## 1 Introduction  
A technique that radiologists use to diagnose breast cancer involves first finding suspicious sites in the mammograms and then comparing the left and right breasts to reduce the number of false positives. The symmetry of the human body is utilized to increase the accuracy of the diagnosis through visual registration of the mammograms. This technique is emulated by combining both computer vision and learning techniques, attempting to capture the diagnosis of the radiologist. Therefore this work is motivated not only by computer science theory and technique, but also by domain-specific knowledge and theory. These ideas were verified through an approach that has been completed with surprisingly good results at diagnosing breast cancer. It is hoped that this work will improve techniques in image similarity and classification, as well as provide insights into medical imaging and especially into the imaging, diagnosis, and classification of breast cancer. Breast cancer remains a leading cause of cancer deaths among women in many parts of the world. In the United States alone, over forty thousand women die of the disease each year [1]. Mammography is currently the most effective method for early detection of breast cancer [2], and example mammograms are shown in Figure 1. Computer-aided detection (CAD) of mammograms could be used to avoid these missed diagnoses, and has been shown to increase the number of cancers detected by more than nineteen percent [3], so there is hope that improving techniques in computerized detection of breast cancer could significantly improve the lives of women across the globe. Studies have shown that CAD can improve the search and detection of cancer associated with micro-calcification clusters [4,5], but cancers associated with masses are often considered to be false positives in the clinical environment [6,7]. Poor performance is caused by high false-positive rates [8] and the use of only one view [9]. The benefit of using CAD systems are still being tested [10,11], and new CAD schemes are being developed [12-26]. Asymmetry, which consists of a comparison of the left and right breast images [27], is a technique that could be used to significantly improve the results. An automated prescreening system only classifies a mammogram as either normal or suspicious, while CAD picks out specific points as cancerous [28]. One of the most challenging problems with prescreening is the lack of sensitive algorithms for the detection of asymmetry [29]. Image similarity methods can capture the asymmetry properties, and then improve both CAD and prescreening of breast cancer. Contextual and spatial comparisons can be combined to determine image similarity, which has been often utilized in image databases [30-33]. Medical image databases have also used image similarity, ranging from rule-based systems for chest radiographs [34] to anatomical structure matching for 3-D MR images [35] to learning techniques [36]. This work applies image similarity concepts to the problem of detecting breast cancer for CAD in mammograms. Detecting breast cancer in mammograms is challenging because the cancerous structures have many features in common with normal breast tissue. This means that a high number of false positives or false negatives are possible. Asymmetry can be used to help reduce the number of false positives so that true positives are more obvious. Previous work utilizing asymmetry has used wavelets or structural clues to detect asymmetry with correct results as often as 77% of the time [27,37]. Additional work has focused on bilateral or temporal subtraction, which is the attempt to subtract one breast image from the other [38,39]. This approach is hampered by the necessity of exact registration and the natural asymmetry of the breasts. Bilateral subtraction tries to utilize the multiple images taken with the same machine by the same technician and analyzed using the same process in an effort to reduce the systematic differences that can be introduced.