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Characterization of Clustered Microcalcifications using

Multiscale Hessian based Feature Extraction

Imad Zyout1, Student Member, IEEE, Ikhlas Abdel-Qader2, Senior Member, IEEE

Abstract: Segmentation of microcalcifications (MCs) significantly influences the performance of shape-based method for the diagnosis of MCs, which continues to be a challenge as it tends to have high false positive results. Texture based characterization of MCs represents a possible alternative that does not require prior segmentation of MCs and may improve the positive predictive value of automated diagnosis of MCs. This paper presents a new approach to extracting textural features, specifically spectral measures, of mammographic MCs using multiscale Hessian filtering (or equivalently second derivative of Gaussian). Extracted features were individually ranked using Fisher-score criterion, which demonstrated the superior predictive ability of the normalized entropy. A set of mammographic regions (20 malignant and 13 benign cases) from the MIAS database were used to evaluate the classification performance of the proposed spectral features. Utilizing k-nearest neighbor classifier and ROC performance measure, the proposed Hessian based extracted features produced ROC curves with performance index Az = 0.83, which demonstrated the effectiveness of the proposed characterization scheme. Index Terms-Mammographic microcalcifications, Hessian based filtering, Fisher-score, k-nearest neighbor.

I. Introduction

Morphological based feature extraction and diagnosis of clustered microcalcifications in digital mammograms demonstrated to be the most effective approach [4, 7]. However, the main challenge of this approach is the need for MCs segmentation stage as priori step to extract

various shape features of MCs. This segmenta-tion process plays a significant role in the overall performance of the diagnosis scheme in any shape (or morphological) based feature extraction and diagnosis scheme [7]. Several studies have employed textural, statistical and spectral feature extraction methods to classify mammographic MCs without the need for a segmentation stage, some of these techniques have achieved a satisfactory performance [8, 13] but their performance still behind that obtained using shape based methods.

Using normalized second derivative and an image Hessian is a standard technique for enhancement, detection and extraction of curvilinear structures such as blood vessels and blobs in medical images [2,8,10-11,15]. The basic idea behind Hessian based filtering is to use two eigenvalues and their correspond-ing eigenvectors obtained from Hessian matrixfor each pixel. Both the sign and the magnitude of the eigenvalues, that is the directional second derivatives, can be used to characterize intensity, shape, and orientation of different 2D/3D image structures [5]. For example, a bright blob like structure in a 2-D image identified by having negative and equal eigenvalues in all directions. Moreover, computing the ratio of the two eigenvalues can also distinguish between a line and blob like structures. Extension for analysis of mammographic abnormalities is limited to enhancement and detection applications [9,12]. Li et al. [9] presented a preliminary work for enhancement of MCs using Hessian based filtering. Nakayama et al. [12] computed elements of the Hessian matrix using perfect

1. Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI, imad.m.zyout@wmich.edu. 2. Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI,abdelqader@wmich.edu.

978-1-4244-6875-1/10/$26.00 ©2010 IEEE

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reconstruction filter banks and demonstrated that the proposed scheme preserved the shape of MCs and might achieve better detection of MCs.

In this study, characterization of MCs is accomplished by first performing multiscale representation of mammographic regions (included MC clusters) using multiscale Hessian based filtering. Then, a set of spectral measures such as spectral entropy and energy extracted at each scale. The performance of the extracted features is evaluated by classifying a set of MC clusters as malignant and benign using simple k-nearest neighbor (kNN) classifier and area under ROC.

The remaining sections of this paper are organiz-ed as follows: Section II briefly discusses the theoretical background of Hessian based image filtering. Our Hessian based feature extraction method is presented in Section III. Experimental results and concluding remarks evaluation are presented in Section IV and V, respectively.

II. Hessian based image filtering Characterizing of MCs in mammogram can be modeled as searching for nodular like structures in digital images. Since no prior knowledge of the sizes of MCs is available and an image may include different objects with various sizes, a multiscale filtering using Gaussian kernel is more appropriate than a fixed size filter. A basic step to construct a Hessian based filtering scheme is based on computing multiscale four directional second derivatives by convoluting a given image with derivative of Gaussian kernel. These four derivatives are used to form Hessian matrix and compute two eigenvalues for each image pixel. Various curvilinear image structures can be filtered by analyzing the sign and magnitude of the directional second derivatives or equivalently the eigenvalues obtained from solving Hessian matrix at each image pixel [5] as given in Table 1.

Table 1: Analysis of the Hessian eigenvalues 1λ and 2λ

Eigenvalue 2-D image structure

1λ >0 and 2λ >0 Dark , nodular

1λ > 0 or 2λ >0 Dark ,linear

1λ <0 and 2λ <0 Bright , nodular

1λ < 0 or 2λ < 0 Bright ,linear

Several studies [5,9,15] have constructed Hessian based filter using two measures. The first measure is structureness [15] defined as function of the magnitude of two eigenvalues and expressed as follows

2121 ),( λλλλ +=C (1)

Since a bright nodular image components usually have a none-zero and negative 2λ and

2λ , one can use a second measure defined as the ratio of the two eigenvalues, which expected to be close to 1, to enhance nodular mammographic features and suppress the linear structures as follows

))/(exp(),(),( 2minmax2121 λλβλληλλ −=R (2)

where ),( 21 λλη is an indicator function, which is unity if both 2λ and 2λ are negative and zero otherwise. β is a constant that can be set empirically.

Using both structureness and ratio measures, an over all response of the Hessian filter at given scale can be defined as a product of two terms

),(),( 2121 λλλλ CRH = (3)

An example of filtering mammographic MCs using Hessian filter is illustrated in Figure 1.

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III. Diagnosis of MCs using Hessian based feature extraction

This study mainly focuses on investigating whether a Hessian based feature extraction can discriminate effectively between benign and malignant MCs or not. Hence, we adopt relatively simple classifier such as kNN instead of more sophisticated classifiers such as support vector machines. The proposed diagnosis methodology is illustrated in Figure 2.

A. Spectral feature extraction

Multiscale representation and transform domain methods using multi-wavelet transforms [13], wavelet packet [13], and discrete cosine transform (DCT) [6] were employed to accomplish spectral feature extraction of MCs clusters by measuring two spectral quantities, namely, the normalized energy and entropy from each subband of the multiscale representation. These studies also accomplished multiscale feature extraction based methods by computing normalized energy and entropy in spectral domain within each scale [6, 13]. Additional two spectral measures extracted in this paper are the total response of Hessian filter defined as pixel based summation and the standard deviation of two-eigenvalue ratio at each scale.

Fig.2. Description of Hessian based MCs diagnosis

B. Univariate feature ranking

Extracted spectral features are evaluated using Fisher criterion or F-score technique [3]. F-score is a univariate feature selection approach, which individually evaluates the prediction performance (i.e. discriminating between two class labels) of each single feature represented by a real variable ix . Ranking criterion ( iF ) using Fisher-score is computed as follows

��==

−−

+−−

−+−=

BM n

k

Bi

Bki

B

n

k

Mi

Mki

M

iB

iiM

ii

xxn

xxn

xxxxF

1

2,

1

2,

22

)(1

1)(

11

)()( (4)

where Mix , B

ix ,and ix are the average of the feature ix of the malignant, benign, and whole samples, respectively. Also, Mn , Bn are the number of samples from malignant and benign classes.

IV. Experimental results

A. Mammogram data

The proposed feature extraction scheme has been evaluated using 33 MCs clusters, of which 20 clusters are malignant and 13 are

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benign, extracted from 23 mammograms from Mini-database [14]. Original MIAS database includes 25 localized MC cluster. In this study, additional 8 malignant clusters, confirmed by an expert radiologist, were extracted from 3 mammograms known to have spread and several islands of MCs.

B. Parameters and feature selection

In image domain, individual MCs are tiny deposits of calcium, which can be modeled as small-scale bright blobs contribute more to the highpass frequency subbands of the spectral domain representation. Hence, analysis using small-scale Gaussian kernel is expected to be more suitable and produces stronger second derivative response and largest magnitude of the eigenvalue. We have empirically selected a set of three Gaussian kernels with ( 25.0=σ , 0.5, and 0.75) and size in pixels of 3×3, 5×5, and 7×7, respectively. These three kernels were applied to all mammographic regions to produce multiscale Hessian based filtering and used to extract different spectral measures.

We have also examined the size of the mammographic region to characterize MC cluster by first selecting a region of size 128 x 128 pixels, contained a true MC cluster in its center. In the second experiment, we used a region best fits each MC cluster for feature extraction. Our results indicated that using a region best fits each cluster is more appropriate and produces more discriminative features.

Using the computed spectral measures obtained from three scales representing each region, we constructed a feature vector representing each MC cluster complemented with the addition of the first statistical moment of the measured spectral quantities leading to a feature vector of 4 features. Extracted features were first evaluated

Individually using Fisher-score method described in (4). Then, simple feature search method was used to find the best feature subset.

C. Performance evaluation The prediction power of the proposed Hessian based feature extraction was evaluated using kNN classifier and leave-one-out (LOO) cross-validation method to classify MC clusters into malignant and benign cases. LOO cross-validation simply trains a classifier using all data samples excluding one sample that kept for a testing purpose, which is more appropriate for a small data set like this study [7].

The small size of the feature set extracted in this paper enables us to search for an optimal subset by evaluating all possible feature subsets. Our experiments indicated that best classification accuracy of 85%, with 2 false negative (FN) and 3 false positive (FP) results, was obtained using three feature subsets. First feature subset includes only one feature represented by mean of the normalize-ed entropy, the second subset included both mean of Hessian filter response and mean normalized entropy. In addition to features included in second feature subset, the third subset also includes the mean of the normalized energy.

Classification performance is evaluated using evaluation metrics such as specificity (false positive rate), sensitivity (true positive rate), classification’s accuracy, and area under receiver operating characteristic (ROC) curve. Experimental ROC curves represented the discrimination performance of each feature subset are shown in Figure 3. We can state that the textural based MCS classification method using a subset of three features has achieved a classification performance of

83.0=Az at most.

5

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

N=3,Az=0.83

N=2, Az=0.81

N=1,Az=0.73

Fig. 3: ROC analysis of the extracted features

* N represents the size of feature subset

V. Concluding remarks

In this paper, we proposed a spectral feature extraction method using multiscale Hessian based filtering to characterize each MC cluster as a malignant or a benign cluster. The proposed feature extraction scheme was tested using 33 MC clusters, extracted from MIAS database. Extracted features were evaluated using kNN classifier and ROC curve. Experimental results indicated that mammographic MCs could be characterized by analyzing the image Hessian that produced a reasonable performance when compared with other textural based diagnosis of MCs. However, empirical evidence of the effectiveness of the proposed approach needs further investigation using a larger database.

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