This research presents supervised classification algorithm based on information fusion for detecting masses in mammography images. Discrete wavelet transform can preserve information regarding both high and low frequencies and offer great discriminatory power between areas with strong similarities. This motivates us to use this type of features to improve image segmentation. So, in the first stage, the suggested technique used this feature extraction approach on mammography images in order to obtain additional information. After that in the second stage, estimated feature vector of each pixel is sent to a neural network classifier for initial-labeling. Then, in the third stage of the suggested technique, Bayes fusion method is used to combine the scores, within a sliding window, obtained by the neural network for each pixel. The performance of the proposed segmentation algorithm was evaluated on mammography images from Mammography Image Analysis Society (MIAS) dataset. The achieved classification results by the proposed fusion system leads to higher classification precision in detecting masses on mammography images, which are one of breast cancer signs.
advantages and disadvantages of the methods and algorithms that have been developed by previous researchers, in this paper we attempt to use one type of feature extraction techniques with the purpose of detecting masses on mammography images. This feature is a structural feature obtained by using the wavelet transform coefficients. For the pre-processing process, which finds to improve image quality such as contrast enhancement to obtain a better image visualization [1], there are different types of filtering techniques. In this study the contrast of the mammogram images was regulated by histogram adjustment which improves the contrast of the output image by spreading out the intensity values.
So, in the first stage of our work, we have used the discrete wavelet transform as feature extraction strategy in order to get more information that enables the classifiers to discriminate between the different areas in the mammography image. In the second stage, an appropriate classification algorithm is applied using the set of extracted features obtained from the previous stage. The Backpropagation Artificial Neural Networks classifier is chosen among the most well-known classifiers, it was initiated in [19-20]. The estimated feature vector of each pixel is sent to the neural networks classifier for initial-labeling.
A sliding window, whose class is assigned to its central pixel, is used. However, this central pixel belongs to other window neighbors that may be classified into other classes. Consequently, in the third stage, in order to obtain a more precise segmentation result, a Bayes fusion method is used for each pixel to combine the scores results of several windows that contain this central pixel. The proposed segmentation algorithm performance was verified on mammography images from MIAS dataset [21]. The obtained results lead to higher classification precision in detecting masses which are one of breast cancer signs.
The rest of this manuscript is divided in three sections. The first one describes the background theory of several techniques used in this paper. Then, section 2 is dedicated to give in details the suggested segmentation process and the reached performance of the proposed fusion technique. Finally, in section 3, we conclude and recommend possibilities for future work.
Since the work of Grossman and Morlet [22], the wavelets transform has appeared as a powerful tool to solve problems in different application. The wavelets transform decomposes the input signal into a series of wavelet functions ( ) derived from a mother function ( ) given by dilatation (factor a) and translation (factor b) operations. Figure1 illustrates some examples of wavelets that are generally used in image processing [23].
a b
c
The most important advantage of wavelets as compared to other frequency methods, as Fourier transform, is that it offers both frequency and spatial locality [25]. In 1989, Mallat [26] suggested a multi-resolution decomposition algorithm based on wavelets transform. The algorithm decomposes an input image into a set of detail images and an approximation image using a filter bank comprising a high pass filter (HP) and a low pass filter (LP). At each decomposition level the size of the transformed images is reduced by a factor of two [24]. The discrete wavelet transform of a 2-D image can be obtained by performing the filtering consecutively along horizontal and vertical directions (separable filter bank) [27]. Four images are then created at each level. Figure 2 shows an example of decomposition of the image on one level.
In Figure 2, the DWT decomposes the image into 4 orthogonal sub-band: low-low (LL), high low (HL), low high (LH), and high-high (HH) consisting of approximation, horizontal, vertical, and diagonal information. The approximations image is the smoothed version of the original image and it contains global information that is similar to the original image with the number of rows and the number of columns being half of the original image. Horizontal, vertical, and diagonal contain the detail and represent the fluctuations of the pixel intensity in horizontal, vertical, and diagonal directions and they have low-intensity areas, whereas areas with high intensity are only found on the edges of the image object.
The values of transformed coefficients in detail and approximation images (sub-band images) represent the necessary features that capture useful discrimination information for masses segmentation [28].
1. Wavelet’s Choice: In our research, we have used a second order biorthogonal spline wavelet. This wavelet is used for masses analysis due to its excellent location in the frequency and spatial domains and its sensitivity to local singularity and correlation of the image [24].
2. Indices’ Calculation: One of the most used indices for characterizing the masses in the spatiofrequency plane is the measurement of energy. Because the transformed images have different frequencies, scales and orientations, the energy index is a local measure of the wavelet coefficient distribution according to the scale, the orientation and the frequency. It has been used successfully for segmentation and classification of masses [24].
The expression of energy is given by [24]: ∑ ( ) ( )
The second index used in conjunction with energy is the measurement of the local mean of the wavelet coefficients given by [24]: ∑| ( )| ( ) where N denotes the number of pixels, designated by the indices ( ), and enclosed in the area R.
The calculation of these indices was done on a sliding window W. The local mean and the energy on the sliding window are calculated from the resultant sub-band images. So the feature vector of each window is made of eight parameters V= [ELL, ELH, EHL, EHH, MLL, MLH, MHL, MHH], as seen in Figure 3.
Several tests were carried out on a series of window sizes going from 5×5 to 25×25. The highest good classification rate was reached for a window of dimension 11×11. The produced features vector of each window is used as an input to the neural network classifier for a primary labeling, and the score for the window delivered by the neural network is assigned to its mid pixel. ( ) ( ) ⁄ ), .
( )
One of the first techniques used to combine images with decision-making was the Bayes fusion. This model was chosen by several authors because it has a very well-defined context with known mathematical properties [29].
Consider , following conditions: , ...
to be a collection of mutually exclusive hypotheses. They satisfy the where represents the hypothesis' space (that is to say, the set of fused image classes). The hypotheses are mutually exclusive and form a partition of .
Consider and to be two characteristic primitives from two different images, representing the same object, or the same hypothesis , the Bayesian theory computes the likelihood of getting the hypothesis from the two measures and through Bayes rule [30]: ) ( )
( ∑ ( ) ( ⁄ )
⁄ ) {
( where ( ⁄ )represents the joint probability of having both measures ( , ) once the hypothesis is realized, and ( ) is the prior probability of the hypothesis , which shows the possibility of occurrences of the hypothesis in the general case [30].
If and are two independent random variables, the conditional probability (
also called the likelihood function, becomes a separable function of the two variables
and
(
⁄ )
(
)
(
)
Hence equation (
( ∑ ( ) ( ) ) ( ( ) )
Consequently, in order to determine the posterior probabilities ( ), we first need to compute the prior probabilities ( ) for all hypotheses , i going from 1 to N, and the likelihood functions ( ) for each image primitive and for each hypothesis. To model the likelihood functions, we work under the Gaussian hypothesis [30]: ( ) √ ( ( ̅̅̅) ) ( ) ( ) where ̅̅̅ denotes the mean and
is the standard deviation of the Gaussian expression.
When the combination of the probabilities realized by equation (
Data obtained from the mammographic images is often, noisy, incomplete, inconsistent, and have low contrast. Therefore, pre-processing is needed in the medical image processing to improve image quality, remove unwanted noise, preserves the edges within an image, and make the feature extraction phase more reliable [1].
There are different types of filtering techniques in the pre-processing. So, in the first step of our work, the contrast of the mammogram images was regulated by histogram adjustment which increases and improves the contrast of the output image by spreading out the intensity values.
After that in the second step, the proposed segmentation method uses Wavelets transform as feature extraction strategy on mammography images in order to get more information in this data set. The parameters of the feature set were selected as mentioned in the previous sections. After a proper features' extraction, each estimated feature vector of each pixel is sent to the neural networks classifier for primary labeling. The MLP neural networks classifier is chosen among the most well-known classifiers, it was initiated in [19], [20]. For the choice of the hidden layers' number and the number of neurons in each layer, we choose the rule proposed by [34] since there is no general rule other than rules of thumb as proposed in [35], [36]. The size of the hidden layer is 75% of the input layer.
For the transfer functions, we retain the most used in the literature, namely the logistic function and the hyperbolic tangent function. The gradient backpropagation algorithm is used for the training of neural networks.
Using a sliding window, the class for this window is assigned to its central pixel. However, this central pixel belongs to other window neighbors that may be classified into other classes. Consequently, in order to achieve a more precise segmentation result, for each pixel a Bayes fusion method is used to combine the scores results of several windows that contain this central pixel:
Consider to be the segmented image comprising the scores neural networks classifier): with i =1…. n,
j =1…. m, where n and m represent the sizes of the mammography image. of each pixel (the output of the
We perused the images by using a sliding window of size , so that every pixel is surrounded by pixels. Each central pixel of window with score belongs to the window in the surrounding windows before the classification process. However, each central pixel of the window , with produced different scores .
For example, in the case of pixel with score and by eight pixels, that are the center of the eight windows which pixel , the central pixel is surrounded belonged to, (see Figure 4).
From the above example, we joined the scores produced by the current block and its eight neighboring ones for the wavelet features: {S33 ,S32 ,S34 ,S23 ,S24 , S22 , S42 , S44 , S43 , S33 , S32 , S34 , S23 , S24 , S22 , S42 ,S44 , S43} (see Figure 5). In this work, a sliding window of size 9×9 is used, so the central pixel is surrounded by 80 pixels, that are the center of the 80 windows which pixel P5,5 belonged to.
The essential fusion algorithm steps are summarized as follows: Step1: Pre-processing of the mammography image.
Step2: Feature extraction via DWT.
Neuronal classification of the estimated feature vector. We obtain:
Scores1: for DWT. while
the recognition rate is changed for each pixel do
Bayesian fusion of Score1 and the neighboring scores. end Calculate the recognition rate.
End
The performance of the proposed algorithm for segmenting mammography images is assessed using many images from the MIAS (Mammographic Image Analysis Society) database [21] containing 322 mammograms sized 1024 x 1024 pixels. The images are arranged in pairs: those with even-numbers correspond to left MLO (medio-lateral oblique Mammograms) and those with oddnumbers are right MLO.
For the learning phase, we have used image mdb028 of the MIAS database, and to test our algorithm we have taken randomly the following MIAS images: mdb025 and mdb132, for Well-defined/circumscribed masses (CIRC) [32]. mdb184, for Spiculated masses (SPIC) [32]. mdb134, mdb271 and mdb274, for Other, ill-defined masses (MISC) [32]. mdb136 and mdb310, for Normal breast (NORM) [32].
Figure 6 illustrates the obtained results (detected masses are displayed in cyan color) compared to expert decision (masses centers coordinates and radiuses shown in blue color). Table 1 demonstrates the Jaccard index that was achieved by utilizing this fusion algorithm.
So, as shown in figure 6 and table 1, the results obtained on these taken images from MIAS database are promising and they show the effectiveness of our fusion algorithm for the masses segmentation on mammography images.
We can see clearly that our algorithm gives a good result whatever the kind of class of abnormality present, CIRC, SPIC, … etc. And also, we don’t ahlasveedeatencytionf in the cases of normal breast. So, the proposed method has the potential to identify the presence of any masses in the mammogram image. (a) mdb184
(b) mdb184 (a) mdb132
(b) mdb132 (a) mdb274
(b) mdb274
Figure 7 illustrates a comparison of our proposed approach, on MIAS images mdb184 and mdb028, with another unsupervised techniques proposed by Kanta Maitra et al [33], based on Divide and conquer algorithm, and Boulehmi Hela et al [2], based on Generalized Gaussian Density.
As seen in figure 7, the proposed approach has the advantage of being simple and precise; we have exactly detected the shape of the present masses.
The outcomes of our contribution demonstrate that it is possible to reach excellent fusion performance by neatly selecting the best fusion method. We also note that by our fusion method, the segmentation results of the mammography images are much improved as compared to other works.
In this article, we have presented and discussed a new approach for the segmentation of mammography images based totally on information fusion. We started by extracting the features using the wavelet transform. After that, the estimated vector of features for every pixel was sent to the neural network classifier for primary labeling. Next, a new fusion model for improving decisionmaking is used, it consists of combining the scores of each pixel within a sliding window. The proposed fusion algorithm was tested on mammography images from MIAS dataset.
This research has shown that this method is very effective for the automatic detection of abnormalities in digital mammogram.
As perspective we will complete the masses detection system by classifying abnormal mammographic images into benign and malignant.
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