- Research
- Open Access

# Microcalcification detection in full-field digital mammograms with PFCM clustering and weighted SVM-based method

- Xiaoming Liu
^{1, 2}Email author, - Ming Mei
^{1}, - Jun Liu
^{1, 2}and - Wei Hu
^{1, 2}

**2015**:73

https://doi.org/10.1186/s13634-015-0249-3

© Liu et al. 2015

**Received:**1 March 2015**Accepted:**13 July 2015**Published:**12 August 2015

## Abstract

Clustered microcalcifications (MCs) in mammograms are an important early sign of breast cancer in women. Their accurate detection is important in computer-aided detection (CADe). In this paper, we integrated the possibilistic fuzzy c-means (PFCM) clustering algorithm and weighted support vector machine (WSVM) for the detection of MC clusters in full-field digital mammograms (FFDM). For each image, suspicious MC regions are extracted with region growing and active contour segmentation. Then geometry and texture features are extracted for each suspicious MC, a mutual information-based supervised criterion is used to select important features, and PFCM is applied to cluster the samples into two clusters. Weights of the samples are calculated based on possibilities and typicality values from the PFCM, and the ground truth labels. A weighted nonlinear SVM is trained. During the test process, when an unknown image is presented, suspicious regions are located with the segmentation step, selected features are extracted, and the suspicious MC regions are classified as containing MC or not by the trained weighted nonlinear SVM. Finally, the MC regions are analyzed with spatial information to locate MC clusters. The proposed method is evaluated using a database of 410 clinical mammograms and compared with a standard unweighted support vector machine (SVM) classifier. The detection performance is evaluated using response receiver operating (ROC) curves and free-response receiver operating characteristic (FROC) curves. The proposed method obtained an area under the ROC curve of 0.8676, while the standard SVM obtained an area of 0.8268 for MC detection. For MC cluster detection, the proposed method obtained a high sensitivity of 92 % with a false-positive rate of 2.3 clusters/image, and it is also better than standard SVM with 4.7 false-positive clusters/image at the same sensitivity.

## Keywords

- Microcalcification detection
- Microcalcification cluster
- Computer-aided diagnosis
- Possibilistic fuzzy c-means
- Support vector machine

## 1 Introduction

Breast cancer is the most frequent form of cancer in women and is also the leading cause of mortality in women each year. The World Health Organization estimated that 521,907 women worldwide died in 2012 due to breast cancer [1]. Studies have indicated that early detection and treatment improve the survival chances of the patients. In order to detect it in its early stage, many countries have established screening programs. Among all the diagnostic methods currently available for detection of breast cancer, mammography is regarded as the only reliable and practical method capable of detecting breast cancer in its early stage [2].

The screening programs generate large volumes of mammograms to be analyzed. However, due to the complexity of the breast structure, low disease prevalence (approximately 0.5 % [3]), and radiologist fatigue, abnormalities are often ignored. It is reported that about 10–25 % abnormal cases shown in mammography have been wrongly ignored by radiologists [4]. Double reading can improve the detection rate, but it is too expensive and time consuming. Thus, computer-aided cancer detection technologies have been investigated. The adoption of a computer-aided detection (CAD) system could reduce the experts’ workload and can improve the early cancer detection rate [5].

Computer-aided detection of microcalcification clusters has been investigated using many different techniques [5, 8]. Roughly speaking, the methods can be classified as traditional enhancement-based method, multiscale analysis, and classifier-based methods. Kim et al. [9] enhanced the mammographic images based on the first derivative (such as Sobel operators and compass operators) and the local statistics.

Laine et al. [10] investigated wavelet multiresolution for mammography contrast enhancement. Three overcomplete multiresolution representations were investigated. Contrast enhancement was applied for each level separately, and edge features were extracted in each level and decomposition coefficients were modified based on edge features. Final images were reconstructed with modified coefficients. Improved contrast for irregular structures such as microcalcification was observed on their experiments. In our previous work [11], a new wavelet-based image enhanced method is proposed. A multiscale measure which matches the human vision system is proposed and used to modify wavelet coefficients. The degree of enhancement can be adjusted by manipulating a single parameter. Ramirez-Cobo et al. [12] used 2D wavelet-based multifractal spectrum for malignant and normal classification.

Several machine learning methods have been used for microcalcification detection. El-Naqa et al. [13] investigated the support vector machine (SVM) classifier for MC cluster detection, and a successive enhancement learning scheme was proposed to improve the performance. On a set of 76 mammogram images containing 1120 MCs, their method obtained a sensitivity of 94 % with an error rate of one false-positive cluster per image. Ge et al. [14] proposed a system to identify microcalcification clusters on full-field digital mammograms (FFDMs) with convolution neural network. The system includes six stages: preprocessing, image enhancement with box-rim filter, segmentation of microcalcification candidates, false-positive (FP) reduction for individual microcalcifications with convolution neural network, region clustering, and FP reduction for clustered microcalcifications. On a dataset of 96 cases with 192 images, they obtained a cluster-based sensitivity of 70, 80, and 90 % at 0.12, 0.61, and 1.49 FPs/image, respectively. Tiedeu et al. [15] detected microcalcifications by integrating image enhancement and the threshold-based segmentation method. Several features were extracted for each region from the enhanced image, and by embedding feature clustering in the segmentation, their method obtained much less false positives than other methods. Experiments were performed on a dataset of 66 images containing 59 MC clusters and 683 MCs, and high sensitivity (100 %) was obtained, balanced by a lower specificity (87.77 %). In the work of Oliver et al. [16], the individual microcalcification detection is based on local image features of the microcalcifications from a bank of filters. A pixel-based boosting classifier is then trained, and salient features were selected. Clusters are found by inspecting the local neighborhood of each microcalcification. Malar et al. [17] utilized wavelet-based texture features and the extreme learning machine (ELM) for microcalcification detection and classification. One hundred and twenty regions of interest (ROIs; with 32 × 32 pixels) extracted from the MIAS [18] dataset are used for the experiments. They obtained a classification accuracy of 94 %.

Most of the previous microcalcification detection works have been performed on film-scanned mammograms. With the development of the imaging technique, FFDMs have been widely deployed, and they have better image quality than film-scanned images. We will concentrate on FFDM images.

In this paper, we proposed a novel weighted support vector machine-based microcalcification cluster detection method for FFDM images. Inspired by the work in [19], the possibilistic fuzzy c-means (PFCM) clustering algorithm is used to derive weights for the samples. Several features are extracted and used to train SVM. The proposed method is evaluated on a publically available FFDM dataset [20], consisting of 410 images.

The contributions of the paper are as follows: (1) The weighted SVM is for the first time introduced for MC and MC cluster detection. (2) A novel weighting scheme based on PFCM clustering is introduced to assign weights to samples; unlike the traditional transductive learning-based “pseudo training dataset generating” method, this integration is more simple and principled. (3) A mutual information criterion-based feature selection is investigated for the MC detection in FFDM, and until now, only very few MC detection works have been done on the FFDM dataset.

The rest of the paper is organized as follows: Section 2 introduces the related PFCM technique used, and our method is introduced in Section 3. Experimental results are shown in Section 4. The conclusions and discussions are provided in Section 5.

## 2 Brief introduction of PFCM clustering

The PFCM is a recently developed clustering algorithm, which has the advantages of the fuzzy c-means (FCM) as well as the possibilistic c-means (PCM) [21] algorithm. Outlier sensitivity is one shortcoming of the FCM clustering. The PCM clustering algorithm [21] can overcome the shortcoming, and it can identify the degree of typicality that a sample has with respect to the group to which it belongs. However, sometimes the prototypes of PCM clusters can coincide, and the PCM will fail in these cases. Pal et al. proposed a hybridized PFCM clustering [22] to cope with the above shortcomings.

*X*= {

*x*

_{1},

*x*

_{2}, …,

*x*

_{ n }} ∈

*R*

^{ p }, a c-partition of

*X*is a set of (

*cn*) values {

*u*

_{ ik }} that can be written as a (

*c*×

*n*) matrix

*U*= [

*u*

_{ ik }],

*i*= 1, …,

*c*,

*k*= 1, …,

*n*. The possibilistic and fuzzy c-partitions of

*X*are defined as [22]

with constraints \( {\displaystyle \sum_{i=1}^c{u}_{ik}=1\ \forall k;\ 0\le {u}_{ik},{t}_{ik}\le 1} \), and the constants *a* > 0, *b* > 0, *m* > 1, and *η* > 1. *v*
_{
i
} ∈ *R*
^{
p
} is the center of the *i* ‐ th cluster, and *x*
_{
k
} is the *k* ‐ th data sample. The values of *a* and *b* represent the relative importance of membership and typicality values in the computation of the prototypes. The parameters *m* and *η* represent the absolute weight of the membership value and typicality value, respectively. One can set *b* > *a* and *m* > *η* to reduce the sensitivity to outliers.

The probability (memberships, or relative typicalities, used in FCM) and possibilities (or absolute typicalities, used in PCM) are different. The membership *u*
_{
ik
} for data *x*
_{
k
} belongs to a class *c*
_{
i
} which is a function of *x*
_{
k
} and all *c* centroids {*v*
_{1}, …, *v*
_{
k
}}, while the typicality value is a function of *x*
_{
k
} and the center *v*
_{
i
} alone, as shown below. For example, in a two-class clustering problem, for a noise data point, which is far away from both clusters, the membership to both cluster *u*
_{
ik
} will be about 0.5 (required by \( {\displaystyle \sum_{i=1}^2{u}_{ik}=1} \)), while the typicality values to both cluster *t*
_{
ik
} will be near zero. For another point which lies between the two clusters (not far away from the centers), the *u*
_{
ik
} will also be about 0.5, but the typicality values *t*
_{
ik
} will be a positive number not approaching zero. The probability and typicality can convey different information about the dataset.

*D*

_{ ikA }= ‖

*x*

_{ k }−

*v*

_{ i }‖ > 0, for every

*i*,

*k*,

*m*> 1,

*η*> 1, and if

*X*contains at least

*c*distinct data points, then (

*U*,

*T*,

*V*) ∈

*M*

_{ fcm }×

*M*

_{ pcm }×

*ℜ*

^{ c × n }may minimize

*J*

_{pfcm}only if

The iterative process of the algorithm is presented in [22].

## 3 Proposed method

### 3.1 Level set-based MC segmentation

*f*(

*x*,

*y*), the edge of a microcalcification to be segmented is a closed contour around a known pixel (

*x*

_{0},

*y*

_{0}), which is the location of the local highest grayscale value pixel. For each pixel, a slope value

*s*(

*x*,

*y*) referred to

*f*(

*x*

_{0},

*y*

_{0}) is defined as [23]

*d*(

*x*

_{0},

*y*

_{0},

*x*,

*y*) is the Euclidean distance between the local maximum pixel (

*x*

_{0},

*y*

_{0}) and pixel (

*x*,

*y*). A pixel is considered on the edge if

*s*(

*x*,

*y*) is maximal along a line segment originating from (

*x*

_{0},

*y*

_{0}). The length of the considered line segment is chosen as 15 (approximately 1 mm as the spatial resolution in INbreast is 70 μm per pixel). The line search is applied in 16 equally spaced directions originating from the seed pixel. Thus, with each local maximal, 16 edge points are located. Note that the segmentation step will encounter some difficulties for small MC, and the approach used in [24] is adopted to overcome the problem. That is, the segmentation step is performed on the upscaled region containing a possible MC.

For a given local maximal with 16 edge points, a circle is fitted to the points. And the circle is used as the initialization of the level set-based segmentation. Level set originates from the active contour model (snake) [25]. Snake can be edge based or region based.

### 3.2 Feature extraction from ROI

After segmenting suspicious MC from the ROI, we compute a set of geometry and texture features related to the boundary and the region. Several features used here have been used in our previous work [7] for mass diagnosis.

#### 3.2.1 Geometry features

*μ*

_{NRL},

*σ*

_{NRL},

*E*

_{NRL},

*AR*

_{NRL}, GF8-GF11) [29], and relative gradient orientation (RGO)-based features (

*μ*

_{RGO},

*σ*

_{RGO},

*E*

_{RGO}, GF12-GF14) [30]. The area is computed by the pixels in the segmented region, and the perimeter is computed by the number of pixels on the boundary.

*C*is a measure of contour complexity versus the enclosed area and is defined as \( C=1-\frac{4\pi \times \left(\mathrm{area}\right)}{{\left(\mathrm{perimeter}\right)}^2} \). For details about geometry features, please see our previous work [7] and the references therein. The 14 geometry features are listed in Table 1.

Geometry features extracted from a MC boundary

Feature index | Feature | Note |
---|---|---|

GF1 | Area of the MC | Number of pixels in the segmented region |

GF2 | Perimeter of the MC | Number of pixels on the border of the MC |

GF3 | Compactness | Calculated with \( C=1-\frac{4\pi \times \left(\mathrm{area}\right)}{{\left(\mathrm{perimeter}\right)}^2} \) |

GF4 | NDM2 | Normalized distance-based moments |

GF5 | NDM3 | |

GF6 | NDM4 | |

GF7 | Fourier feature | Fourier feature calculated taking boundary pixel as a complex number |

GF8 | NRL mean | Statistical values from normalized radial length |

GF9 | NRL standard deviation | |

GF10 | NRL entropy | |

GF11 | NRL area ratio | |

GF12 | RGO mean | Statistical values from relative gradient orientation, measure spiculation, and defined as the acute angle |

GF13 | RGO standard deviation | |

GF14 | RGO entropy |

#### 3.2.2 Texture features

Besides the shape information of a MC contour, the texture information of the region surrounding the suspicious MC boundary also contains important information for MC analysis [8]. Thus, texture features are also used for MC detection. For each suspected MC, a patch with size 16 × 16 is extracted [14, 31], whose center is determined by the center of the suspected MC. Besides the average grayscale in the segmented region in a block (denoted as TF1, where TF means texture feature) (16 × 16 window) and the grayscale difference between the average suspicious region and background (TF2) (the window without taking into account the segmented region), the gray level co-occurrence matrix (GLCM) [32, 33] and wavelet texture features are also extracted.

GLCM has been widely used in mammographic microcalcifications [8] and masses [34]. We use several GLCM features, including autocorrelation (TF3), contrast (TF4), correlation (TF5), cluster prominence (TF6), cluster shade (TF7), energy (TF8), entropy (TF9), homogeneity (TF10), maximum probability (TF11), sum of squares (TF12), sum average (TF13), sum variance (TF14), sum entropy (TF15), difference variance (TF16), difference entropy (TF17), information measure of correlation (TF18, TF19), inverse difference normalized (TF20), and inverse difference moment normalized (TF21).

*N*×

*N*(

*N*= 16) sub-image, normalized energy and entropy are computed as follows [24]:

*x*

_{ ij }is the

*ij*-th pixel value of the sub-images, and

Twelve sub-images are generated for each ROI with a three-level wavelet decomposition, and as the first-level decomposition consists of mostly noise, features are extracted from the levels 2 and 3 sub-bands. Thus, 16 wavelet features are extracted for each ROI and are denoted with TF22-TF23 from the energy and entropy feature of the level 2 approximation coefficient matrix, and TF24-TF25, TF26-TF27, and TF28-TF29 from horizontal, vertical, and diagonal coefficient matrices, respectively. TF30-TF37 are defined similarly for level 3 decomposition.

### 3.3 Feature selection based on mutual information

With the above procedure, a lot of features are extracted to represent the possible MC. However, not every feature is useful to discriminate non-MC and MC. Each feature used here has its physical meaning, and it is important to preserve the intelligibility of the result; several methods, such as principal component analysis (PCA) and linear discriminant analysis (LDA) [36], are not applicable.

Feature selection methods can be categorized into two types: filter methods and wrapper methods [37]. The performance of wrapper methods is dependent on the specific classifiers, while the performance of filter methods is usually independent of the classifiers. In this paper, we concentrate on the mutual information (MI)-based filter feature selection method.

Positive (MC) and negative (non-MC) samples are needed to select features. The positive samples are obtained with the annotation in the image database, and the negative samples are those ROIs segmented by active contour but do not contain MC. In this way, the selection of non-MC samples is tuned with the whole detection procedure. It is an advantage compared with other commonly used random sample methods, as used in [13].

*X*and

*Y*is defined as

*p*(

*x*,

*y*) is the joint probability density function of continual random variables, and

*p*(

*x*) and

*p*(

*y*) are the marginal probability density functions. MI can also be defined with Shannon entropy

where *H*(*x*) = − ∫*p*(*x*)log *p*(*x*)*dx*, *H*(*y*|*x*) = − ∬*p*(*x*, *y*)log *p*(*y*|*x*)*dxdy*, and *H*(*x*, *y*) = − ∬*p*(*x*, *y*)log *p*(*x*, *y*)*dxdy* are the Shannon entropies. An explanation of MI for feature selection is as follows: Let *Y* be a variable representing the class label (e.g., MC or non-MC) and *X* a variable denoting a feature. The entropy *H*(*Y*) is known to be a measure of the amount of uncertainty about *Y*, while *H*(*Y*|*X*) is the amount of uncertainty left in *Y* when knowing an observation *X*. Therefore, MI can be seen as the amount of information that the measure at *X* has about the class label *Y*. Thus, MI measures the capability of this feature to predict the class label.

*k*single features are usually not the best

*k*combined features, since there may exist redundancy between these features. The minimum redundancy maximum relevance (mRMR) method [38] considered this problem, and it selects features that have the highest relevance with the target class and are also minimally redundant. Denote the

*i*‐ th feature as

*f*

_{ i }and the class variable as

*c*. The maximum relevance criterion selects the top

*m*features in the descent order of

*I*(

*f*

_{ i },

*c*), i.e., the best

*m*individual features correlated to the class labels:

where *S* is the set of selected features, and |*S*| is the cardinality of the set.

*m*best separated features are not the best combined

*m*features. The minimum redundancy criteria are introduced to remove the redundancy among features:

*m*‐ th feature after obtaining the

*m*− 1 features

*S*

_{ m − 1}, by solving the following optimization problem [38]:

### 3.4 Clustering with PFCM and weight samples

With the obtained MC and non-MC samples, using the features selected by the mRMR criterion, PFCM is applied to cluster the samples. Each sample with selected feature values is regarded as a data point. As shown above, for each sample after PFCM clustering, it has a probability and a typicality value.

Let *y*
_{
i
} denote the label of sample *i*, and let *y*
_{
i
} ∈ {+1, − 1} denote the class variable (MC or non-MC) which we can obtain by the doctor’s manual annotation. Let *MU*
_{
i
} denote the probability of sample *i* belonging to calcification, let \( M{T}_i^{+1} \) denote the typicality value of sample *i* belonging to MC, and let \( M{T}_i^{-1} \) denote the typicality value of it belonging to non-MC. *MU*
_{
i
}, \( M{T}_i^{+1} \), and \( M{T}_i^{-1} \) can be obtained by PFCM clustering, and their value ranges are between 0 and 1.

*W*1

_{ i }as

If a sample is MC (*y*
_{
i
} = + 1), we can simplify it to *W*1_{
i
} = *MU*
_{
i
}, and if it is non-MC (*y*
_{
i
} = − 1), *W*1_{
i
} can be simplified to be 1 − *MU*
_{
i
}. In this way, if a sample is MC and the possibility value of it belongs to MC obtained by PFCM is high, the weight *W*1_{
i
} is high; otherwise, the weight is low.

For a typical sample belonging to MC or non-MC, its weight *W*2_{
i
} is high. For example, for a typical MC sample *x*
_{
i
}, the first term in *W*2_{
i
} approaches 1, since \( {y}_i=1,M{T}_i^1\approx 1,M{T}_i^{-1}\to 0 \). For a typical non-MC, *W*2_{
i
} is also large due to the second term, while *W*2_{
i
} is small for a noise point, since in this case, both \( M{T}_i^{+1} \) and \( M{T}_i^{-1} \) approach 0.

*i*we defined is

### 3.5 Weighted SVM-based classification

Given a set of vectors (*x*
_{1}, …, *x*
_{
n
}) and their corresponding labels (*y*
_{1}, …, *y*
_{
n
}) with *y*
_{
i
} ∈ {+1, − 1}, the SVM classifier defines a hyperplane (*w*, *b*) in kernel space that separates the training data by a maximal margin.

For the weighted SVM, each sample consists of a data vector *x*
_{
i
}, a label *y*
_{
i
} as in standard SVM; besides, a sample also contains a confidence value *v*
_{
i
}. Define the effective weighted functional margin of weighted sample (*x*
_{
i
}, *y*
_{
i
}, *v*
_{
i
}) with respect to a hyperplane (*w*, *b*) and a margin normalization function *f* to be *f*(*v*
_{
i
})*y*
_{
i
}(〈*w* ⋅ *x*
_{
i
}〉 + *b*), where *f* is a monotonically decreasing function. To tolerate noise and outliers, more training samples than just those close to the boundary need to be considered.

*γ*> 0, the margin slack variable of a sample (

*x*

_{ i },

*y*

_{ i }) with respect to the hyperplane (

*w*,

*b*) and target margin

*γ*is defined to be

The quantity measures how much a point fails to have a margin *γ* from the hyperplane (*w*, *b*). If *x*
_{
i
} is misclassified by (*w*, *b*), then *ξ*
_{
i
} > 0. To generalize the soft margin classifier to the weighted soft margin classifier, the weighted version of the slack variable is introduced.

*x*

_{ i },

*y*

_{ i },

*v*

_{ i }) with respect to a hyperplane (

*w*,

*b*) and margin normalization function

*f*, slack normalization function

*g*, and target margin

*γ*is defined as

where *f* is a monotonically decreasing function such that *f*(⋅) ∈ (0, 1], and *g* is a monotonically increasing function such that *g*(⋅) ∈ (0, 1].

*S*= ((

*x*

_{1},

*y*

_{1},

*v*

_{1}), …, (

*x*

_{ n },

*y*

_{ n },

*v*

_{ n })), the hyperplane (

*w*,

*b*) that solves the following optimization problem

realizes the maximal weighted soft margin hyperplane. If both functions *f* and *g* are set to be constant at 1, then the WSVM coincides with standard SVM.

In the above formulation, the final decision plane will be less affected by those margin-violating samples with low confidence, and samples with high confidence have higher impact on the final decision plane. The optimization problem can be solved using the sequential minimal optimization technique as in standard SVM. The function *f*(*x*) and *g*(*x*) are set as used in [39].

## 4 Experimental results

### 4.1 Mammogram database

The proposed method was tested on the publically available INbreast database [20]. The database was acquired from the Breast Centre in CHSJ, Porto, between April 2008 and July 2010, and the acquisition equipment was the MammoNovation Simens FFDM. The database has a total of 115 cases (410 images), from which 90 cases are from women with both breasts affected (four images per case) and 25 cases are from mastectomy patients (two images per cases). Several types of lesions (masses, calcifications, architectural distortion) were included. The pixel size is 70 μm, with 14-bit resolution. The image matrix was 3328 × 4084 or 2560 × 3328 pixels. All images were saved in DICOM format. The database has a large portion of calcifications. Among the 410 images, calcifications presented in 301 images, and 27 sets of microcalcification clusters occurred in 21 images (≈1.3 clusters per image). A total of 6880 microcalcifications were individually identified in 299 images (≈23.0 calcifications per image).

For our investigation, very small MCs (number of pixels less than 3) are ignored and treated as normal. Note that the tiny MC can be detected with techniques such as wavelet transform. With such criterion, we obtained 2748 MCs on 232 images (≈11.8 MCs per image). Since the MC cluster in this criterion in the dataset is small, and a cluster can contain dozens of MC, we used a variant criterion about the MC cluster [40]. That is, a group of objects classified as MCs is considered to be a true-positive (TP) cluster only if at least three true calcifications should be detected by an algorithm within an area of 1 cm^{2}. A group of objects classified as MCs is labeled as a FP cluster provided that the objects satisfy the cluster requirement but do not contain true MCs. In this way, 76 MC clusters are defined.

### 4.2 Results

#### 4.2.1 Segmentation results

To quantitatively evaluate the segmentation results, we used Dice coefficient *D*, which has been widely used for segmentation evaluation. The value of *D* ranges from 0 (no overlap) to 1 (perfect overlap) and is defined by \( D=\frac{2\left(A\cap G\right)}{\left(A\cap G+A\cup G\right)}\times 100\% \), where *A* is the region segmented by a method, and *G* is the manually labeled region. The averaged value for *D* on 100 MC images was 93.8 %, and it indicates that the proposed method is accurate for MC segmentation.

#### 4.2.2 Selection of features

As there are 2748 MCs in total, about half of them are used as training dataset, and 1382 MCs from the 116 images containing MC are used in the training as positive samples. In addition, twice as many non-MC examples were selected from the 117 images (one contains only MC cluster) and 88 images not containing MC or MC cluster. That is, in total, 205 images are used for training (containing 1382 MCs, 38 MC clusters, and 2764 non-MCs), and the remaining 205 images (117 images containing MC or MC cluster and 88 images not containing MC or MC cluster) are used for testing; the test dataset contains 1366 MCs on 116 images and 38 MC clusters on 10 images.

Unlike usually random selection, the non-MC examples are selected considering the initial detection procedure. That is, the non-MC examples are selected from the level set segmented regions not containing MC. Thus, the negative examples are specific to the used segmentation method, which is an advantage over the traditional random selection method. There were 4146 (1382 × 3) training examples in total.

Each MC or non-MC was covered by a 16 × 16 (about 1.12 mm × 1.12 mm with pixel spatial resolution of 0.07 mm) window whose center coincided with the center of the suspected MC. Geometry features are extracted from the level set segmentation, and GLCM and wavelet texture features are extracted from the window.

Top 30 features ranked by mutual information filter

Order | Feature no. and name | Order | Feature no. and name | Order | Feature no. and name |
---|---|---|---|---|---|

1 | TF2, grayscale difference | 11 | TF31, entropy in approximate matrix of level 3 with wavelet | 21 | GF11, NRL area ratio |

2 | GF3, compactness | 12 | TF3, autocorrelation with GLCM | 22 | GF13, RGO standard deviation |

3 | TF17, difference entropy with GLCM | 13 | GF10, NRL entropy | 23 | TF20, inverse difference normalized with GLCM |

4 | TF23, entropy in approximate matrix of level 2 with wavelet | 14 | TF6, cluster prominence with GLCM | 24 | TF22, energy in approximate matrix of level 2 with wavelet |

5 | TF4, contrast with GLCM | 15 | GF8, NRL mean | 25 | TF9, entropy with GLCM |

6 | GF1, area of the MC | 16 | GF4, NDM2 | 26 | TF33, entropy in horizontal coefficient matrix of level 3 with wavelet |

7 | GF7, Fourier feature | 17 | TF25, entropy in horizontal coefficient matrix of level 2 with wavelet | 27 | TF12, sum of squares with GLCM |

8 | TF1, the average grayscale in segmented region | 18 | TF36, energy in diagonal coefficient matrix of level 3 with wavelet | 28 | TF10, homogeneity with GLCM |

9 | GF12, RGO mean | 19 | TF15, sum entropy with GLCM | 29 | TF28, energy in diagonal coefficient matrix of level 2 with wavelet |

10 | GF2, perimeter of the MC | 20 | GF5, NDM3 | 30 | TF32, energy in horizontal coefficient matrix of level 3 with wavelet |

We used a fivefold cross-validation method to select the number of features; the training samples were equally split into five subsets, four subsets were used as the training dataset and the remaining one subset was used for testing. The averaged performances were recorded to set parameter values. For the classifier here, we used a standard SVM (with radial basis function kernel) without weights; more specifically, the LIBSVM toolbox [41] was used. The parameters *C* and *σ* in the SVM were obtained with cross-validation from set {2^{− 5}, 2^{− 4}, …, 2^{0}, …, 2^{5}}. Denote the true-positive number of a classifier as TP, the false-positive number as FP, the true-negative number as TN, and the false-negative number as FN. Then the TPR (true-positive rate), TNR (true-negative rate), and accuracy are defined as \( \mathrm{T}\mathrm{P}\mathrm{R}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{F}\mathrm{N}} \), \( \mathrm{T}\mathrm{N}\mathrm{R}=\frac{\mathrm{TN}}{\mathrm{TN}+\mathrm{F}\mathrm{P}} \), and \( \mathrm{Accuracy}=\frac{\mathrm{TP}+\mathrm{T}\mathrm{N}}{\mathrm{TP}+\mathrm{F}\mathrm{N}+\mathrm{T}\mathrm{N}+\mathrm{F}\mathrm{N}} \).

#### 4.2.3 Detection results and comparison with unweighted SVM

After deciding the number of selected features, each data sample is represented by a 22-feature vector. Then the samples in the training are clustered and weighted as in Section 3.4. A weighted SVM is trained as introduced in Section 3.5 and then used for testing.

We measured both MC detection and MC cluster detection for the experiments. The MC cluster was identified by grouping the objects that have been determined by the algorithm to be MC. The receiver operating characteristic (ROC) curves are used to evaluate the performance of MC detection, and the free-response receiver operating characteristic (FROC) curves are used to evaluate the performance of MC cluster detection. The standard SVM without weighting is used to evaluate the effect of the PFCM-based weighting scheme. An ROC curve is a plot of operating points which can be considered as a plot of true-positive rate as a function of false-positive rate. The curve is generated by thresholding the output possibilities of MC of the classifier. A FROC curve is a plot of the correct detection rate (true-positive rate) achieved by a classifier versus the average number of false positives (FPs) per image varied over the decision threshold. A FROC curve can provide a summary of the trade-off between detection sensitivity and specificity.

*A*

_{ z }), which is the area under the ROC curve, is used to compare the performance of the two classification methods. The AUC for standard unweighted SVM is 82.68 %, and the AUC of the proposed PFCM-based weighted SVM is 86.76 %. We can see that with the same training samples and test samples, the proposed weight SVM achieved better performance than the standard unweighted SVM.

## 5 Discussion and conclusion

Automatic detection of microcalcification in mammograms has been investigated by many researchers in the past two decades. In [15], Tiedeu et al. segmented microcalcifications with an adaptive threshold method on the enhanced image, and a set of moment-based geometrical features were used for false-positive reduction. On a dataset of 66 images containing 59 MC clusters and 683 MCs, they obtained a sensitivity of 100 % with a low specificity of 87.77 %. They also performed benign/malignant classification. Oliver et al. [16] extracted image features with a bank of filters, and a boosting method is used to separate MC from non-MC. The dataset they used included the MIAS dataset (322 mammograms) and another 280 FFDM mammograms. Their method’s performance for MC is *A*
_{
z
} = 0.85 with ROC analysis, and for MC clusters, the result is 80 % sensitivity at one false-positive cluster per image.

In [42], Nunes et al. obtained *A*
_{
z
} = 0.93 for MC detection on a database of 121 mammograms by combining three contrast enhancement techniques. Papadopoulos et al. [43] investigated five image enhancement techniques and obtained *A*
_{
z
} = 0.92 for MC detection on a database consisting of 60 mammograms from the MIAS and Nijmegen databases. Linguraru et al. [44] proposed MC cluster detection based on a biologically inspired contrast detection algorithm, integrated with a preprocessing step (curvilinear structure removal and image enhancement). They obtained a 95 % sensitivity with 0.4 false positives per image on a small subset of the Digital Database for Screening Mammography (DDSM) dataset [45] (82 images, 58 of which contain microcalcification and the other 24 were normal ones, the number of MC cluster is 82). Ge et al. [46] developed two systems to detect microcalcification clusters, one for FFDM and the other one for screen-film mammograms (SFMs). They obtained an average of 0.96 or 2.52 false positives per image at 90 % sensitivity on FFDMs and SFMs, respectively. The FFDM dataset they used includes 96 mammograms with microcalcifications and 108 normal mammograms.

It is hard to directly compare different methods, since the used datasets are different, and the definition for MC cluster sometimes is also different. On the DDSM dataset [45], usually different subsets are used in investigations. Most of the above techniques are developed for film-scanned mammograms. Here we developed the method on the FFDMs, as images from FFDM have better image quality than file-scanned images and are also widely deployed. From the above results, it can be seen that the performance of our method with 92 % sensitivity at 2.3 false-positive clusters per image is better or similar to the above results. It should be noted that our method is investigated on a larger dataset.

In this paper, we proposed a weighted SVM technique for detection of MC clusters in FFDM. In this approach, suspicious MC regions are first segmented with active contour, and then the regions are classified by a trained weighted SVM. The non-MC training samples are selected from the segmented regions, which can be better tuned to the whole procedure than random sampling. Mutual information criterion was used to select important features, and among the extracted 51 features, 22 features are selected and used in the training and test process. The training samples are weighted with the possibility and typicality value of a sample belonging to MC output by the novel introduction of possibilistic fuzzy c-means (PFCM) clustering. Experimental results with ROC and FROC analysis using a set of 410 FFDM mammograms demonstrated that the proposed method outperformed the standard unweighted SVM. The proposed weight scheme may be also applicable to other classifiers, such as random forest, and we will investigate these problems in the future. Besides, we will try to adapt the method for traditional film-scanned mammograms.

## Declarations

### Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (No. 61403287, No. 61472293, No. 31201121) and the Natural Science Foundation of Hubei Province (No. 2014CFB288).

## Authors’ Affiliations

## References

- GLOBOCAN 2012 v1.0,
*Cancer Incidence and Mortality Worldwide: IARC CancerBase No. 11 [Internet]*(International Agency for Research on Cancer, Lyon, France, 2013). Available from: http://globocan.iarc.frGoogle Scholar - CH Lee, DD Dershaw, D Kopans, P Evans, B Monsees, D Monticciolo, RJ Brenner, L Bassett, W Berg, S Feig, E Hendrick, E Mendelson, C D'Orsi, E Sickles, LW Burhenne, Breast cancer screening with imaging: recommendations from the Society of Breast Imaging and the ACR on the use of mammography, breast MRI, breast ultrasound, and other technologies for the detection of clinically occult breast cancer. J. Am. Coll. Radiol.
**7**, 18–27 (2010)View ArticleGoogle Scholar - M Giger, Current issues in CAD for mammography, in
*Digital Mammography*(Elsevier, Philadelphia, 1996), pp. 53–59Google Scholar - SV Destounis, P DiNitto, W Logan-Young, E Bonaccio, ML Zuley, KM Willison, Can computer-aided detection with double reading of screening mammograms help decrease the false-negative rate? Initial experience 1. Radiology
**232**, 578–584 (2004)View ArticleGoogle Scholar - J Tang, RM Rangayyan, J Xu, I El Naqa, Y Yang, Computer-aided detection and diagnosis of breast cancer with mammography: recent advances. IEEE Trans. Inf. Technol. Biomed.
**13**, 236–251 (2009)View ArticleGoogle Scholar - X Liu, Z Zeng, A new automatic mass detection method for breast cancer with false positive reduction. Neurocomputing
**152**, 388–402 (2015)View ArticleGoogle Scholar - X Liu, J Tang, Mass classification in mammograms using selected geometry and texture features, and a new SVM-based feature selection method. IEEE Syst. J.
**8**, 910–920 (2014)MathSciNetView ArticleGoogle Scholar - H-D Cheng, X Cai, X Chen, L Hu, X Lou, Computer-aided detection and classification of microcalcifications in mammograms: a survey. Patt. Recog.
**36**, 2967–2991 (2003)View ArticleGoogle Scholar - JK Kim, JM Park, KS Song, H Park, Adaptive mammographic image enhancement using first derivative and local statistics. IEEE Trans. Med. Imaging
**16**, 495–502 (1997)View ArticleGoogle Scholar - AF Laine, S Schuler, J Fan, W Huda, Mammographic feature enhancement by multiscale analysis. IEEE Trans. Med. Imaging
**13**, 725–740 (1994)View ArticleGoogle Scholar - J Tang, X Liu, Q Sun, A direct image contrast enhancement algorithm in the wavelet domain for screening mammograms. IEEE J. Sel. Top. Sign. Proces.
**3**, 74–80 (2009)View ArticleGoogle Scholar - P Ramírez-Cobo, B Vidakovic, A 2D wavelet-based multiscale approach with applications to the analysis of digital mammograms. Comput. Stat. Data. An.
**58**, 71–81 (2013)View ArticleGoogle Scholar - I El-Naqa, Y Yang, MN Wernick, NP Galatsanos, RM Nishikawa, A support vector machine approach for detection of microcalcifications. IEEE Trans. Med. Imaging
**21**, 1552–1563 (2002)View ArticleGoogle Scholar - J Ge, B Sahiner, LM Hadjiiski, HP Chan, J Wei, MA Helvie, C Zhou, Computer aided detection of clusters of microcalcifications on full field digital mammograms. Med. Phys.
**33**, 2975–2988 (2006)View ArticleGoogle Scholar - A Tiedeu, C Daul, A Kentsop, P Graebling, D Wolf, Texture-based analysis of clustered microcalcifications detected on mammograms. Digit. Signal Process.
**22**, 124–132 (2012)MathSciNetView ArticleGoogle Scholar - A Oliver, A Torrent, X Lladó, M Tortajada, L Tortajada, M Sentís, J Freixenet, R Zwiggelaar, Automatic microcalcification and cluster detection for digital and digitised mammograms. Knowl.-Based Syst.
**28**, 68–75 (2012)View ArticleGoogle Scholar - E Malar, A Kandaswamy, D Chakravarthy, A Giri Dharan, A novel approach for detection and classification of mammographic microcalcifications using wavelet analysis and extreme learning machine. Comput. Biol. Med.
**42**, 898–905 (2012)View ArticleGoogle Scholar - J Suckling, J Parker, DR Dance, S Astley, I Hutt, C Boggis, I Ricketts, E Stamatakis, N Cerneaz, SL Kok, P Taylor, D Betal, J Savage, The mammographic image analysis society digital mammogram database, in
*Exerpta Medica. International Congress Series*, (Excerta Medica, Amsterdam 1994), pp. 375–378Google Scholar - J Quintanilla-Domínguez, B Ojeda-Magaña, A Marcano-Cedeño, MG Cortina-Januchs, A Vega-Corona, D Andina, Improvement for detection of microcalcifications through clustering algorithms and artificial neural networks. EURASIP J. Adv. Sig. Proc.
**2011**, 91 (2011)View ArticleGoogle Scholar - IC Moreira, I Amaral, I Domingues, A Cardoso, MJ Cardoso, JS Cardoso, INbreast: toward a full-field digital mammographic database. Acad. Radiol.
**19**, 236–248 (2012)View ArticleGoogle Scholar - R Krishnapuram, JM Keller, A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst.
**1**, 98–110 (1993)View ArticleGoogle Scholar - NR Pal, K Pal, JM Keller, JC Bezdek, A possibilistic fuzzy c-means clustering algorithm. IEEE Trans. Fuzzy Syst.
**13**, 517–530 (2005)MathSciNetView ArticleGoogle Scholar - IN Bankman, T Nizialek, I Simon, OB Gatewood, IN Weinberg, WR Brody, Segmentation algorithms for detecting microcalcifications in mammograms. IEEE Trans. Inf. Technol. Biomed.
**1**, 141–149 (1997)View ArticleGoogle Scholar - H Soltanian-Zadeh, F Rafiee-Rad, S Pourabdollah-Nejad D, Comparison of multiwavelet, wavelet, Haralick, and shape features for microcalcification classification in mammograms. Patt. Recog.
**37**, 1973–1986 (2004)View ArticleGoogle Scholar - M Kass, A Witkin, D Terzopoulos, Snakes: active contour models. Int. J. Comput. Vision
**1**, 321–331 (1988)View ArticleGoogle Scholar - J Tang, X Liu, Classification of breast mass in mammography with an improved level set segmentation by combining morphological features and texture features, in
*Multi Modality State-of-the-Art Medical Image Segmentation and Registration Methodologies*(Springer, New York, 2011), pp. 119–135View ArticleGoogle Scholar - C Li, C-Y Kao, JC Gore, Z Ding, Minimization of region-scalable fitting energy for image segmentation. IEEE Trans. Image Processing
**17**, 1940–1949 (2008)MathSciNetView ArticleGoogle Scholar - L Shen, RM Rangayyan, JL Desautels, Application of shape analysis to mammographic calcifications. IEEE Trans. Med. Imaging
**13**, 263–274 (1994)View ArticleGoogle Scholar - J Kilday, F Palmieri, M Fox, Classifying mammographic lesions using computerized image analysis. IEEE Trans. Med. Imaging
**12**, 664–669 (1993)View ArticleGoogle Scholar - B Sahiner, H-P Chan, N Petrick, MA Helvie, LM Hadjiiski, Improvement of mammographic mass characterization using spiculation measures and morphological features. Med. Phys.
**28**, 1455–1465 (2001)View ArticleGoogle Scholar - J Fu, S-K Lee, ST Wong, J-Y Yeh, A-H Wang, H Wu, Image segmentation feature selection and pattern classification for mammographic microcalcifications. Comput. Med. Imaging Graph.
**29**, 419–429 (2005)View ArticleGoogle Scholar - RC Gonzalez, RE Woods,
*Digital Image Processing*(Prentice Hall, New Jersey, 2002)Google Scholar - R Haralick, I Dinstein, K Shanmugam, Textural features for image classification. IEEE Trans. Syst. Man Cybern.
**3**, 610–621 (1973)View ArticleGoogle Scholar - X Liu, J Liu, D Zhou, J Tang, A benign and malignant mass classification algorithm based on an improved level set segmentation and texture feature analysis, in 2010 4th International Conference on Bioinformatics and Biomedical Engineering (iCBBE), Chengdu, 18-20 June 2010, pp. 1–4Google Scholar
- S Mallat,
*A Wavelet Tour of Signal Processing*(Academic Press, New York, 1999)Google Scholar - RO Duda, PE Hart, DG Stor,
*Pattern Classification*(Wiley, New York, 2001)Google Scholar - R Kohavi, GH John, Wrappers for feature subset selection. Artif. Intell.
**97**, 273–324 (1997)View ArticleGoogle Scholar - H Peng, F Long, C Ding, Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy. IEEE Trans. Patt. Anal. Mach. Int.
**27**, 1226–1238 (2005)View ArticleGoogle Scholar - X Wu, R Srihari, Incorporating prior knowledge with weighted margin support vector machines, in
*Proceedings of the Tenth ACM SIGKDD*, 2004, pp. 326–333Google Scholar - M Kallergi, GM Carney, J Gaviria, Evaluating the performance of detection algorithms in digital mammography. Med. Phys.
**26**, 267–275 (1999)View ArticleGoogle Scholar - C-C Chang, C-J Lin, LIBSVM: a library for support vector machines. ACM T. Intel. Syst. Tec.
**2**, 1–27 (2011)View ArticleGoogle Scholar - FL Nunes, H Schiabel, CE Goes, Contrast enhancement in dense breast images to aid clustered microcalcifications detection. J. Digit. Imaging
**20**, 53–66 (2007)View ArticleGoogle Scholar - A Papadopoulos, DI Fotiadis, L Costaridou, Improvement of microcalcification cluster detection in mammography utilizing image enhancement techniques. Comput. Biol. Med.
**38**, 1045–1055 (2008)View ArticleGoogle Scholar - MG Linguraru, K Marias, R English, M Brady, A biologically inspired algorithm for microcalcification cluster detection. Med. Image Anal.
**10**, 850–862 (2006)View ArticleGoogle Scholar - M Heath, K Bowyer, D Kopans, R Moore, P Kegelmeyer, The digital database for screening mammography, in
*Proceedings of the 5th International Workshop on Digital Mammography*, 2000, pp. 212–218Google Scholar - J Ge, LM Hadjiiski, B Sahiner, J Wei, MA Helvie, C Zhou, HP Chan, Computer-aided detection system for clustered microcalcifications: comparison of performance on full-field digital mammograms and digitized screen-film mammograms. Phys. Med. Biol.
**52**, 981–1000 (2007)View ArticleGoogle Scholar

## Copyright

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.