## 1 Introduction  
Segmentation of clinically relevant regions of interest (ROIs) represents a significant challenge in the medical imaging domain, central to the performance of computer-assisted diagnostic systems. Within the context of screening mammography, segmentation is typically performed to extract and delineate possible lesions from the surrounding normal tissue. Additionally, although the transition to full-field digital mammography is ameliorating the need for mammographic background removal,segmentation of the entire breast from a film mammogram with potentially significant acquisition noise represents a challenge in the many facilities which are as yet unable to transition to fully digital solutions, and in mining legacy data. Interestingly, these segmentation tasks are related: as we will show, the same approaches used to segment the entire breast profile are also useful for ROI extraction. However, existing breast and ROI segmentation approaches, such as approaches based on k-means [1], fuzzy c-means [2,3], gray level co-occurrence matrices (GLCM) [4], and the watershed transform [5], suffer several shortcomings. For example, k-means and fuzzy c-means tend to find spherical clusters, k-means cannot differentiate between significant and nonsignificant clusters (_i.e._, all pixels receive a label), GLCM makes assumptions on the texture of the underlying region, and watershed transforms have high sensitivity to noise and a well-known tendency to oversegment (See Figure 1). Many clustering algorithms are natively insensitive to locality, and may consider spatially dispersed regions part of the same cluster without the inclusion of additional spatial features-a property which is sometimes useful, but is often undesirable for the purpose of segmentation. Additionally, many clustering algorithms scale superlinearly with image area, and are therefore impractical for mining large medical imaging datasets. These properties typically render clustering algorithms unsuitable on their own for segmentation, necessitating construction of complex multi-step segmentation methodologies on top of them. In this paper, we make use of the WaveCluster [6] clustering algorithm in the context of mammographic segmentation to address these challenges. WaveCluster has linear runtime with respect to image area and can provide a usable segmentation without additional preprocessing steps beyond  
Figure 1: **(a)** Left craniocaudal view of a patient with a malignant mass, manually segmented by a domain expert (circled). Low-power salt and pepper acquisition noise, not visible at scale, corrupts the image; **(b)** k-means clustering (\(k=4\)) identifies regions of interest (ROIs), but loses part of the image border and does not distinguish between important and unimportant ROIs (e.g. the pectoral muscle, the lesion, and normal tissue all fall into the same cluster). Increasing k simply resulted in empty clusters; **(c)** Watershed segmentation of the gradient identifies the overall contour of the breast, but fails to identify any regions within and oversegments the noisy background; **(d)** WaveCluster with a low density threshold (15%) segments the entire breast, while **(e)** WaveCluster with a higher threshold (85%) isolates and highlights the suspicious regions. basic image normalization and noise removal. The algorithm is also versatile enough to segment both the breast profile and regions of interest within the breast simply by varying one parameter. However, one major limitation of WaveCluster as initially proposed is its inability to cluster real-valued data, such as an intensity image-the algorithm as originally proposed can only operate on binary images [6]. Therefore, we make use of a novel \"weighted WaveCluster\" extension, which we have originally derived for use in fMRI imaging of the brain [7], which aggregates grid cell values via a weighted sum of neighborhood intensity values rather than a count of points.