Robust Techniques For Enhancement Of Microcalcifications In Digital Mammography
PETER HEINLEIN Image diagnost International GmbH Balanstrafie 57, 81541 Miinchen, Germany Email: post(at)peterheinlein.de
We present methods for the enhancement of microcalcifications in breast radiographs. The result of such an algorithm is a manipulated image where calcifications appear more clearly. By making these very subtle signs more visible, the radiologist can be aided in detecting a cancer. This can help to improve both efficiency and accuracy of the diagnosis.
Our main contribution to enhancement of microcalcifications is the improvement of the underlying wavelet methods. Based on the continuous wavelet decomposition we apply a novel method to discretize the continuous wavelet transform. By choosing discrete wavelet scales that match the size of microcalcifications we obtain contrast improvements that outperform hitherto used wavelet transforms. We present new results which indicate that the algorithm is very robust with respect to different mammographic imaging modalities.
The flexibility of our approach is also demonstrated in applications as detection of microcalcification and as artifact free image denoising.
Keywords: Robust techniques; digital mammography; microcalcifications.
1. Introduction
Easily interpretable xray mammograms have been a clinicians dream for quite a long time. The recent introduction of dedicated digital review workstations for mammography starts the departure from conventional filmbased reading. This development opens up new opportunities for medical image processing. Our emphasis is on enhancement of features that are relevant for diagnosis.
Breast cancer is the main cause of death for women between the ages of 35 to 55. Early detection and treatment of breast cancer are the most effective methods of reducing mortality. Microcalcifications are among the earliest signs of a breast carcinoma. Actually, as radiologists point out,17 microcalcifications can be the only mammographic sign of nonpalpable breast disease. Due to the subtle nature of these microcalcifications these are often overseen in the mammogram. Some retrospective studies state that in up to 40% of the cases unambiguous signs of a cancer were missed by the reader, with in some cases fatal consequences for the patient. Thus the reliable detection and classification of microcalcifications plays a very important role in early breast cancer detection.
Computer assisted detection (CAD), which is reality today, was a first step to simplify the detection of malignant lesions. Up to now, however, CAD systems just put markers on suspicious regions. They do not generate a processed image that might show relevant features more clearly. This restriction is due to two reasons. First, most mammograms are still filmbased, and are read using a lightbox. Thus commercial CAD systems digitize the film and present markers on a small display or on a separate printout. Second, for the purpose of detection the image is just decomposed to generate features for a classifier. The task of enhancement is more complex, as it also requires an image reconstruction. Only a very sophisticated reconstruction algorithm can provide images that are still suitable for diagnostic reading.
Our focus in this article is on providing algorithms for the enhancement of microcalcifications in breast radiographs. The result of such an algorithm is a manipulated image where calcifications appear more clearly. By making these very subtle cancer signs more visible, the radiologist can be aided in detecting a cluster of calcifications. Further, if the features of the calcifications are made more evident, the radiologist might be aided in determining whether the calcifications originate from a benign or a malignant lesion. This can help to improve both efficiency and accuracy of the diagnosis. Thus enhancement of microcalcifications can efficiently complement the markers generated by a standard CAD system.10
Considerable research has been undertaken in the development of automated image analysis methods to assist radiologists in the identification of abnormalities. In a recent overview article, H. D. Cheng et al.8 gathered more than 120 citations on the topic of microcalcification detection and classification. Among these techniques, there are many promising waveletbased approaches.
Our contribution to enhancement of microcalcifications is the improvement of the underlying wavelet methods. Based on the continuous wavelet decomposition we apply a novel method to discretize the continuous wavelet transform. This discretization permits arbitrary scales and orientations while maintaining the reconstruction property of the continuous transform. It allows to adapt the wavelet filterbank optimally to the size and shape of microcalcifications. This is the basis for our microcalcification enhancement algorithm.
We start with a short introduction to the medical background in Sec. 2. It includes an overview of the available mammographic imaging modalities and introduces the relevant aspects of xray image formation.
An overview of known methods for enhancement of microcalcifications is given in Sec. 3. We explain the role of wavelets for enhancement and we sketch the basic concept of transform based enhancement.
Section 4 introduces a novel discrete wavelet transform, so called integrated wavelets. Integrated wavelets provide flexible discrete versions of the continuous wavelet transform (CWT). This idea firstly appeared in an article by
M. DuvalDestin, M. A. Muschietti and B. Torresani15 on affine wavelets. We have generalized the concept and have introduced directional integrated wavelets.20'21 We show that these integrated wavelets can be specifically tailored for analysis applications where an image reconstruction is needed.
Results of enhancement are presented in Sec. 5. We study in detail the ingredients of wavelet based enhancement methods. We derive an adapted wavelet from a model for microcalcifications. Our enhancement operator on wavelet coefficients is a refinement of known approaches by A. Laine et al.26 '27 With integrated wavelets, we can chose the discrete scales to match the size of the interesting structure. This yields contrast improvements that outperform hitherto used wavelet transforms by about 5 to 10%. Further, we present new results that indicate that the algorithm is very robust with respect to different mammographic imaging modalities.
Finally, Sec. 6 sketches further applications. We present how in the setting of integrated wavelets directional information can be used to distinguish microcalcifications from similar structures. A second application is uncorrelated denoising. Based on the Morlet reconstruction we introduce a denoising procedure that is not correlated in space. For example, applied to mass detection in mammograms, we find that this denoising method does not disturb the local image statistics that we use for feature extraction.
2. Preliminaries
At first glance, given just a single mammogram, the task of detecting microcalcifications seems almost easy. But each breast is different in anatomy. Further, there exist various different microcalcification patterns. To complicate matters even more, there are several xray imaging technologies that each have their own characteristics.
Thus, from the point of view of image analysis, the main challenge of mammography is diversity. An algorithm must be reliable under all the varying biometric and technical parameters. This section provides some background that helps to understand the challenges an algorithm for enhancement of microcalcifications has to face.
2.1. Medical background
The earlier a breast cancer is diagnosed, the easier it is to cure it. Microcalcifications are an early sign of a breast carcinoma. In fact, as S. HeywangKobrunner et al.23 point out, microcalcifications can be the only mammographic sign of nonpalpable breast disease. Microcalcifications account for over 50% of all the nonpalpable lesions detected using mammography. For this reason, the reliable detection of microcalcifications is one of the major goals of mammographic image processing.24
The main reason for xray mammography is the fact that other imaging methods such as magnetic resonance imaging or ultrasound imaging cannot capture and
visualize microcalcifications. Figure 1 shows mammograms from different imaging modalities.
Calcification shows up on a mammogram when calcium deposits have collected in the ducts of the breast. In many cases, calcification can occur without there being a cancer there. If there is a breast cancer in that area, then the pattern of the calcium that shows up on the mammogram can have a particular look to it that a specialist in reading mammograms will recognize.
It is a difficult task to detect microcalcifications in a mammogram with the naked eye. Studies indicate, compare an overview by U. Bick,7 that in up to 30% of the cases analyzed the radiologist oversees definite signs of a cancer. In a mammogram, microcalcifications appear as small spots that are brighter than the surrounding tissue. They can be very small, actually at the limit of the spatial resolution of the imaging system. Imaging noise and dense breast tissue can further occlude theses signs. In a screening scenario the problem of detection is increased by low incidence. In 100.000 screening cases there are typically no more than 200 cases of cancer.
Basic breast anatomy
The breast is a mound of glandular, fatty and fibrous tissue located over the pectoralis muscles of the chest wall and attached to these muscles by fibrous strands.
A layer of fat surrounds the breast glands and extends throughout the breast. The actual breast is composed of fat, glands with the capacity for milk production, blood vessels and milk ducts to transfer the milk from the glands to the nipples.
Normal, nonfat breast tissue is water dense and appears light. Fatty tissue is practically radiotransparent and appears very dark in a mammogram. The dynamic range in mammography is large, since there are large variations in breast anatomy. Individual breast appearance is influenced by the volume of a woman's breast tissue and fat, her age, a history of previous pregnancies and lactation, her heredity, the quality and elasticity of her breast skin, and the influence of hormones. Normal anatomy on a mammogram will image differently depending on a woman's weight, age, presence of surgical scars and presence of superficial or submuscular implants, as well as the amount of fatty tissue in her breasts.
Microcalcifications
Calcifications are small deposits of calcium. They occur in the breast as a result of secretions within structures that have become thickened and dried. The diameter of microcalcifications is about 0.05mm up to 1 mm.23'24 On a digital image with a pixel spacing of 0.1 mm this equals an area of less than ten pixels. In comparison, the overall image matrix is about 4.500 x 5.500 pixels.
When microcalcifications indicate breast cancer, they are most frequently present in clusters of 10 to 100 single findings. Relevant for diagnosis are clusters with at least four findings per square cm. Single findings in a cluster can vary significantly in shape and size. Microcalcifications that originate from malignant lesions are typically very small, irregular in shape and size. The average distance of findings in a cluster is below 1 mm. There are also calcifications that originate from normal phenomena, for example in blood vessels, or as large deposits of calcium with diameters of several millimeters. Figure 2 shows a classification for clusters based on different morphology of individual findings as it was identified by Le Gal.19 This classification helps deciding whether the cluster belongs to a malignant lesion or a benign process.
2.2. Mammographic imaging modalities
Mammographic images pose a tough challenge for image processing. The images have poor signaltonoise ratio. They are blurred by scattered xray photon
radiation and by intensifying screen glare. In addition, there is a compromise between radiation dose and image quality. An xray mammogram is a twodimensional projection of a threedimensional anatomical structure. Thus the image inevitably superimposes tissue regions that are in fact not connected.
Today, there are three different xray mammography imaging technologies available:
• Full field direct digital mammography (FFDM)
• Digital luminescence radiography, also called Computed Radiography (CR)
• Secondary capture of analog film using a film digitizer (Laser or CCD).
Figure 1 shows examples of mammograms from these different technologies.
Due to the fact that direct digital systems are still significantly more expensive than conventional filmscreen based systems, there will be a coexistence of these three technologies for at least the next decade. This is a grand challenge for image analysis techniques designed for mammography: For an algorithm to be widely applicable, it has to perform well on all these image types.
To obtain a digital image from a conventional film, the film is digitized using a high quality laser scanner with optical densities of 4.0. Recently, novel CCDbased scanners also provide an acceptable digital image quality. The spacial resolution of film is about 13 to 15 line pairs per millimeter (LP/mm). Mammography scanners can digitize at a spacial resolution of 10 LP/mm. This corresponds to 50 microns. A filmbased system has as a nonlinear transfer function, due to film sensitivity depending on the dose.
Since structures indicating cancer might be very tiny, image quality requirements in digital mammography are extremely high. This was the main reason that for a long time there has been no adequate digital alternative to conventional filmscreen mammography. Actually, filmscreen technology used in conventional mammography is the last remaining nondigital imaging modality used in radiology. First digital systems were based on the storage of phosphor, so called digital luminescence or computed radiography (CR). However, at normal dose these systems have a relatively poor signalto noise ratio. Higher contrast is an advantage of CR systems.
Novel direct digital systems for mammography based on silicium or selenium detectors have been introduced in the last three years. The main advantage of full field direct digital mammography (FFDM) is high quanta efficiency. This allows for higher contrastdetail resolution at reduced dose. Further there is a linear relationship between dose and detector signal. This simplifies image processing based on dose models. Further there is significantly lower noise, because of less processing steps. A problem is still relatively low spacial resolution of only 5 up to 8 LP/mm. Thus very small microcalcifications are blurred or can not be detected at all.
Figure 3 shows an example of microcalcifications in digitized film versus a direct digital mammogram. The example hints the robustness that is required for an enhancement algorithm to be able to handle both types of images.
2.3. Image formation
In this section, we give a short explanation of how a digital mammographic image is generated. From this we develop a model that allows for the relevant imaging effects relevant for microcalcifications. These effects are noise and unsharp projection as described by K. Even.16 In Sec. 5.1 we apply this model to design an adapted filter.
Originating from a radiation source, an xray beam passes through the compressed breast. An intensifying screen is used as a signal amplifier before the dose is measured by a flat detector. The xray beam is attenuated depending on the absorption properties of the breast tissue. Calcium absorbs tens of times more xray photons than does other breast tissue. Thus xray mammography can make calcifications visible in the image.
This capability to visualize calcifications at a high spacial resolution is the main reason why clinicians use xray mammography for early breast cancer detection. Other modalities such as ultrasound and especially MR are better suited to distinguish malign tumors from healthy tissue. But they can not visualize microcalcifications, the earliest signs of cancer.
Main sources for noise are the limited number of xray quanta which form a Poissondistributed process, film granularity, varying absorption due to changing energy of the photons on their path through the breast, and random inhomogeneities in or on the intensifying screen.
Classical xray image formation generates geometric distortions. The main effect is the projection of a threedimensional anatomical structure onto image plane. This leads to superimposed tissue regions which can be a difficult source for artifacts. A magnification V := D/O results from the quotient of the distance from the focal spot to the film O and the distance from the focal spot to the object D. This magnification is about 1.1 to 1.4 for standard systems. The source of the xray beam has a diameter B. For mammography system the focal spot size is typically 0, 36 to 0, 6 mm,16'24 the area Br is about 0.01 to 0.2 mm.2 As a result there is a blur U := B(V — 1) of about 0,001mm and 0, 08 mm. microcalcifications have a diameter of about 0.05 to 1 mm, this blur is of almost the same order as the size of microcalcifications.
3. Method
In the last years, huge effort was spent on the enhancement and detection of microcalcifications.
It became clear quite early that mammograms cannot be enhanced by "from the book" global or fixneighborhood techniques due to their lack of adaptiveness. Most conventional enhancement techniques enhance not only the microcalcifications but also the background and noise. H. D. Cheng, X. Cai, X. Chen, L. Hu and X. Lou8 give a good overview of this history.
3.1. Known approaches
Microcalcifications appear at a range of varying sizes. Thus it is natural to approach this problem by multiscale techniques. Among the more recently developed techniques, most share a feature based approach based on multiscale filterbank decompositions. The most successful methods apply filterbanks that are variations of the standard discrete wavelet transform decomposition.
All authors used digitized film to evaluate their results. Thus evaluation of robustness was limited to that imaging technology. We go one step further, and derive a method that we evaluated on film as well as on images from direct digital modalities.
H. Yoshida et al.42 apply a discrete wavelet transform (DWT) with dyadic scales. They multiply every wavelet scale by a weight factor. Then they reconstruct an image by applying the inverse transform. The weights are determined by supervised learning, using a set of training cases. This approach results in an overall enhancement of edges and structures. There is no coefficient selection scheme in wavelet domain. Further, the DWT is not translation covariant. Thus if the origin of the image is shifted, then the result is inherently different.
R. Strickland et al.38 use the discrete wavelet transform (DWT) with biorthogonal spline filters. To overcome the restriction of dyadic scales and to adapt the transform better to microcalcifications they abandon the reconstruction property. They compute four dyadic scales plus two additional interpolating scales (voices). On every wavelet scale a binary thresholdoperator is applied. The responses of the individual wavelet scales are then combined by the rule of probability summation. The output is used as a feature for detection of microcalcifications. Despite being a very simple algorithm, the detection results of R. Strickland et al. demonstrate the power of a waveletbased approach. However, due to the thresholding, there is no way to reconstruct an image from the filterbank used. R. Strickland et al. also develop a matched filter model that we apply in Sec. 5.1 to determine wavelet functions that are appropriate for detection of microcalcifications.
L. P. Clarke et al.9'34'35 apply a denoising step to the image and then take the highpass scale of a discrete wavelet transform using spline wavelets. This results in a general edge detector which finds calcifications but also several other structures such as film artifacts or lines.
J. K. Kim et al.25 apply several directional Sobel operators. The results are weighted, depending on local variance, and then are recombined. An important advantage of this approach is the application of directional features with the capability to discriminate linelike structures from spotlike structures. Again, here the common approach is applied, consisting of applying a set of filters, modifying the coefficients, and recombining the result to an image. Unfortunately, the Sobel operators do not allow a perfect reconstruction. Thus this method, as is, is not suitable for enhancement of isolated structures such as microcalcifications. Due to the fact that the Sobel filters detect edges and are not specific with respect to microcalcifications, a preprocessing step to remove film artifacts is needed. This is done by setting pixels that differ from the neighborhood by values larger than a given threshold to the neighborhood average. Results of a receiver operating characteristic (ROC) analysis show, that this preprocessing step is an essential improvement to the method. The enhancement method of J. K. Kim et al. works fine on a phantom which consists of pixel size structures. It fails with larger structures, due to the fact that the Sobel filters are not scalable.
A. Laine et al.26'27 apply several wavelettype filterbank decompositions such as the dyadic wavelet transform, also called MallatAlgorithm, as described in S. Mallat and W. L. Hwang.29 An adaptive enhancement operator is defined on the wavelet coefficient scales. A. Laine et al. carefully design the adaptive enhancement operator in a very robust manner. Evaluating the method on phantoms they obtain good contrast improvement values for irregular structures such as microcalcifications. The enhancement operation is defined for each scale separately. However, A. Laine et al. do not exploit the correlation of wavelet coefficients over scales. Furthermore, the dyadic wavelet transform does not allow flexibility in the choice of discrete scales. In Sec. 5.2 we apply a variation of their adaptive enhancement operator which will be tailored specifically to detect microcalcifications.
There are extensions to the discrete wavelet transform, that allow interpolating scales, also called voices, as for example described by A. Aldroubi and M. Unser.1 There, the original dyadic wavelet scheme is repeated with auxiliary dilated wavelet functions. Thereby, for every dyadic scale a0 computed, one obtains additional scales a = a0 ■ 2i/M with i = 0,...,M — 1. The drawback of such an approach is the calculation of a rising number of irrelevant scales: in an iterative scheme one cannot omit computing intermediate scales. In 1D signal analysis this may not be a serious problem. Applied to images such as mammograms, where each scale costs 40 MB of storage, such an approach would be very inefficient.
3.2. The role of wavelets
For local image enhancement, waveletbased multiscale methods appear among the most successful techniques; an observation not limited to the enhancement of mammograms. Why is this the case?
One basic aim in image analysis is to decompose an image into well localized, interpretable components that make local features in the image easily accessible. Especially for mammograms, as was pointed out in Sec. 2.3, we need a feature extraction method that is robust with respect to images coming from different image sources such as digitized film or direct digital mammography.
A local decomposition of an image can be accomplished by the twodimensional continuous wavelet transform (CWT) over the Euclidean group with dilation G := R2 x (R+ x SO(2)). This transform was investigated in depth by J.P. Antoine, P. Carette, R. Murenzi and B. Piette.4 The CWT provides an image decomposition into coefficients that describe the local geometry of the image in terms of scale and orientation. Further, the continuous wavelet decomposition is flexible with respect to image resolution as well as the size of the objects of interest.
However, it is not trivial to translate the continuous model into a discrete algorithm. Analyzing the approaches cited above, we find that in most cases limitations arise from the discrete wavelet transform applied. How can we fix this problem? Obviously, there is need for a discrete wavelet filterbank that is less restrictive and provides more flexibility to support model based approaches to enhancement of microcalcifications.
To discretize means to compute the wavelet coefficient on a discrete subset of the continuous group only. The resulting discrete transform should retain the interesting properties of the continuous wavelet transform. For image enhancement in digital mammography the most important properties are invertibility, translation covariance and flexibility in the choice of discrete scales.
Invertibility of the transform provides a means to reconstruct the image from its discrete wavelet coefficient. This implies that there is no information lost in the decomposition step.
Translation covariance means, that if the original image is shifted, the wavelet coefficient should also only be shifted. This leads to equidistant sampling of translations, independent of scales, and forces a redundant transform, compare A. Teolis.39
Details of image structures often exist between commonly used dyadic scales. For precise localization in scale we thus need flexibility to discretize scale and orientation depending on the specific problem. The standard discrete wavelet transform (DWT) only fulfills the first requirement, i. e. invertibility. The dyadic wavelet transform or MallatAlgorithm is also translation covariant. But none of the classic discrete versions of the continuous wavelet transform provide flexibility with respect to scale and choice of wavelet.
However, this problem can be solved: There is a suitable method, so called integrated wavelets, that was proposed first by M. DuvalDestin, M. A. Muschietti and B. Torresani15 for affine wavelets. We extended their original approach to wavelet transforms over semidirect product groups G = Rm x H and provided an implementation.20'21 An introduction to integrated wavelets is given in Sec. 4.
3.3. Transform based enhancement
It is a classical approach in image processing to transform an image into a representation that is more suited for solving a specific problem than working with its representation on the original coordinate grid. For enhancement of microcalcifications in digital mammograms we propose the use of wavelets, especially the integrated wavelet transform.
The method consists of the following steps: At first, we compute a multiresolution decomposition of the image into wavelet coefficients, using an appropriate wavelet transform WT. Then we define a local enhancement operator E and apply it to the wavelet coefficients. Finally, we reconstruct the enhanced image using perfect reconstruction filters generated by a reconstruction operator WT1.
Our aim is enhancement of microcalcifications in digital mammograms without introducing artifacts. We show in Sec. 5, that using the integrated wavelet transform we can improve other methods that were based on dyadic wavelets. The wavelet plays the role of a matched filter and determines the magnitude of the wavelet coefficients, especially the points of local extrema. A model based approach leads us to a Gaussian wavelet that matches the unsharp projection of a microcalcification on the film plane in a noisy background. The enhancement operation E on the wavelet coefficients is defined by a heuristic rule. A. Laine et al.27 introduced so called spot enhancement. As operation on wavelet coefficients we use a refined version.22
Original image > Enhanced microcalcifications
WT1
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