A digital density equalization technique to improve ... - Semantic Scholar

The British Journal of Radiology, 73 (2000), 410±420

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2000 The British Institute of Radiology

A digital density equalization technique to improve visualization of breast periphery in mammography A P STEFANOYIANNIS, MSc, L COSTARIDOU, PhD, P SAKELLAROPOULOS, MSc and G PANAYIOTAKIS, PhD Department of Medical Physics, School of Medicine, University of Patras, Patras 26500, Greece

Abstract. In mammographic imaging, the ®lm area corresponding to the breast periphery is overexposed, resulting in high optical density and degraded contrast in this region. A digital, model-driven density equalization technique was designed and developed to overcome this overexposure problem, taking into account the non-linear characteristic curve of the ®lm-digitizer system. The method is based on several image processing and analysis techniques, such as thresholding, which is used to segment the pixels of the mammogram belonging to the breast region from the background, and wavelet-based fusion, which is used to equalize the pixels of breast periphery selectively while leaving the remaining breast region unaffected. Initial application of the method resulted in density-equalized mammographic images, characterized by improved contrast at the breast periphery. Mammography is at present the most reliable and effective method for the early detection of breast cancer. To achieve good visualization of low contrast mammographic abnormalities, use of high contrast screen±®lm combinations is essential. However, increase in ®lm contrast is obtained at the expense of the useful exposure range (latitude) of the ®lm. This, in combination with the fact that exposure parameters are determined so as to ensure good visualization of the mammary gland, results in an overexposure of the ®lm area corresponding to the breast periphery, leading to high optical density and degraded contrast in this region [1±4]. The degree of overexposure depends on the reduced thickness of the periphery as well as the degree of compression of the breast. To overcome this overexposure problem, which leads to poor visibility of the anatomical details of the breast periphery (although radiologists differ as to the importance of the periphery), several equalization techniques have been proposed. Exposure equalization techniques aim at reducing the exposure dynamic range (i.e. the ratio of the maximum to the minimum X-ray exposure at the image detector). The simplest techniques reduce the exposure delivered at the area of the screen± ®lm system corresponding to the breast periphery, using solid or elastic anatomical ®lters [1±5]. Received 21 December 1998 and in ®nal form 4 August 1999, accepted 19 October 1999. Address correspondence to Dr George Panayiotakis. This work has been supported by the General Secretariat of Research and Technology (GSRT, PENED '95, contract No 1474). 410

These techniques are inexpensive and easy to use, but they are not easily applicable in the case of oblique views. More sophisticated techniques modulate the entrance exposure, based on feedback of the regional variations in X-ray attenuation [6±13]. These methods result in improved imaging not only at the peripheral tissues, but also at inner breast regions. However, the methods are quite complex and have not yet been substantiated by clinical results. Recently, the possibility of embedding digital concepts in an exposure equalization technique has also been pointed out [14]. A completely different, and relatively new, approach incorporates the application of computer-based techniques [15±17]. These techniques make the density at the peripheral breast tissues equal to the density at the mammary gland and some of them also improve the contrast at the periphery to a certain extent. In the present paper we present a computerbased, model-driven density equalization technique for mammographic images. The method is based on several image processing and analysis techniques, such as thresholding, which is used to segment the breast region pixels from the background pixels, and wavelet-based fusion, which is used to equalize the density of the pixels of breast periphery selectively with the density at the mammary gland. Equalization is obtained by adaptive shifting of the range of densities of breast periphery to the linear, high contrast part of the ®lm-digitizer system characteristic curve. Initial application of the method has demonstrated that it is able to equalize the density of mammographic images and to improve the The British Journal of Radiology, April 2000

Digital equalization in mammography

contrast at the breast periphery. (A glossary of the image processing and analysis terminology used in the paper can be found in the Appendix.)

Materials and methods The basis of the proposed method is processing of the information stored on ®lm, without taking into account the processes of image formation. Our present study considers the non-linear behaviour of the ®lm-digitizer system as the main cause of degraded image quality in breast periphery. Figure 1 depicts the major steps of the proposed method (System Curve based Density Equalization (SCuDE)), which are described in the following subsections. The ®rst step is digitization of the mammogram under consideration, transforming the ®lm optical density values into a set of grey level values, which can be later processed by a computer system. The problem that has to be dealt with afterwards is segmentation of the breast region, i.e. the region of interest (RoI), from the background of the mammogram. This is done according to a model of the mammographic image, which is presented schematically in Figure 2. The segmented breast is subsequently ®ltered to achieve good visualization of the image region corresponding to the overexposed breast periphery. The resulting ®ltered image is characterized by density equalization of the entire breast region, but is of degraded contrast at the area corresponding to the mammary gland. The well visualized mammary gland area of the initial image must therefore be combined with the well visualized breast periphery area of the ®ltered image, which is done in the fusion step. The end product of this technique is a high quality image, both at the periphery and the mammary gland.

Figure 1. Flow chart of the SCuDE technique. The British Journal of Radiology, April 2000

Figure 2. The mammographic image model. Different mammographic image regions (background, breast periphery, mammary gland) are denoted. Determination of breast contour and inner breast border is based on a pixel classi®cation procedure, whereas for the inner breast border, system characteristic curve data are also taken into account.

Segmentation Segmentation aims to partition an image into disjointed regions, each uniform with respect to a certain characteristic (such as brightness or texture), but such that no union of adjacent regions is uniform. It is a process of pixel classi®cation: the picture is segmented into subsets by assigning the individual pixels to different classes, corresponding to different image regions. We employ segmentation to deal with the problem of isolation of the breast region from the background of the mammogram. The main effort behind this step is the search for various features that can be used to discriminate the breast region from the background and thus locate the breast contour. These features will be utilized to assign a pixel to either the breast or the background region, through a classi®cation process. According to our observations, the background image differs from the breast image with respect 411

A P Stefanoyiannis, L Costaridou, P Sakellaropoulos and G Panayiotakis

not only to the degree of blackening but also to texture. The background is an almost uniform black region: any sources of inhomogeneity result from the statistical character of the imaging process. The breast region, on the other hand, is characterized by a lower degree of blackening and greater inhomogeneity, owing to the presence of anatomical details. The mean and standard deviation of grey level values were selected to represent the degree of blackening and texture, respectively. With respect to texture, several second-order statistical features [18] were considered and evaluated in a preliminary study, taking into account both discriminating ability and computational cost. Standard deviation was selected owing to low computational cost, as compared with other highly discriminating features. Since the segmentation process depends on grey level based features, a pre-processing stage is necessary to reduce the level of background noise. Pre-processing combines the use of mathematical erosion [19] with a smoothing operation. Erosion acts as a local minimum ®ltering operation, which enhances the dark, low grey level areas of the ®lm and produces a more uniform background. Erosion is followed by a smoothing step, acting as a local average in a 565 pixel neighbourhood, and therefore further reducing local background variations. The pre-processed mammogram is only used in the segmentation stage, while in subsequent processing steps the initial mammogram is utilized. The segmentation method applied is sequential [20]. Thus, while processing a pixel, results of previously processed pixels are taken into account. The segmentation steps are: (1) de®nition of a 565 pixel neighbourhood centered at the starting pixel; (2) calculation of the mean and standard deviation of grey level values of the neighbourhood. This set of features forms the pattern of the pixel and is subsequently used in classi®cation; (3) repetition of the above steps for pixels of the same row, scanning the picture row by row; (4) estimation of the distance in feature space (mean grey level vs standard deviation of grey level plane) between the patterns of two adjacent pixels. If this distance is below a prede®ned threshold, estimated in the preliminary study, the second pixel is also assigned to the background and the background pattern is reevaluated. If this difference is above the threshold, the pixel is assigned to the breast region, labelled as a contour pixel, and the algorithm starts scanning a new row; (5) repetition of the scanning in a reverse (bottom-up, right-to-left) fashion, in case the last contour pixel is not as close as possible to the ®lm edge (elongated breast 412

towards the bottom of the ®lm), to locate border points in the opposite side of the breast.

Equalization by ®ltering After segmentation, a digital grey level equalization ®lter is applied to the optical density values of the breast region. The objective of this step is restoration of the modulated beam information, recorded on ®lm, which is degraded by the non-linear behaviour of the ®lm-digitizer system. The system characteristic curve, supplemented by a grey level vs optical density curve of the digitizer used in this study, is presented in Figure 3. Since the pixels of breast periphery are overexposed, their corresponding density values are gathered at the toe of the system characteristic curve. This range of density values is directly related to a range of exposure values. Equalization is obtained by shifting the range of exposure values to the linear, high contrast part of the curve, so that it is centred at the exposure value corresponding to the mean density of the mammary gland. The shifting results not only in density equalization, but also in contrast enhancement. The ®ltering steps are: (1) collection of data concerning the ®lm detector and the image digitizer characteristic curves; (2) derivation of the system characteristic curve by means of a ®fth-degree polynomial interpolation scheme [21]; (3) calculation of the maximum exposure value corresponding to the linear part of the system characteristic curve; (4) segmentation of the breast periphery, based on the same sequential scheme as described in the segmentation subsection above. The feature utilized in this step is the mean grey level value, and its threshold corresponds to the previously calculated lower end-point of the linear part of the system characteristic curve, since the breast periphery region is modelled as the set of pixels with density values corresponding to the low contrast toe of the ®lm-digitizer curve. This segmentation stops at inner border pixels; (5) calculation of the exposure range corresponding to the breast periphery, based on the system characteristic curve; (6) calculation of the mean grey level value and the corresponding exposure value at the mammary gland, utilizing the inner breast contour derived at the previous segmentation step. This calculation does not depend very strongly on the exact localization of the inner breast contour; (7) shifting of the calculated breast periphery exposure range to the linear part of the system characteristic curve, and centring at the exposure value corresponding to the mean grey level value of the mammary gland. However, the above-described ®ltering results The British Journal of Radiology, April 2000


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(b)

Figure 3. (a) Film-digitizer system (Kodak MIN-R and Lumiscan 75) characteristic curve. The SCuDE technique exploits this curve to equalize the density in the mammographic image. (b) Digitizer characteristic curve used in this study.

in shifting the density values corresponding to the mammary gland to the shoulder of the ®lmdigitizer characteristic curve. Consequently, the contrast of the ®ltered image at the mammary gland is degraded as compared with the original image. This introduces the need for the next step.

Fusion The main goal of this step is to utilize the well visualized mammary gland, available at the initial image, with the well visualized ®ltered breast periphery. This is performed by means of a fusion scheme, based on the well established wavelet transform [22±24]. The selection of fusion scheme is based on the assumption that visualization is related to texture. For example, the well visualized mammary gland in the initial image and the ®ltered breast periphery are both characterized by high texture. Since texture is directly related to the presence of edges, a wavelet-based fusion scheme utilizing edge information is adopted [25]. The steps of the fusion algorithm are: (1) calculation of wavelet transform of both the initial and the ®ltered image. It consists of magnitude and phase wavelet coef®cient matrices, computed at ®ve scales, as well as an approximation image; (2) comparison of corresponding magnitude coef®cients between the initial and the ®ltered mammogram, higher coef®cients being selected for the construction of the fused image magnitude wavelet coef®cient matrix for each scale; this selection of maxima is based on the fact that a higher value of a certain magnitude coef®cient denotes a stronger presence of the corresponding edge; (3) derivation of the approximation image and the phase wavelet coef®cient matrix of the fused mammogram, utilizing the corresponding areas of the initial or the ®ltered image, where the background, the mammary gland and the breast periphery are optimally visualized; (4) application of the inverse wavelet transform on the wavelet The British Journal of Radiology, April 2000

representation of the fused image, to revert to the image domain.

Implementation details The mammographic images utilized in this study were acquired with medium screens and ®lms (Kodak MIN-R, Kodak, CA, USA) and digitized by a Lumiscan 75 (Lumisys Inc, Sunnyvale, CA, USA) at 12-bit pixel depth, a spatial resolution of 100 mm and 200062500 pixel image matrix. The characteristic curve of the Lumiscan 75 digitizer was found to be adequately linear up to an optical density (OD) of approximately 3.3, which was the maximum measured in this study. The noise level, calculated as the standard deviation for a certain grey level value divided by that grey level value, was less than 4% for all grey level values. These performance characteristics make the Lumiscan 75 ®lm digitizer suitable for the purposes of this study. A set of 15 mammographic images was used to derive the threshold used in the segmentation step. Images are displayed on a monitor, utilizing digital medical image visualization software [26, 27]. However, if a ®lm printer is available, the images can also be printed in ®lm and viewed by means of a lightbar. Processing was carried out with a Pentium 200 MHz, 64 MB RAM. The technique was developed in C language. The wavelet transform routines were taken from the Wave2 source code [28] and interpolation routines were taken from the literature [21]. The execution time of the program for this speci®c con®guration of computer and software and a 5126512 image is approximately 2.5 min.

Results The result of application of the technique to three mammograms of different breast patterns is demonstrated in Figures 4±6. Figure 4a shows a mammographic image, characterized by good 413


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Figure 4. Mammogram corresponding to ®brocystic breast pattern. (a) Initial mammographic image, with the breast periphery poorly visualized. (b) The breast region produced by the segmentation step. All subsequent processing is done in this region. (c) Result of the equalization by ®ltering step. Breast periphery visualization improves but image quality at the mammary gland is degraded. (d) Final mammographic image, after application of the fusion step. Both breast periphery and mammary gland are visualized. The nipple, areola, skin, subcutaneous fat, surface veins and some of the peripheral Cooper's ligaments are better visualized than in the original mammographic image (a).

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The British Journal of Radiology, April 2000


visualization of the mammary gland and overexposure of the breast periphery; the various anatomical features of breast periphery are poorly visualized. Figure 4b depicts the breast region of the mammographic image in Figure 4a, as estimated by the segmentation step. The result of the equalization by ®ltering is depicted in Figure 4c; visualization of breast periphery is substantially improved. In particular, the nipple, areola, skin, subcutaneous fat, surface veins and some of the peripheral Cooper's ligaments are visualized better than in the original mammographic image of Figure 4a. However, all information concerning mammary gland anatomical structures is essentially lost. Application of the fusion scheme combines the mammary gland in the initial mammogram with the ®ltered breast periphery. The ®nal resulting image, presented in Figure 4d, is characterized by good visualization of both the mammary gland and the periphery. Two further examples of initial and ®nal images, corresponding to mammograms of different breast patterns, are presented in Figures 5 and 6.

The technique produced successful results with 30 mammograms of three breast patterns (dense mammary gland with ®brocystic changes, uniformly dense parenchyma with smooth contour, normal parenchyma occupying ,25% of breast volume in retroareolar location) examined so far. Density pro®les along the same line for the original and the ®nal mammographic images are shown in Figure 7. The density equalization effect of the technique is illustrated, since its application results in an average density of breast periphery that matches the mean density of the mammary gland; the density of the mammary gland remains practically unaffected. Figure 8 provides a further demonstration of the equalization effect of the SCuDE technique. A histogram of the breast region of the ®nal image is shifted to higher grey level values, resulting in an average density of breast periphery that is closer to the mean density of the mammary gland. Histograms of the magnitude of wavelet coef®cients, corresponding to the breast periphery

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(b)

Figure 5. Mammogram corresponding to dense breast. (a) Initial mammographic image. (b) Final mammographic image. Application of the SCuDE technique resulted in nipple, areola and skin becoming visible, as well as surface veins and peripheral Cooper's ligaments being better visualized than in the original mammographic image. The British Journal of Radiology, April 2000

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Figure 6. Mammogram corresponding to breast pattern with partial fatty replacement and normal parenchyma occupying the retroareolar region. (a) Initial mammographic image. (b) Final mammographic image, characterized by improved visualization of the skin, areola, subcutaneous fat and peripheral Cooper's ligaments.

of the initial and ®nal mammographic image, are presented in Figure 9a and Figure 9b, respectively. Contrast is considered to be represented by the magnitude of the wavelet coef®cients [23, 29, 30], corresponding in this ®gure to the second scale. Examination of Figure 9 demonstrates the contrast improvement of breast periphery in the ®nal image, as characterized by the higher magnitude of the wavelet coef®cients. Contrast enhancement of breast periphery inevitably results in noise increase at this region. Noise level in breast periphery in both the initial and the ®nal images was estimated as the mean power of the magnitude wavelet coef®cients of the ®rst-scale, ranging from zero up to a reference noise power; the reference noise power was estimated as the mean power of the ®rst-scale 416

Figure 7. Density pro®les along the same line of the original and ®nal mammographic images. Application of the technique results in an average density of breast periphery that matches the mean density of the mammary gland, while leaving the density at the mammary gland practically unaffected. The British Journal of Radiology, April 2000


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Figure 8. Histogram of the breast region in (a) the initial mammographic image and (b) the ®nal mammographic image. Low grey level values, corresponding to pixels of the overexposed breast periphery, are shifted to higher values.

A digital density equalization technique was designed and developed to overcome the problem of breast periphery overexposure in mammographic images. This technique, driven by a model of the mammographic image, takes into account the non-linear characteristic curve of the ®lm-digitizer system in order to restore the

modulated beam information that is degraded by the recording and digitization process. The technique is applicable to any ®lm-digitizer system, but its performance is expected to be affected by the characteristic curves of the ®lm and the digitizer. This is more evident when using digitizers that are unable to handle the very high optical densities achieved by certain kinds of ®lm. Mammographic density is equalized by matching the mean density value of the breast periphery in the ®nal image to the mean density value of the mammary gland in the initial mammogram. The SCuDE technique is independent of breast size, breast symmetry, imaging geometry and type of mammographic unit used. Application of the technique results in density equalization, as well as improvement of the contrast of the breast periphery. Density equalization combined with contrast enhancement enhances the visualization of the breast periphery, and so the diagnostic information conveyed by the ®nal mammographic image should be improved as well. This expected improved visualization of the breast periphery is obtained with no additional dose to the patient, as there is no need to acquire a second

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magnitude wavelet coef®cients in the background of the mammogram [31]. Noise increase was computed as the percentage difference of the ®nal noise level and the original noise level, and was quanti®ed to be about 25%. Similar calculations for other scales resulted in lower values of noise increase. On the other hand, contrast improvement at the breast periphery is around 200%, as calculated by the shift of the mean value of the histograms of the magnitude of wavelet coef®cients of the initial and the ®nal mammographic image. The breast periphery contrast enhancement and density equalization override the noise increase, resulting in a ®nal image where the corresponding region is better visualized.

Discussion

Figure 9. Histogram of the magnitude of wavelet coef®cients (second scale), corresponding to the periphery of (a) the initial mammographic image and (b) the ®nal mammographic image. The periphery of the ®nal image is characterized by higher magnitude wavelet coef®cients, and therefore improved contrast. The British Journal of Radiology, April 2000

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mammographic image selecting exposure parameters that would result in good visualization of breast periphery. The digital character of the technique should allow it to be integrated into a digital mammographic image processing and analysis workstation; and the technique might well be suitable, after certain modi®cations, for dealing with other equalization problems such as those encountered in chest imaging [32]. Digital processing of mammographic images could be of great bene®t to the radiologist. Nevertheless, it has been pointed out that general purpose image processing that is not model-driven is likely to be of little use [33]. Furthermore, imaging should be regarded as a way of optimally storing information on ®lm or in a computer and visualization enhancement should be applied afterwards in a separate process from acquisition [34]. Our approach in the present study goes along with both these trends. Finally, future work needs to be carried out to improve the SCuDE technique. First, a density correction scheme must be incorporated to take into account variations in thickness of the breast periphery. Second, optimization of the segmentation and fusion steps, with respect to visualization performance and execution time, remains an open question. Third, application of a de-noising algorithm before applying the SCuDE technique would control the increase in noise level. Last but not least, the SCuDE technique must be evaluated quantitatively as well as clinically, to test its performance with mammograms of all types and breast patterns, and to check whether it affects the image quality of the main breast area.

Acknowledgments The authors would like to thank the staff of the Department of Radiology of the University Hospital of Patras for their contribution.

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Appendix: Image processing and analysis terminology Approximation image: original image, ®ltered by a smoothing scaling function at the coarsest scale. Class: one of a set of mutually exclusive, preestablished categories to which an object can be assigned. Density: see grey level. Digital ®lter: any digital image processing technique that increases subjective and/or objective image quality, by sharpening certain features (e.g. edges, contrast) and by reducing noise, or that moderates the degradations introduced by the sensing and acquisition devices. Digitization: the process of converting an analogue image of a scene into digital form. Edge: a set of pixels belonging to an arc and having the property that pixels on the opposite side of the arc have signi®cantly different grey levels. The British Journal of Radiology, April 2000

Feature: a characteristic of an object; something that can be measured and that assists in classi®cation of the object (e.g. size, texture, shape). Feature space: in pattern recognition, an ndimensional vector space containing all possible feature vectors (patterns). Grey level: the value associated with a pixel in a digital image, representing the brightness in the original scene at the point represented by that pixel. It is inversely proportional to the degree of blackening at the corresponding point (a low degree of ®lm optical density corresponds to a high value of grey level). Image fusion: combination of two or more registered images, with the objective of producing a single image of additional diagnostic information. Image segmentation: partition of an image into disjoint regions, each of which is uniform with respect to a certain characteristic (such as brightness or texture), but such that no union of adjacent regions is uniform. Image transform: mapping of image data into image data. An image transform generates one or several resultant images out of one or several given images. It is generally considered to be a process of analysis, breaking the image down into its elemental components (basis images) and providing further information that is not readily available in the raw image data. Inverse image transform: process of synthesis, reassembling the original image from its components via summation. Matrix of magnitudes of wavelet coef®cients: matrix of the magnitudes of the horizontal and vertical wavelet coef®cient matrices. Magnitudes of wavelet coef®cients represent local intensity variations, corresponding to edges. Mathematical erosion: mathematical morphology process that acts in a neighbourhood as a local minimum ®lter. Neighbourhood: a set of pixels located near a given pixel. Neighbourhood operation: an image processing operation that assigns a grey level to each output pixel on the basis of the grey level of pixels located in the neighbourhood of the corresponding input pixel. Noise: irrelevant components of an image that hamper recognition and interpretation of the data of interest. Object: in pattern recognition, a pixel or connected set of pixels, usually corresponding to a physical object in the scene represented by the image. 419


Pattern: a vector of features, expressing a meaningful regularity characterizing members of a class, which can be measured and used to classify objects. Pattern classi®cation: process of categorizing input data into identi®able classes via the extraction of signi®cant features from a background of irrelevant detail. Pattern recognition: the detection, measurement and classi®cation of objects in an image by automatic or semi-automatic means. Phase gradient vectors: matrix of the phases of the matrix of gradient vectors. Pixel: contraction of picture element. The basic unit of which a digital image is composed. Region: a connected set of pixels in an image. Registered images: two or more images of the same scene that have been positioned with respect to one another so that the objects in the scene occupy the same positions. Scale: in wavelet analysis, a term meaning the same as scale in geographical maps. Very large scales mean global views, while very small scales mean detailed views. System: anything that accepts an input and produces an output in response. System characteristic curve: curve that relates a system input value to the corresponding system output value (e.g. an optical density vs exposure curve for a ®lm detector, or a

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grey level vs optical density curve for a digitizer). Texture: in image processing, an attribute representing the amplitude and spatial arrangement of the local variation of grey level in an image. It is a measure of image coarseness, smoothness and regularity. Thresholding: one of the most important approaches to image segmentation. It is the process of producing a binary image from a grey scale image by assigning each output pixel the value 1 if the grey level of the corresponding input pixel is at, or above, the speci®ed threshold, and the value 0 if the input pixel is below that level. Thresholding can be applied to a property other than grey level by ®rst using an operation that converts that property to grey level. Transform domain ®ltering: modi®cation of the weighting coef®cients (transform coef®cients) prior to reconstruction of the image via the inverse transform. Wavelet coef®cients: result from ®ltering of the original image by spatially oriented horizontally and vertically two-dimensional wavelet transform. Wavelet transform: signal decomposition onto a set of basis functions, which are waves of limited duration and are referred to as wavelets.

The British Journal of Radiology, April 2000