Detection of clustered microcalcifications in small field digital ...

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 81 (2006) 56–65

journal homepage: www.intl.elsevierhealth.com/journals/cmpb

Detection of clustered microcalcifications in small field digital mammography Tomasz Arodz´ a , Marcin Kurdziel a,∗ , Tadeusz J. Popiela b,1 , Erik O.D. Sevre c,2 , David A. Yuen c,2 a b c

´ Poland Institute of Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, ´ Poland Collegium Medicum, Jagiellonian University, ul. Kopernika 19, 31-501 Krakow, Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, MN 55455, USA

a r t i c l e

i n f o

a b s t r a c t

Article history:

The most frequent symptoms of ductal carcinoma recognised by mammography are clus-

Received 20 September 2004

ters of microcalcifications. Their detection from mammograms is difficult, especially for

Received in revised form 2 October

glandular breasts. We present a new computer-aided detection system for small field digital

2005

mammography in planning of breast biopsy. The system processes the mammograms in

Accepted 4 October 2005

several steps. First, we filter the original picture with a filter that is sensitive to microcalcification contrast shape. Then, we enhance the mammogram contrast by using wavelet-based

Keywords:

sharpening algorithm. Afterwards, we present to radiologist, for visual analysis, such a

Mammogram analysis

contrast-enhanced mammogram with suggested positions of microcalcification clusters.

Microcalcification detection

We have evaluated the usefulness of the system with the help of four experienced radiolo-

Wavelets

gists, who found that it significantly improves the detection of microcalcifications in small

2D filtering

field digital mammography. © 2005 Elsevier Ireland Ltd. All rights reserved.

1.

Introduction

Breast cancer is one of the leading causes of cancer-related deaths. As various studies show [1], early detection of suspicious lesions is crucial for the prognosis of the patient. In cases where a lesion is detected before cancer cells spread into the surrounding tissue, the 5-year survival rate is 97.9%. It drops sharply to 81.3% and 26.1% for regionally advanced and metastatic cancer, respectively.

∗

Detection of breast cancer is conducted by means of two most widely used diagnostic methods, i.e., mammography and ultrasonography (USG) imaging. These two methods are best suited for unveiling different types of cancer. The most frequent type of breast cancer, detected before the invasion stage, is ductal carcinoma in situ (DCIS). In this type of cancer, the most frequent markers are clusters of microcalcifications. Therefore, we will focus on the mammogram-based approach, as it is particularly suitable for detecting this type of lesion.

Corresponding author. Tel.: +48 12 617 3497; fax: +48 12 633 9406. Tel.: +48 12 421 35 83; fax: +48 12 421 35 83. 2 Tel.: +1 612 624 9801; fax: +1 612 625 3819. ´ [email protected] (M. Kurdziel),[email protected] (T. Popiela), E-mail addresses: [email protected] (T. Arodz), [email protected] (E.O.D. Sevre), [email protected] (D.A. Yuen). 0169-2607/$ – see front matter © 2005 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2005.10.002 1

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However, microcalcification detection from mammograms may be troublesome. The breast contains a variable amount of connective, glandular and fatty tissue. These are organised in structures of different shapes, densities and scales. In cases involving a large amount of glandular tissue (so-called glandular breasts) mammograms are very bright, which significantly decreases visibility of subtle microcalcifications. In situations involving examination of large number of mammograms, the efficiency of visual inspection also drops down considerably. Therefore, computer-aided detection of microcalcifications is attracting a great deal of attention from the radiologist community. Up to now, a wide range of algorithms has been proposed for detection of microcalcifications in mammogram images. Among the most important are methods that use physics-based mammogram representation [2–5], wavelet transform [6–9], machine learning algorithms [10–16], morphological filters [17], multiresolutional analysis [18] and fuzzy logic [19]. For preprocessing mammogram images, local contrast enhancement [20,21], noise equalisation [22] and tissue thickness correction [23] have been used. Finally, classification algorithms have been applied to identification of microcalcifications that, with certain probability, indicate malignant process within a breast [24,25]. The vast amount of research related to analysis of digital mammograms, as well as widespread interest from the medical community, stimulated the development of commercial computer-aided detection systems [26]. Currently, three such systems have U.S. Food and Drug Administration approval. These are: ImageChecker by R2 Technology Inc., MammoReader by Intelligent Systems Software Inc. and Second Look by CADx Medical Systems Inc. A detailed report on the performance of those CAD systems is provided in Ref. [27]. The paper is arranged as follows. In Section 2, the goals of the developed system are outlined. In Section 3, we describe the medical data and procedures used prior to the system operations. The algorithms used by our system and the results of their evaluation are presented in Section 4. At the end (Sections 5 and 6) we discuss the results and give the conclusions.

2.

Goals

We present here a novel system for detecting clustered microcalcifications in small field digital mammography [28]. The system uses digital mammograms, obtained from a mammography-guided breast biopsy. Its purpose is to support the radiologist in planning of the biopsy by marking the suspicious regions in mammograms and improving the image contrast. The system was designed to meet several criteria that are important in cancer detection support. Above all, the algorithms are not demanding computationally. This aspect is a necessary prerequisite for interactive work. The parameters of the algorithms were tuned to optimise the sensitivity to microcalcifications. A drawback of these design decisions is that slightly more mammogram regions can be falsely classified as being “suspicious”.

3.

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Materials and methods

The system is typically provided with two digital mammograms from stereotactic biopsy table. The mammograms depict a suspicious region of the breast from two projection angles, differing by 30◦ . On the system’s input the images are converted to 8 bits per pixel TIFF format with a resolution of 1024 × 1024 pixels. The images are not compressed. The system processes the images separately. As a first step, the system filters the mammograms, using a filter sensitive to typical appearances of microcalcifications. Next, the pixels with a high filter response are selected and clustered, to identify the suspicious regions further called regions of interest (ROIs). Afterwards, the mammograms undergo contrast enhancement. The contrastenhanced mammograms with the ROIs marked by rectangles are presented to the radiologist. In Section 4 we give a detailed description of the algorithms and visualisation methods used by this system. The system was evaluated on a set of 50 digital mammograms provided by Collegium Medicum, Jagiellonian Univer´ Poland). The mammograms were obtained from sity (Krakow, stereotactic biopsy table. Each of them depicts a region of the breast with an area of 25 cm2 containing the suspicious lesion. The mammograms were converted to the TIFF format and processed by the system. Four experienced radiologists independently evaluated the original mammograms. Afterwards, they evaluated the mammograms provided by our system. The system was automatically marking the regions of interest and was enhancing the contrast. For each mammogram, the radiologists noted the number of clusters of microcalcifications detected on the original mammogram and on the mammogram processed by the system. In addition, the radiologists estimated the cancer detection improvement resulting from the use of the system. It was measured in a scale that extends from 1 (no improvement) to 5 (great improvement). After the evaluation, each mammogram was classified according to the Wolfe breast parenchymal patterns [29], while the clusters of microcalcifications were classified according to LeGal types [30]. It should be noted, that the lowest possible usability rating, i.e., no improvement, includes also rare situations where the detection degraded after the application of the system. However, this may influence the detection outcome only in the artificial scenario used in testing, where the radiologist cannot evaluate both original and enhanced image simultaneously. In the normal clinical usage the radiologist can perform simultaneous evaluation. Thus, the detection ratio should not be degraded. The above methodology of evaluating the system stems from several reasons. First, the system was devoted to assist the radiologist in small field digital mammography for planning of breast biopsy. Contrary to screening mammography, in such operating conditions almost every image contains suspicious lesions. Thus, the use of classical ROC analysis is not suitable in this case. Next, an important goal of the system is to allow for more precise positioning of the biopsy needle. This is achieved using contrast enhancement algorithm. The performance of such an algorithm cannot be easily evaluated with sensitivity and specificity analysis. Instead, we adopted

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Fig. 1 – Components of the system.

a methodology based on the feedback from the radiologists as described above.

4.

Results

4.1.

Architecture of the proposed system

As shown in Fig. 1, the system operates in several phases. After acquisition of the image, the regions of interest are selected. These regions contain clustered microcalcifications. Then, the image is further enhanced for improving the visibility of lesions. Finally, the contrast-enhanced mammogram is visualised. Moreover, the microcalcifications within regions of interest can be attenuated using isoline visualisation technique.

4.2.

Selection of regions of interest

The key element of the breast cancer detection system is the method for pinpointing the suspicious regions. We propose a new algorithm, which is based on detecting clustered microcalcifications as an indication of a lesion. The algorithm operates in two phases. First, the individual microcalcifications are detected. Then, we group the microcalcifications into clusters, and define square bounding boxes around them.

4.2.1.

Microcalcification detection

The microcalcification is detected by means of a filter developed to accentuate the standard appearance of this type of lesion. The designed filter belongs to the family of finite impulse response filters [31]. The real and model microcalcifi-

cation, along with its cross-section by a single line crossing the lesion in any direction, are presented in Fig. 2. As can be observed, the microcalcifications are spots with a higher intensity on a background with lower intensity. Thus, when cross-sectioned to a single line, the microcalcification takes form of a sharp rise followed by a sharp decrease in the image intensity along this line. On the basis of this observation, we have developed a dedicated filter to detect the microcalcifications. Such a filter should produce sharp responses in places, where the microcalcifications are located, while keeping lower responses elsewhere. Let us assume that we expect a microcalcification of width w in a given image position. The direct measurement of the presence of the microcalcification consists of the measurement of its height relative to the surrounding background. This can be done with a filter depicted in Fig. 3 by assuming that the width of the filter is equal to w + 2wb . The wb parameter specifies the width of the border of the microcalcification. The value of the filter response is equal to the difference of average intensity within the microcalcification and the average intensity outside its borders. For attaining this level, the 1 value of the filter coefficients is set to w within the microcalcification, while in the part that should match the border of 1 microcalcification, it is set to − 2w . b The main obstacle to using this filter is the varying width of the microcalcifications. It changes not only between different lesions, but also between different 1D cross-sections of a single microcalcification taken at different orientation, as the microcalcifications are rarely circular in shape. There are several solutions to this problem. One is to filter the image several times, each time searching for lesions with a different width, independently for a set of orientations of the filter.

Fig. 2 – Real (marked, left) and model (center) microcalcification. 1D cross-section of 2D model microcalcification with height h, width w and boundary width wb (right).

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Fig. 3 – Shape of the filter used for measurement of the height of the microcalcification of a fixed width w and border width wb .

Fig. 5 – A 2D version of the filter from Fig. 4.

Fig. 4 – A sum of the microcalcification width-specific filters from Fig. 3.

Then, we take the maximum value of the filter responses at a given position. While yielding good results, this approach may be prohibitively demanding computationally. Therefore, we use a simplified construction. The filters with the widths within a specific range are summed together, thus producing an averaged response. The resulting filter is therefore sensitive to varying widths stemming from orientation and size of microcalcifications. The composite filter is depicted in Fig. 4. As noted above, microcalcification is a 2D object. Therefore, as shown in Fig. 5, the 2D filter is constructed by a circular rotation of the 1D filter from Fig. 4. While this favours the circular microcalcifications, the filter also recognizes the microcalcifications of different shapes. This is because, in each direction, the filter is an average of 1D filters of different widths. First, we de-noise the image with a 3 × 3 median filter. Then, the responses of the constructed 2D localised filter are calculated. This operation enhances the microcalcifications and suppresses the surrounding tissue. However, some noise is still present. Two additional procedures are conducted for noise reduction. First, the image resulting from the filtering is again filtered with the same 2D filter. This results in further enhancement of microcalcifications. Second, the original, de-noised image is filtered with two 1D filters from Fig. 4, operating horizontally and vertically, respectively. Both 1D filter responses are summed up. As a result, we obtain three images with microcacifications enhanced: filtered with the 2D filter once, filtered with the 2D filter twice, and filtered with 1D filters. These three images are multiplied pixel-wise

to obtain the final image. The multiplication preserves only the suspicious locations, which are present in all three filtered images, thus reducing the noise. Using 1D filters leads also to better recognition of irregular microcalcifications. The horizontal and vertical widths of microcalcifications are treated individually. Finally, the brightest T = 0.3% of the area of the image is selected as the locations of microcalcifications. The value of T has been determined experimentally, based on seven mammograms which are used only in the preparation of the system. The range of T from 0.1% to 0.7% was inspected and the free-response receiver operating characteristic (FROC) [32] curve has been prepared (Fig. 6). By analysing the curve, the value of T with the best trade-off between sensitivity and the number of false positives was chosen.

4.2.2.

Microcalcifications clustering into regions of interest

The result of the process for detecting the suspicious lesions contains microcalcification, and some noise. To reduce the amount of signatures which are not microcalcifications, we perform a sequence of morphological operations on the filtered image [33,34]. This procedure eliminates small or isolated signatures, while retaining the clustered signatures.

Fig. 6 – The free-response receiver operating characteristic of the system on seven mammograms used to determine the best parameters of the system.

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First, we perform the area opening operation. We remove all objects that are smaller than 5 pixels (243 ␮m), which can be considered as noise. Small, isolated microcalcifications are not considered as markers of a cancerous change. Therefore, the next step is to eliminate signatures that are not members of compact clusters. To achieve this, the image is dilated with disk structuring element of radius equal to 5 pixels (243 ␮m). Then, the area opening is performed again. As a result of the two previous procedures, the signatures with diameter less then 6 pixels (291 ␮m), which do not have any neighbouring signature closer than 16 pixels (769 ␮m), are removed. Finally, the same processes of dilation and area opening is repeated, removing objects with diameter less than 8 pixels (387 ␮m) which do not have any neighbouring signatures closer than 28 pixels (1332 ␮m). These distances and object sizes have been determined experimentally, to obtain the best trade-off between removing noise and preserving the valid microcalcification clusters. Experiments using seven annotated mammograms used only for the parameter study were carried out. For different values of the parameters above, the number of selected microcalcification clusters was observed. Also, the number of false positives was analysed. Another factor considered was the preservation of the integrity of clusters, to avoid their excessive fragmentation. The parameter study procedure involved several rounds of optimal selection of each parameter with other parameters remaining constant. The previous steps provide information on compact clusters of microcalcifications. This information is used to select the rectangular regions of interest. In particular, for each of the clusters, we determine a bounding box, with margin of 20 pixels (958 ␮m) in each direction. If the two bounding boxes overlap, the clusters are merged, and a new bounding box is calculated. This process is iterated until no further merging is possible. If several dense, small clusters are in close proximity of each other, the process will group them into a single, bigger cluster. This gives the radiologist more information on the spread of the microcalcifications. An example result of microcalcification detection, clustering and selection of regions of interest is presented in Fig. 7. The system has detected the only microcalcification cluster present in the image.

4.3.

Mammogram contrast enhancement

The contrast of a mammogram image is often poor, especially for dense, glandular tissues. In these cases the radiologist may miss some diagnostically important microcalcifications. This obstacle can be overcome by using contrast enhancement algorithms [35]. Our system first removes the noise from the mammogram image and then performs automatic contrast enhancement, using a method based on a 2D discrete wavelet transform [36]. These steps are carried out on mammogram images with the pixel intensities normalised (i.e. rescaled) to the interval 0, 1.

4.3.1.

Noise cancellation

Small field digital mammograms often contain a noticeable amount of “salt and pepper” type noise. This noise

Fig. 7 – An example of a result of the selection of regions of interest. The selected region, marked by a box, corresponds to the only cluster of microcalcifications present in the mammogram, according to all of the radiologists.

should be removed for avoiding impairment of the contrast enhancement algorithm and negative influence on the whole detection procedure. To achieve this goal, the proposed system computes the difference in pixel intensities between a 4 × 4 median filtered mammogram and the original image. Next, thresholding is applied to produce a binary mask M. The threshold value was set to 0.1. After thresholding, all elements different from isolated pixels are removed from M. To remove them we employ the following operation: M = M − AreaOpen(M, 1)

(1)

where AreaOpen(M, 1) is a morphological area opening with disc-like structural element. The radius of the structural element is equal to 1. Isolated pixels that remain in the mask M are presumed to indicate locations of the noise on the mammogram. To remove this noise, the original mammogram is filtered at specific positions, as indicated by a mask M, with a 3 × 3 median filter.

4.3.2. Contrast enhancement using discrete wavelet transform The discrete wavelet transform decomposes the image into approximation coefficients and three sets of detailed coefficients, i.e., horizontal, vertical and diagonal. The approximation coefficients contain large-scale components of the image. For example, global intensity changes are reflected mostly in the approximation. On the other hand, the detailed coefficients contain small-scale components of the image. In terms of frequency analysis, low-frequency coefficients represent this approximation, whereas high-frequency coefficients represent the details.

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Microcalcifications usually appear on a mammogram image as small, bright, spot-like protrusions in the breast tissue. Consequently we can assume that a wavelet decomposition of the mammogram image will contain the microcalcifications mostly within the detailed coefficients. This assumption lies at the basis of the proposed mammogram contrast enhancement algorithm. This algorithm constructs a mask Me that emphasises microcalcifications while, to some extent, suppressing the normal tissue. First, the mammogram is filtered with a 3 × 3 median filter. The filtered image is subjected to a five-level discrete wavelet decomposition using Daubechies wavelet of order 4 [37]. This produces an approximation and five sets of horizontal, vertical and diagonal detailed coefficients. After the decomposition, the algorithm performs inverse wavelet transform, using these five sets of detailed coefficients. The approximation coefficients are set to zero. The resultant image, Ir , is used to create the mask Me using the following formula: Me (i, j) = etIr (i,j)

(2)

where i, j ∈ {1, . . . , n}. The parameter t > 0 controls the strength of enhancement. Before it is applied to the mammogram, the mask Me is normalised to the 0, 1 interval. Afterwards, the contrast enhanced mammogram Ie is obtained via pixel-wise multiplication of the original mammogram image I (i.e. with the noise removed but without the additional 3 × 3 median filtering) by the mask Me : Ie (i, j) = I(i, j)M(i, j),

i, j ∈ {1, . . . , n}

(3)

In Fig. 8 we present the results of our algorithm for contrast enhancement.

4.4. The prospect for evaluation of microcalcifications using isolines visualisation technique Once the regions of interest have been selected and enhanced by the system, it is important for the radiologist to have visualisation tools at hand, that can be used for further interactive evaluation of the microcalcifications. The Amira1 [38] visualisation package is a series of tools that allow for interactive processing of 2D and 3D images. The Amira interface facilitates the examination of various aspects of the data and provides powerful tools to generate image files for further examination. Therefore we believe that this package might be useful for analysis of contrast-enhanced mammograms. Among many visualisation techniques provided by Amira, isolines seems to be particularly useful for evaluating clusters of microcalcifications. The isolines connect pixels of an image with similar brightness. As the distribution of pixel intensities within contrast enhanced mammograms is, to some extent, continuous the isolines can be used to accentuate shapes of microcalcifications. This can be particularly useful for a radiologist when assessing the probability of malignancy of detected clusters of microcalcifications. An example of a result obtained

1 Advanced 3D Visualisation and Volume Modelling, http://www. amiravis.com.

Fig. 8 – An example of a result of the system. The original mammogram is presented above. Below the same mammogram is depicted, but after the system has enhanced the contrast and detected four clusters of microcalcifications.

using the proposed visualisation technique is presented in Fig. 9.

4.5.

Results of evaluating the system

Table 1 contains the results of the system evaluation grouped according to the LeGal classification of clusters of microcalcifications. The table contains the average number of clusters of microcalcifications that were detected on the mammogram processed by the system, but were not detected on the original mammogram (per one mammogram). The average estimate of detection improvement given by the radiologists is also provided. The results, grouped according to the Wolfe breast parenchymal patterns, are presented in Table 2.

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Fig. 9 – Results of applying isolines to a mammogram region of interest (ROI). The top row contains the contrast-enhanced ROIs, whereas the bottom row contains the same ROIs with isolines marked.

5.

Discussion

The results collected in Tables 1 and 2 show the estimates of the detection improvement obtained by introducing the proposed computer-based support system.

The lowest improvement is present in the N1 Wolfe parenchymal pattern type [29]. This pattern type is associated with breasts containing large amounts of fatty tissue. Therefore, the radiologist can detect microcalcifications easier on the original images than for other types of Wolfe patterns.

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Table 1 – Results of the system evaluation grouped according to the LeGal classification LeGal type of cluster of microcalculation

Type 1 Type 2 Type 3 Type 4 Type 5

Average number of clusters of microcalculation detected on processed mammograms but not detected on original mammograms

Average estimate of detection improvement given by the radiologist

0.2 0.4 0.8 0.3 0.2

2.9 3.1 3.8 3.1 2.8

Average number of clusters of microcalcifications that were detected on mammograms processed by the system but were not detected on original mammograms and the average estimate of detection improvement resulting from using the system. The average numbers are provided for each mammogram.

Table 2 – Results of the system evaluation grouped according to the Wolfe classification Wolfe type of breast parenchymal patterns

N1 P1 P2 DY

Average number of clusters of microcalculation detected on processed mammograms but not detected on original mammograms 0.2 0.4 1.0 0.7

Average estimation of detection improvement given by the radiologist

1.4 2.4 4.2 3.2

Average number of clusters of microcalcifications that were detected on mammograms processed by the system but were not detected on original mammograms and the average estimate of detection improvement resulting from using the system. The average numbers are provided for each mammogram.

This does not leave much room for further improvement by a computer-based method. The improvement in detection rises for Wolfe type P1, and the highest improvement is for types P2 and DY. This shows the usefulness of the system, as these types of breast contain more glandular tissue than the N1 type, which make microcalcifications less visible. Our system allows the radiologist to find more clusters of microcalcifications. The efficiency of the system, defined as the average number of microcalcification clusters detected using our method but not detected by classical medical procedures, varies with the type of microcalcifications defined by LeGal [30]. For the LeGal type 1, the efficiency of the computer support on the detection is small. However, according to LeGal, this type of microcalcifications does not usually lead to malignancy. Thus, the high efficiency of the computer-aided detection is not crucial. The efficiency increases for microcalcifications of LeGal types 2–4. An estimate of the system usefulness given by radiologist, as well as its efficiency is the highest for type 3. For types 2 and 4, the usefulness is not as evident. For the LeGal type 5 microcalcifications, which usually are correlated with malignancy, the results are not as good as for the types 2–4. In general, the system is most useful for microcalcification clusters with a medium probability of malignancy. The radiologists noted that the most useful feature of the system is the automatic enhancement of the contrast. The contrast improvement is performed after the selection of ROIs. Therefore, even in cases where the region detection algorithm does not localise a cluster of microcalcifications, the radiologists still have the opportunity to detect it. The radiologists noted that the detection of regions of interest still needs improvement. In several cases the algorithm failed to

detect the clustered microcalcifications or did not detect all of the clusters. Moreover, one radiologist noted, that the original images are of poor quality, which may lead to overestimate of the usefulness. However, in the image acquisition scenario described in Section 3, such poor quality images may be present due to the image acquisition mechanisms and/or equipment used. While the radiologist can improve the contrast manually, this slows down the detection process. The proposed system can improve the contrast automatically. Furthermore, the mammogram enhancement offered by the proposed system leads to a better contrast improvement than the traditional, manual method.

6.

Conclusions and perspectives

We have proposed a computer system devised to support a radiologist in small field digital mammography for planning of breast biopsy. We focused on the detection of clusters of microcalcifications. The proposed algorithm operates in several phases. First, the suspicious regions in the mammogram are detected. Then the contrast of the whole mammogram is enhanced. Finally, the contrast-enhanced image with suspicious regions marked is presented to the radiologist. The radiologist can attenuate the microcalcifications with isoline visualisation technique. The system was evaluated by four radiologists. Their results show that the system introduces an improvement in the breast cancer detection. This improvement is particularly present in the Wolfe type P2 and DY breasts, and in the LeGal type 2, type 4 and especially in type 3 microcalcifications.

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In the future, our work will focus on several parts of the system. First, we plan to inspect the possibility of improving the microcalcification detection by using a filter or a group of filters, which are designed by a machine-learning algorithm. This machine-learning algorithm can be automatically fed by the knowledge streaming from decisions made by the radiologists who use the system. Another goal of our research are fast methods for microcalcification clustering, with an intrinsic mechanism for discarding isolated, noise signatures. The contrast enhancement algorithm might be further improved by incorporating additional information on the local features of the mammogram, e.g. the homogeneity measure [39]. We will also work on a system for detecting clustered microcalcifications in high resolution, whole-breast mammograms. The system will use an algorithm based on 2D discrete wavelet transform for detecting possible locations of microcalcifications. To reduce a number of false alarms, we plan to use an advanced classification method. Currently we are evaluating a Support Vector Machine [40] algorithms for this purpose. This classifier will work on a set of statistical features computed from ROIs chosen by the wavelet-based algorithm. The set of features that optimally describe a mammogram ROI will be designed with the aid of an evolutionary algorithm. In high resolution mammograms microcalcifications are large enough for determining their shape, area and other geometrical properties. This future system might use such information to assess the probability of detecting a malignant lesion.

Acknowledgements We thank Ben Holtzman, Lilli Yang and Katya Shukh for their artistic rendering. This research has been supported by a grant from the University of Minnesota Digital Technology Center, grant on wavelet analysis from CMG of National Science Foundation, the Polish State Committee for Scientific Research (KBN) research grant no. 3 T11C 059 26 and the Polish Ministry of Science and Information Society Technologies grant no. 3 T11F 019 29.

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