microcalcification, ir denotes the distance between the point

o and iA , iθ is the angle of rotation, ( ),i in k denotes the

coordinate of iA ,and is written by

sincos

i i i

i i i

n rk r

θθ

==

(14)

Let ( )iP A denote the probability of the point

iA belonging to the microcalcification boundary, then, the

condition probability ( )1i iP A A+ is defined by

( ) 1 11

1

i i i ii i

i i

r r r rP A A

r r others+ +

++

>= (15)

In edge image, we examine each point line by line, for two adjacent edge points B and oA shown in the figure 2, the

point o is taken as origin, both iA and 1iA + are obtained by

rotating through the angle iθ and 1iθ + ,respectively. The

condition probability ( )1i iP A A+ can be provided by (15), if

it is larger than11ir

− , then, the point 1iA + is labeled as edge

point, otherwise, the point 1iA + is removed as background tissue edge. Then the other edge points processing proceed, using this way and producing the final result.

VI. SIMULATION RESULTS AND COMPARISON

Several experiments were carried out on different ROI with microcalcification clusters to test the performance of our algorithm. The same as other previous works, the quality of edge detection results is evaluated subjectively. Canny’s edge detector is a very popular edge operator. It is always among the best performers in various edge operation evaluation experiments, and has become part of the standard against which the performance of a newly developed edge detector is compared [12] . We compare the result of our algorithm with one of Canny’s edge detector. Figure 3 is a part of experiment results. (a) is original ROI with microcalcification clusters, (b) is the extracting results of our algorithm, (c) is the extracting results of canny operator. As can be seen from Figure 3, our algorithm can obtain closed boundary with less noise and background tissue edges.

(a)

(b)

(c)

Figure 3. Results of edge detection

VII. CONCLUSION

In this paper, we propose a new edge detection algorithm of microcalcification clusters in digital mammograms based on kirsch operator and Markov model. The proposed approach was applied to boundary extraction of micocalcification clusters. We compared the extraction results with canny operator. Our study showed that in terms of noise, over-detected points, closed boundary, our algorithm was better, compared to the canny method. These results demonstrated that our method is an effective way to extract microcalcification clusters. Therefore, the proposed algorithm can be applied to characteristic extraction of microcalcification clusters.

REFERENCES

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