Michael E. Mavroforakis

A fully automated scheme for mammographic segmentation and classification based on breast density and asymmetry

This paper presents a fully automated segmentation and classification scheme for mammograms, based on breast density estimation and detection of asymmetry. First, image preprocessing and segmentation techniques are applied, including a breast boundary extraction algorithm and an improved version of a pectoral muscle segmentation scheme. Features for breast density categorization are extracted, including a new fractal dimension-related feature, and support vector machines (SVMs) are employed for classification, achieving accuracy of up to 85.7%. Most of these properties are used to extract a new set of statistical features for each breast; the differences among these feature values from the two images of each pair of mammograms are used to detect breast asymmetry, using an one-class SVM classifier, which resulted in a success rate of 84.47%. This composite methodology has been applied to the miniMIAS database, consisting of 322 (MLO) mammograms -including 15 asymmetric pairs of images-, obtained via a (noisy) digitization procedure. The results were evaluated by expert radiologists and are very promising, showing equal or higher success rates compared to other related works, despite the fact that some of them used only selected portions of this specific mammographic database. In contrast, our methodology is applied to the complete miniMIAS database and it exhibits the reliability that is normally required for clinical use in CAD systems.

A Geometric Nearest Point Algorithm for the Efficient Solution of the SVM Classification Task

Geometric methods are very intuitive and provide a theoretically solid approach to many optimization problems. One such optimization task is the support vector machine (SVM) classification, which has been the focus of intense theoretical as well as application-oriented research in machine learning. In this letter, the incorporation of recent results in reduced convex hulls (RCHs) to a nearest point algorithm (NPA) leads to an elegant and efficient solution to the SVM classification task, with encouraging practical results to real-world classification problems, i.e., linear or nonlinear and separable or nonseparable.

Multi-scaled morphological features for the characterization of mammographic masses using statistical classification schemes

OBJECTIVE A comprehensive signal analysis approach on the mammographic mass boundary morphology is presented in this article. The purpose of this study is to identify efficient sets of simple yet effective shape features, employed in the original and multi-scaled spectral representations of the boundary, for the characterization of the mammographic mass. These new methods of mass boundary representation and processing in more than one domain greatly improve the information content of the base data that is used for pattern classification purposes, introducing comprehensive spectral and multi-scale wavelet versions of the original boundary signals. The evaluation is conducted against morphological and diagnostic characterization of the mass, using statistical methods, fractal dimension analysis and a wide range of classifier architectures. METHODS AND MATERIALS This study consists of (a) the investigation of the original radial distance measurements under the complete spectrum of signal analysis, (b) the application of curve feature extractors of morphological characteristics and the evaluation of the discriminative power of each one of them, by means of statistical significance analysis and dataset fractal dimension, and (c) the application of a wide range of classifier architectures on these morphological datasets, in order to conduct a comparative evaluation of the efficiency and effectiveness of all architectures, for mammographic mass characterization. Radial distance signal was exploited using the discrete Fourier transform (DFT) and the discrete wavelet transform (DWT) as additional carrier signals. Seven uniresolution feature functions were applied over these carrier signals and multiple shape descriptors were created. Classification was conducted against mass shape type and clinical diagnosis, using a wide range of linear and non-linear classifiers, including linear discriminant analysis (LDA), least-squares minimum distance (LSMD), k-nearest neighbor (k-NN), radial basis function (RBF) and multi-layered perceptron (MLP) neural networks (NN), and support vector machines (SVM). Fractal analysis was employed as a dataset analysis tool in the feature selection phase. The discriminative power of the features produced by this composite analysis is subsequently analyzed by means of multivariate analysis of variance (MANOVA) and tested against two distinct classification targets, namely (a) the morphological shape type of the mass and (b) the histologically verified clinical diagnosis for each mammogram. RESULTS Statistical analysis and classification results have shown that the discrimination value of the features extracted from the DWT components and especially the DFT spectrum, are of great importance. Furthermore, much of the information content of the curve features in the case of DFT and DWT datasets is directly related to the texture and fine-scale details of the corresponding envelope signal of the spectral components. Neural classifiers outperformed all other methods (SVM not used because they are mainly two-class classifiers) with overall success rate of 72.3% for shape type identification, while SVM achieved the overall highest 91.54% for clinical diagnosis. Receiver operating characteristic (ROC) analysis has been employed to present the sensitivity and specificity of the results of this study.

The Augmented Complex Kernel LMS

Recently, a unified framework for adaptive kernel based signal processing of complex data was presented by the authors, which, besides offering techniques to map the input data to complex reproducing kernel Hilbert spaces, developed a suitable Wirtinger-like calculus for general Hilbert spaces. In this short paper, the extended Wirtingers calculus is adopted to derive complex kernel-based widely linear estimation filters suitable for applications involving noncircular data. Furthermore, we illuminate several important characteristics of the widely linear filters. We show that, although in many cases the gains from adopting widely linear estimation filters, as alternatives to ordinary linear ones, are rudimentary, for the case of kernel based widely linear filters significant performance improvements can be obtained.

A novel SVM Geometric Algorithm based on Reduced Convex Hulls

Geometric methods are very intuitive and provide a theoretically solid viewpoint to many optimization problems. SVM is a typical optimization task that has attracted a lot of attention over the recent years in many pattern recognition and machine learning tasks. In this work, we exploit recent results in reduced convex hulls (RCH) and apply them to a nearest point algorithm (NPA) leading to an elegant and efficient solution to the general (linear and nonlinear, separable and non-separable) SVM classification task

Reproducing Kernel Hilbert Spaces and fractal interpolation

Reproducing Kernel Hilbert Spaces (RKHSs) are a very useful and powerful tool of functional analysis with application in many diverse paradigms, such as multivariate statistics and machine learning. Fractal interpolation, on the other hand, is a relatively recent technique that generalizes traditional interpolation through the introduction of self-similarity. In this work we show that the functional space of any family of (recurrent) fractal interpolation functions ((R)FIFs) constitutes an RKHS with a specific associated kernel function, thus, extending considerably the toolbox of known kernel functions and introducing fractals to the RKHS world. We also provide the means for the computation of the kernel function that corresponds to any specific fractal RKHS and give several examples.

A fully automated complete segmentation scheme for mammograms

This paper presents a fully automated complete segmentation method for mammographic images. Image preprocessing techniques are first applied to mammograms to remove the noise and then a breast boundary extraction algorithm is implemented, in order to distinguish breast tissue from the background. Next, an improved version of an existing pectoral muscle scheme is performed and a new nipple segmentation technique is applied, detecting the nipple when it is in profile. This improves the estimated breast boundary and serves as a key-point for further processing of the image. This composite method has been implemented and applied to miniMIAS, one of the most well-known mammographic databases. This database consists of 322 mediolateral oblique (MLO) view mammograms, obtained via a digitization procedure. The results are evaluated by an expert radiologist and are very promising. Accordingly, it is expected that this procedure can produce improved results, when applied to high-quality digital mammograms.

A game-theoretic approach to weighted majority voting for combining SVM classifiers

A new approach from the game-theoretic point of view is proposed for the problem of optimally combining classifiers in dichotomous choice situations. The analysis of weighted majority voting under the viewpoint of coalition gaming, leads to the existence of analytical solutions to optimal weights for the classifiers based on their prior competencies. The general framework of weighted majority rules (WMR) is tested against common rank-based and simple majority models, as well as two soft-output averaging rules. Experimental results with combined support vector machine (SVM) classifiers on benchmark classification tasks have proven that WMR, employing the theoretically optimal solution for combination weights proposed in this work, outperformed all the other rank-based, simple majority and soft-output averaging methods. It also provides a very generic and theoretically well-defined framework for all hard-output (voting) combination schemes between any type of classifier architecture.