## 2 Mammogram Image Description and Feature Extraction
The filter calculates the percent of the pixels in the outer ring that are less bright than the least bright of the pixels in the inner disk to produce a suspiciousness value, and an example is given in Figure 3b. This suspiciousness value represents the degree to which the surrounding region of a point radially decreases in intensity, and is done over several sizes. This results in focusing on the bright central core of the cancer and ignoring the radiating lines of spiculation. A second filter can be used to detect the radiating lines of spiculation, as shown in Figure 3c, but a combined filter shown in Figure 3d that detects both the cores and the spiculation could improve the performance, especially if the relative weighting of the measurements is learned on an appropriate data set. The CAD suspiciousness calculation is performed at each pixel location (_x,y_) in the images. The minimum intensity \(I_{min}\) within \(r_{l}\) is found, and then the fraction of pixels between \(r_{l}\) and \(r_{2}\) with intensities less than \(I_{min}\) is calculated. This yields the fraction under the minimum (FUM) for one set of \(r_{l}\) and \(r_{2}\). Keeping \(r_{l}-r_{2}=b\) constant and averaging the FUM over a range of \(r_{l}\) determines the  
Figure 3: (a) Mammographic image of a spiculated lesion. (b) AFUM filter. (c) Cosine Gabor filter. (d) Combined filter. Figure 2: The variations in density a mammogram, the least dense in (a) being characterized as mostly fat to the very dense breast in (d). The American College of Radiology (ACR) Breast Imaging Reporting and Data System (BIRADS) characterizes these as ranging from 1–4, with 4 being the most dense. average fraction under the minimum (AFUM) [31]. The AFUM is then considered to be a suspiciousness value, and represents the extent to which the surrounding region of a point radially decreases in intensity. The CAD prompt output is a set of these suspicious points that are above a certain threshold. Since this is done over a range of sizes, it can respond to cancers of different sizes. This focuses on the bright central core of the cancer and ignores the radiating lines of spiculation. The distribution of these features on a mammogram is shown in Figure 4.  
Features with a high suspiciousness value have a higher chance of corresponding to an occurrence of cancer. The centroid of each local maxima in the filtered image is initially marked as a candidate feature site with its suspiciousness value. This collection of sites is then sorted in decreasing order of suspicion. All suspicious sites that are closer than 5 mm from a more suspicious site are removed to prevent multiple reporting of the same site. This yields a set of potential feature sites that can be analyzed. A further improvement might be possible by first transforming the data before filtering, such as applying wavelet analysis to the images before simply thresholding or applying the filter. This has been successfully attempted previously [27] with good results. However, an optimal solution would first combine all of the various filtering and transform methods which create meaningful suspicious points, and then learn an effective analysis from them. This is similar to the effective combination of  
Figure 4: The distribution of the AFUM features on a mammogram are shown as small circles, while the larger oval shapes are hand-drawn annotations by a radiologist of the cancer. Note that the feature does find a cancer, but there are many false positives. weak classifiers into a single strong classifier through ensemble learning methods like boosting, which has been successfully used before in tumor classification [49]. Many of the images like mammograms come in pairs, so they form a set that should be very similar. If one of the pair contains cancer and the other does not, then that pair should be different. Thus, the mammogram image set provides both positive and negative examples to build on for image similarity classification.