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FIGURE 5 The scheme of multiorientation wavelet transform implemented by an adaptive directional filter bank.

FIGURE 5 The scheme of multiorientation wavelet transform implemented by an adaptive directional filter bank.

orientation of the striation in the window. In this manner each pixel is filtered according to an adaptive orientation with an adaptive width allowing more orientation details and more complex orientations to be enhanced. The result is that the filters appear to be "tuned" to the orientation and size of structures to enable better enhancement. The filters are applied globally to the entire image to obtain a set of high-frequency features in different directions. The gradient operators are commonly used in directional feature detection and edge detection, such as isotropic operation, compass operation, and Laplace operator and stochastic gradient operation [20-22].

3 Experimental Results

3.1 Image Database

The hybrid enhancement approach was tested with a database that contained (a) 100 single-view mammograms at a resolution of 105 microns and 12 bits per pixel, including 50 cases of normal mammograms and 50 mammograms with biopsy-proven malignant MCCs; (b) 100 single-view mammograms at a resolution of 180 microns and 12 bits per pixel with 50 normal and 50 abnormal cases with masses. Both normal and abnormal mammograms manifested typical variations in parenchymal density and structure, ranging from very dense to fat breasts. The location and geometry of the MCCs were identified on the digitized images and films by expert radiologists. A truth file was thus established for each of the abnormal images, which was used to determine the TP and FP rates. A cluster of three or more detected calcifications per cm2, i.e., an area of 95 x 95 pixels on the images in database (a), was interpreted as on FP if it was not identified in the truth file.

Each abnormal mammogram in database (b) contained at least one mass of varying size and location. The database contained 20 stellate, 14 circumscribed, and 19 irregular masses, all with biopsy-proven cancers. A reference image or electronic truth file was formed for all abnormal mammograms, including location information on each tumor provided by an expert mammographer based on visual criteria and biopsy results. Histograms of the effective size and contrast of the masses in the database are shown in Qian et al. [7] and Qian et al. [17].

The visual evaluation was conducted with a dual-monitor workstation used for image enhancement, receiver operating characteristic (ROC) analysis, and free response ROC (FROC) analysis [15]. The computer was a Sun ULTRA 2 workstation with two 200-MHz CPUs, running computer software to generate FROC/ROC curves, and connected to two highresolution 5-megapixel monitors for image display. The computational time for the full analysis did not exceed 2 minutes per case, but, to facilitate efficient operation, images were batch-processed prior to analysis by radiologists since the algorithms were fully automatic.

3.2 Visual Evaluation of Enhanced Images

The outcome of enhancing the original mammogram image shown in Fig. 6a is shown in Figs 6b and 6c, using the hybrid filter (Fig. 1) with a two-channel WT and a four-channel WT, respectively. The importance of the noise suppression and enhancement filter, prior to the use of the MMWT algorithm, as outlined in Fig. 1, is demonstrated by the representative subimages (512x512 pixels) shown in Fig. 7. This figure shows a comparison of the enhanced image using the hybrid filter of Fig. 1, the enhanced image by eliminating the AMNF step of Fig. 1, and the enhanced image by replacing the AMNF by the tree structured filter in Fig. 1. The hybrid filter provides better noise suppression and results in more detail of the extent of the MCC in terms of their morphology and spatial distribution of the microcalcifications. Comparison of the

FIGURE 6 Representative mammographic images with a single biopsy proven mass showing (a) the original digitized image, (b) enhanced image using the hybrid filter (Fig. 1) with a two-channel multi-resolution WT, (c) enhanced image using the hybrid filter with a four-channel multiresolution WT.

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