We report on a morphological study of 192 breast masses as seen in mammograms, with the aim of discrimination between benign masses and malignant tumors. From the contour of each mass, we computed the fractal dimension (FD) and a few shape factors, including compactness, fractional concavity, and spiculation index. We calculated FD using four different methods: the ruler and box-counting methods applied to each 2-dimensional (2D) contour and its 1-dimensional signature. The ANOVA test indicated statistically significant differences in the values of the various shape features between benign masses and malignant tumors. Analysis using receiver operating characteristics indicated the area under the curve, A(z), of up to 0.92 with the individual shape features. The combination of compactness, FD with the 2D ruler method, and the spiculation index resulted in the highest A(z) value of 0.93.
The evolution of the concept of sustainability and the availability of new statistical information requires constant checks on the set of indicators so that they accurately perform the task of representing well-being in our society. The Sustainable Development Goals refer to various development domains relating to environmental, social, economic, and institutional issues that have been placed at the basis of the Missions envisaged by the National Recovery and Resilience Plan (NRRP). Specifically, the subject of ecological transition and the related statistical indicators and the evaluations of the effectiveness of the programming implemented by the NRRP to pursue it in practice are of significant interest. The numerous data available were analyzed at a regional level through multivariate statistical methodologies (Totally Fuzzy and Relative method) capable of synthesizing the various information to evaluate the territorial adequacy of the economic planning of its various components. Through the representation on a GIS basis of the geographical distribution of the synthesis values of the fuzzy indices, the paper highlights the different starting point existing between Italian regions. So, these integrated statistical indicators can help public policies to be oriented in a more coherent way with their environmental declared objectives. Starting from the availability of multiple data, it is developed an integrated approach to the evaluation of the local government policies in place and to monitor the progress of subsequent interventions by the Italian government.
In this paper, we propose a novel approach for the automatic breast boundary segmentation using spatial fuzzy c-means clustering and active contours models. We will evaluate the performance of the approach on screen film mammographic images digitized by specific scanner devices and full-field digital mammographic images at different spatial and pixel resolutions. Expert radiologists have supplied the reference boundary for the massive lesions along with the biopsy proven pathology assessment. A performance assessment procedure will be developed considering metrics such as precision, recall, F-measure, and accuracy of the segmentation results. A Montecarlo simulation will be also implemented to evaluate the sensitivity of the boundary extracted on the initial settings and on the image noise
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