Int J CARS (2012) 7:573–583 DOI 10.1007/s11548-011-0659-0 ORIGINAL ARTICLE Breast masses detection using phase portrait analysis and fuzzy inference systems Arianna Mencattini · Marcello Salmeri Received: 11 January 2011 / Accepted: 21 September 2011 / Published online: 11 October 2011 © CARS 2011 Abstract Purpose Breast masses exhibit variability in margins, shapes, and dimensions, so their detection is a difficult task in mammographic computer-aided diagnosis. Mass detection is usually a two-step procedure: mass identification and false- positive reduction. A new method to automatically detect mass lesions in mammographic images with tuning accord- ing to the breast tissue density was developed and tested. Methods A modified phase portrait analysis method was introduced, based on the eigenvalue condition number and an eigenvalue intensity map. The method uses an iter- ative and tissue density-adaptive segmentation procedure with extraction of geometric features. False-positive reduc- tion is accomplished using a fuzzy inference-based classi- fier. A leave-one-image-out cross-validation procedure was implemented, and stepwise regression analysis was used to automatically extract an optimal set of features. Testing and validation were performed on two different data sets contain- ing at least one malignant mass D1 (388 images) and D2 (674 images), and a third data set N1 (50 images) was used con- sisting of normal controls. These three data sets were taken from the Digital Database for Screening Mammography. Results For sensitivities of 0.9, 0.85, 0.80, and 0.75, the best results on cancer images exhibit an False-Positive per Image (FPpI) equal to 0.6, 0.45, 0.35, and 0.3, respectively, using a Bayes Linear Discriminant Analysis (LDA) classifier and an FPpI of 0.85, 0.7, 0.55, and 0.45 using a fuzzy inference sys- tem (FIS) for false-positive reduction. When the algorithm is tested on normal images, an FPpI equal to 0.4, 0.3, 0.25, A. Mencattini (B ) · M. Salmeri Department of Electronic Engineering, University of Rome Tor Vergata, Rome, Italy e-mail: mencattini@ing.uniroma2.it M. Salmeri e-mail: salmeri@ing.uniroma2.it and 0.2 was observed using LDA and 0.3, 0.25, 0.2, and 0.15 using the FIS. Conclusion A preclinical study of an automatic breast mass detection algorithm provided promising results in terms of sensitivity and low false-positive rate. Further development and clinical testing are justified based on the results. Keywords Breast masses detection · Fuzzy inference systems · Phase portrait analysis Introduction In the last years, the work of many researchers has been devoted to the development of systems to assist radiologists in the early identification of breast cancer [1, 2]. According to the forth edition of Breast Imaging Reporting and Data System (BIRADS) [3], subtle signs of breast cancer are four: calcifications, masses, architectural distortion, and bilateral asymmetry. The latest two signs do not necessarily mean that cancer is already present, but that something abnormal is happening in the breast. At the moment, the problems of the automatic identification and location on the mammogram of suspicious signs, such as calcifications and masses [4–7], are still an open problem, particularly directed to the search for high performance in difficult clinical cases. A mass is defined as a space-occupying lesion seen in more than one projec- tion. Masses exhibit a great variability in margins, shapes, and dimensions, thus making masses detection an interesting and difficult task to be solved for computer-aided diagnosis (CAD) in mammography. Moreover, the variability in the breast tissue, fatty, fibroglandular, heterogeneously dense, dense and homogeneous [3], increases this difficulty. Most of the mass detection algorithms are composed of two stages [8]: (1) detection of suspicious signs on the mam- mogram and (2) classification of suspicious signs as mass 123