Introduction

In Chapter  different proposals for mass detection were reviewed. We concluded that the pattern matching approach using mutual information was an adequate solution for finding small masses. This is a crucial issue in radiology, where successful prognosis (or life expectancy) is drastically increased when the cancers are detected in their early stages. However, this approach fails when looking for larger masses, which is likely due to the range of shapes present. On the other hand, the performance of the classifier-based approaches do not highly depend on the size of the masses. This is probably due to the fact that these algorithms learn how to detect the masses based on pixel-based features, regardless of the global mass shape. If the training database includes enough representative cases, the algorithm should be able to detect them.

Furthermore, we have seen that few of the reviewed mass segmentation algorithms incorporate prior knowledge about the shape of the masses. Looking into Table  only some works classified as ``Region" and ``Model" strategies used shape information. In the ``Region" approaches such information was mainly used as a stopping criteria of a region growing algorithm: when the segmentation reaches some particular shape, the algorithm stops the growing step. In contrast, in the ``Model" approaches, this information is a fundamental issue. For instance, the works of Lai et al. [98] and Constantinidis et al. [36] were based on a template matching scheme, where region and shape information are equally important.

As also noticed in Chapter , the main problem of most of the mass detectors algorithms is the number of false positives, being large. This is particularly true for the template matching algorithm designed in Section . Thus, as our approach is likely to suffer from this drawback, we postpone the analysis of possible solutions for false positive reduction to Chapter . Moreover, we have seen in the survey of Chapter  that the breast tissue influences the algorithms' performance. The introduction of such information into our mass detection proposal will be investigated and incorporated in Chapter .

Therefore, our aim in this chapter is to develop a model-based algorithm able to find small and larger masses by means of shape and size analysis of real masses. Briefly, the algorithm follows a template matching scheme, but with two main differences with respect to the rest of the proposed algorithms. Firstly, contour and shape information coming from the analysis of roughly manually annotated masses is used, instead of using region information. Secondly, instead of using a similarity criterion, the algorithm is probabilistic based, following a Bayesian scheme [80]. Let us explain in more detail both differences.

Existing pattern matching approaches [36,98] construct a rigid and ``synthetic'' pattern based on the following three facts: the brightness of the mass is higher than its surrounding tissue, the density of the mass is uniform, and the mass has a circular shape. The result of such assumptions is a template similar to the one shown in Figure . In contrast, in our proposal, we will firstly find the most probable contours of a mass using real information, obtained from the analysis of the contours of a set of known masses. This step is based on the well-known eigenfaces algorithm [180], initially designed for the face recognition problem. This way, similar to the classifier-based approaches, our algorithm, initially learns the morphology of the masses from real cases. Note that the inherent assumption of such works is, as already commented, that the initial training database has sufficient variability to provide samples for all cases.

Once the template is constructed, it is searched in a mammogram. This is usually done using a similarity measure, such as normalized cross correlation [98] or mutual information (see Section ). However, these approaches do not allow the template to vary according to the images. In contrast, with our proposal, the constructed template can be adapted to the edges of the image. Hence, instead of using traditional similarity measures, we follow a Bayesian template matching scheme.

The rest of this chapter is structured as follows. In next section, we briefly describe ``modern'' template matching techniques. Subsequently, to describe the construction of the template, we explain the eigenfaces approach, and why this algorithm is useful for our objective. Afterwards, the design of the template and the pattern matching algorithm are explained. The results, using FROC and ROC analysis and two different databases, are shown in Section . Finally, the chapter ends with discussion and conclusions.