British Journal of Radiology 74 (2001),913-919 © 2001 The British Institute of Radiology
Quantifying image quality at breast periphery vs mammary gland in mammography using wavelet analysis
L Costaridou, PhD
P Sakellaropoulos, MSc
A P Stefanoyiannis, MSc
E Ungureanu, MSc
and
G Panayiotakis, PhD
Department of Medical Physics, School of Medicine, University of Patras, 26500 Patras, Greece
Correspondence: George Panayiotakis
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Abstract
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Use of high contrast film–screen systems in mammography, in combination with the fact that exposure parameters are selected to ensure good visualization of the mammary gland, results in overexposure of the film area corresponding to the breast periphery, therefore decreasing image quality. The aim of this work was to provide a quantitative evaluation of image quality at the breast periphery compared with the mammary gland. To deal with the difficulties in quantification of image quality introduced by low contrast encountered at the breast periphery, wavelet analysis has been used for derivation of a contrast indicator (CI) and a noise indicator (NI), taking into account local grey level variations. Gradient magnitude coefficients corresponding to region of interest (ROI) grey level values are the basis of CI definition. Mammary gland and breast periphery were sampled by equally spaced ROIs, the quantity of which was determined by a heuristic method. For NI definition, the power values of gradient magnitude coefficients corresponding to the ROI were utilized. Image quality at the breast periphery compared with the mammary gland was evaluated using 150 craniocaudal images from the Digital Database for Screening Mammography. Measurements were carried out using a tool developed in our department. A 50% contrast decrease at the breast periphery was observed, while noise decreased by approximately 2%.
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Introduction
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Mammography is the most effective method for the early detection of breast cancer. The earliest mammographic indicators associated with breast disease are often very subtle features, thus the use of high contrast film–screen combinations is essential. High contrast film has a narrow latitude. The reduced thickness of breast periphery compared with the main breast area results in a lower attenuation of the X-ray beam in this region. This, in combination with the fact that exposure parameters are determined to ensure good visualization of the mammary gland, leads to an overexposure of the film area corresponding to the breast periphery. Consequently, image quality is degraded at the periphery and information concerning anatomical features may be lost.
Although poor visualization of breast periphery is a fact, acknowledged by efforts to optimize film design and use [1] as well as developing exposure and density equalization techniques [2–9], there have been few attempts to quantify image quality in this region. Visualization of breast periphery in mammography has been qualitatively assessed for the need for an observer performance study of an exposure equalization technique based on an anatomical filter [10, 11]. More recently, mammographic image quality has been assessed quantitatively, in terms of optical density and contrast, in three anatomical regions of the mammogram: pectoral muscle; main breast; and breast periphery [12].
The aim of this work is to provide a quantitative evaluation of image quality at the breast periphery compared with the mammary gland in mammography. Image contrast and noise have been selected as image quality characteristics. To deal with the low contrast encountered at the breast periphery, multiresolution analysis has been used as a visualization aid, as well as for contrast indicator (CI) and noise indicator (NI) derivation. Measurements have been carried out locally in regions of interest (ROIs) sampling the mammary gland and breast periphery.
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Materials and methods
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Using wavelet analysis to represent contrast/noise at the breast periphery
Definitions of image quality parameters include the notions of "signal" and "background". Contrast is defined as the difference in optical density (OD) or grey level (GL) values between the signal and its surrounding background. Noise is usually calculated as the standard deviation of OD or GL values over expected uniform areas. In mammograms, the degraded contrast of breast periphery relative to the mammary gland introduces difficulties in quantification of image quality in this region. Recently, mammographic image quality has been quantified with respect to contrast in three distinct areas of the mammogram, including breast periphery, by means of a contrast index [12]. This index is defined as the difference between the maximum and the minimum OD in the main breast area, the pectoral muscle and the breast periphery, and offers a global estimation of contrast, without taking into account local GL variation. Wavelet transform is a mathematical tool that provides information about local GL variations, having basis functions localized in both spatial frequency and spatial position [13–18]. Specifically, the non-subsampled biorthogonal discrete wavelet transform (NB DWT) of Mallat and co-workers, whose basis functions are partial first order derivatives of a smoothing function, provides multiscale GL gradients, associated with local contrast [19, 20]. Figure 1
demonstrates this property by depicting gradient magnitude images of two regions of the Leeds phantom [21] at four scales. The first region contains a uniform area and the second a 6 mm, 2% nominal contrast circular detail under calibrated X-ray beam conditions [21].
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Figure 1. Example of local contrast visualization at the first four scales of gradient magnitude images of the non-subsampled biorthogonal discrete wavelet transform. 1.a and 2.a show original uniform and low contrast detail regions of interest, respectively. 1.b–1.e and 2.b–2.e show corresponding gradient magnitude images.
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In addition, wavelet analysis can be utilized for noise estimation. For this reason, the signal decomposition in multiple frequency bands, as well as the signal compression property of the transform, are exploited.
Contrast indicator
To derive the CI and NI, four scales of the NB DWT have been used. The magnitude of wavelet coefficients in scales other than the first scale (scale of highest spatial frequency), corresponding to a certain ROI sampling the breast periphery or the mammary gland region, are used for contrast estimation. Specifically, the wavelet coefficient magnitudes are averaged to derive the CI of the ROI. The CIs for all ROIs sampling a region are then averaged to derive the CI of the region. Thus, the CI of a region at scale s (CIs) is given by
where N is the number of ROIs, Ms(m,n) is the gradient magnitude at scale s corresponding to pixel x(m,n), Ri is the ROI i and Ci is the number of pixels at ROI i.
Noise indicator
Wavelet analysis can also be exploited for noise measurements, as it decomposes the signal in multiple scales (spatial frequency bands) [18, 22, 23].
The first scale of the NB DWT is used for noise estimation, as it is the scale that is mostly contaminated by noise owing to its high frequency content. In addition, due to the signal compression property of the wavelet transform, coefficients corresponding to signal are expected to be higher than coefficients corresponding to noise. Thus, application of a threshold to the first scale magnitude of wavelet coefficients to separate signal from noise is justified. This threshold is derived from a reference ROI, corresponding to a signal-free area belonging to the background of the mammogram. It is computed as the mean power of the first scale magnitude of wavelet coefficients of the reference ROI. Subsequently, noise level in a ROI where measurement is carried out is estimated as the mean power of the first scale wavelet coefficient magnitudes ranging from zero up to the threshold [24]. Finally, the NI of a region is computed as the average of the NIs of the ROIs sampling the region. Thus, the NI of a region can be expressed as
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in which
where P1(m,n) is the power of gradient magnitude at scale 1 corresponding to pixel x(m,n), RT,i is the set of pixels belonging to ROI i for which x(m,n)<T holds, CT,i is the number of pixels at set RT,i, Rref is the reference region and Cref is the number of pixels at the reference ROI.
Sampling the mammary gland and breast periphery regions
Measurements were carried out in craniocaudal mammograms in two anatomical areas of interest; the mammary gland and the breast periphery. These two areas were sampled with an adequate number of equally spaced ROIs to decrease the total number of measurements required. Due to significant overexposure of the breast periphery, this area can hardly be discriminated from the background of the mammogram (discrimination of breast border) and the mammary gland area. Local contrast visualization, provided by gradient magnitude images, facilitates breast border discrimination and subsequent ROI size selection and positioning. Figure 2 demonstrates positioning of the sampling ROIs and the selection of sampling ROI size, facilitated by wavelet visualization.
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Figure 2. Sampling mammary gland and breast periphery regions in a craniocaudal mammogram. (a) Positioning of regions of interest (ROIs). (b) Example of ROI positioning and size selection, facilitated by gradient magnitude images.
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The number of ROIs required to adequately sample the mammary gland and the breast periphery was determined using a subset of 10 images from the case sample. The ROI size was adjusted to the size of the breast periphery and remained constant for each image. For each image, the two regions were initially densely sampled by a maximum number of non-overlapping ROIs. Subsequently, the CIs for the second, third and fourth scale and the NIs were measured for each ROI, providing a maximum set of measurements. For a given number of ROIs, corresponding to a certain degree of sampling of a region, 10 subsets of measurements, randomly selected from the maximum set of measurements, were used to derive region CIs and NIs. The variability of region CIs and NIs for a given number of ROIs is assessed by their standard deviation. The procedure is repeated to estimate the variability of the region CIs and NIs for different numbers of sampling ROIs. Finally, the number of sampling ROIs is determined as the number for which the standard deviation shows no further practical reduction with increasing numbers of ROIs. Figure 3 presents the variability of the region CIs and NIs as a function of the number of ROIs for the second and first scale, respectively. The same trend was observed for CI measurements for the third and fourth scale.
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Figure 3. (a,b) Assessment of adequate number of sampling regions of interest (ROIs) for contrast indicator of mammary gland and breast periphery regions, corresponding to the second scale. (c,d) Assessment of adequate number of sampling ROIs for noise indicator of mammary gland and breast periphery regions, corresponding to the first scale. Arrows indicate the adequate number of ROIs.
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Image visualization and measurements
CI and NI measurements have been performed on each of the digitized mammograms using a tool developed in our department [25, 26]. This tool is domain-specific to medical imaging, especially mammographic imaging. In addition to conventional visualization operations, it provides wavelet functionality applied locally or globally.
Figure 4 presents instances of the medical image visualization tool in CI and NI measurements for a single ROI situated at the mammary gland. In Figure 4a, the original ROI is positioned at the mammary gland, while the reference ROI for noise estimation is positioned at the background of the mammogram. Figure 4b shows the gradient magnitude images corresponding to the first two scales of these two ROIs. The ROI mean value in Figure 4c, measured at the second scale, corresponds to the CI, while the NI measured at the first scale is represented by ROI noise level (Figure 4d).
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Figure 4. Instances of the medical image visualization tool used. (a) The original region of interest (ROI) is positioned at the mammary gland, while the reference ROI for noise estimation is positioned at the background of the mammogram. (b) Gradient magnitude images corresponding to the first two scales of the original and reference ROI. (c,d) Histogram plots and statistical information for the gradient magnitude images including the contrast indicator (ROI mean value) at the second scale (c) and the noise indicator (ROI noise level) measured at the first scale (d).
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Case sample
This study analyses digital images from the Digital Database for Screening Mammography (DDSM), a collaborative effort involving Massachusetts General Hospital, the University of South Florida and Sandia National Laboratories [27, 28]. For the purpose of this study 150 craniocaudal images were selected and digitized with the Lumisys 200 laser digitizer (Sunnyvale, CA), a device linear in the OD range 0–3.6 OD units. Images have a spatial resolution of 50 µm and 12 bits pixel depth.
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Results
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Preliminary phantom validation
The validity of the proposed contrast and noise indicators has been demonstrated by means of a phantom study. For contrast measurements, a 1 cm circular detail of varying nominal contrast, representing signal, was superimposed on a ROI taken from the mammogram background of Figure 1,
to mimic mammographic contrast detection. For each value of nominal contrast as well as for the signal-free background ROI, the CI was derived for four scales. Subsequently, the relative differences of CI values with respect to the CI corresponding to the signal-free ROI were calculated for the four scales. As seen from Figure 5a, signal detection sensitivity increases with increasing scale with respect to nominal contrast. The first scale is almost insensitive to nominal contrast changes, since it is mostly contaminated by noise and therefore not suggested for measurements.
For noise measurements a circular detail was digitally superimposed on a series of Gaussian noise backgrounds with normalized standard deviation ranging from 0 to 0.05. Figure 5b demonstrates that the sensitivity of the proposed NI decreases with increasing scale thus indicating that the first scale is most appropriate for noise measurements.
Clinical evaluation
Table 1 summarizes the results for the CIs and NIs at four scales. The numbers in the first two columns represent the CIs and NIs, averaged over the 150 images used in this study (CI is expressed as GL per pixel size and NI is expressed as the square of GL per pixel size). The last column shows the relative differences in contrast and noise estimates between the two areas of interest.
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Table 1. Average (±SD) contrast indicator and noise indicator at the mammary gland and the breast periphery for the 150 images studied
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We have performed the CI measurements at four scales to ensure that the obtained difference in CI between the two areas of interest is consistent for more than one scale. If GL variations corresponding to an edge exist at a location, they will be detected at more than one scale. However, if such variations are just noise, they will not be present at adjacent scales. At the lowest scale the recorded relative difference in CI between the two areas is very small (p>0.01), owing to the fact that GL variations are greatly affected by noise, which is mainly associated with high frequencies. At higher scales the contribution of noise becomes less significant and the recorded differences correspond mainly to differences in contrast. We can observe from Table 1 that lower values are recorded for the breast periphery, thus indicating decreased contrast in this area compared with the mammary gland. If we exclude the first scale, which is mostly contaminated with noise, the relative contrast decrease at the breast periphery is 50% on average.
The last row in Table 1 shows the NIs for the two areas averaged over the same images. This level remained almost unaffected, decreasing by approximately 2%. This noise is the total noise resulting from quantum mottle and digitizer noise. The systematic decrease in breast tissue thickness from the thoracic wall to the breast periphery results in quantum mottle reduction. On the other hand, the digitizer noise tends to increase with increasing OD. In the case of ideal digitizer performance, the total noise reduction would be expected to be larger. Even if the relative difference in noise levels in the two areas is low, the t-test performed showed that the recorded difference of the means is statistically significant (p<0.01). For 6% of the cases the noise level is slightly higher at the breast periphery compared with the mammary gland, without a statistically significant difference.
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Discussion
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In the present study, quantitative evaluation of image quality at the breast periphery compared with the mammary gland in terms of CI and NI has been carried out. To deal with low contrast encountered at the breast periphery, the parametric space of wavelet coefficients has been used both as a visualization aid as well as the basis for the measurements reported in this study.
Use of the proposed CI has proven that image quality is degraded at the breast periphery compared with the mammary gland, with respect to contrast. This is in agreement with similar reported results [1, 9–12]. Noise levels measured by the proposed NI are lower at the breast periphery, with a statistically significant difference. This is mainly attributed to the quantum component of total noise, which is dominant, compared with film graininess and digitization [29–31]. Specifically, quantum noise is higher where fewer X-ray photons are detected, i.e. the mammary gland area, owing to higher absorption in this region and lower absorption at the breast periphery where more X-ray photons are detected. Unfortunately, no information about the digitization noise with changing OD values for the Lumisys 200 scanner used in the DDSM database is available. However, at the present stage the proposed CI and NI can only be used for relative contrast and noise measurements between two regions. More work is being carried out in our department to explore the relationship between the absolute values of the proposed CI and NI at various scales and the values of other established measures.
The proposed wavelet-based CI and NI have been validated in a preliminary validation study. According to this study, CI measurements can be performed at scales 2–4, while the first scale is most appropriate for NI measurements.
A major factor affecting the presented measurements is the selection of size and position of ROIs used in this study. An alternative investigation would be the use of segmentation to isolate two large ROIs, i.e. mammary gland and breast periphery [12]. The proposed indicators could then be derived directly, eliminating the need for averaging over a considerable number of ROIs, as in our case.
A possible limitation of the present evaluation effort is the composition of the case sample, consisting only of craniocaudal mammograms. A more complete study should include profile views as well as different breast types.
Finally, it is felt that use of the wavelet, or similar multiresolution techniques, can help in the visualization and subsequent measurement of non-visible and thus usually missed very low contrasts, such as those encountered at the breast periphery. The CI and NI derived on the basis of the wavelet method have proven image quality degradation at the breast periphery with respect to contrast, compared with the mammary gland.
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Acknowledgments
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Elena Ungureanu was supported by a grant of the State Scholarship Foundation (SSF), Greece.
Received for publication June 30, 2000.
Revision received January 31, 2001.
Accepted for publication April 17, 2001.
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Abstract
Introduction
of a Gaussian noise distribution 
. Standard deviation values are normalized to the maximum pixel value for 12 bit pixel depth. 
, scale 1; 
, scale 2; 
, scale 3; x , scale 4.