The effectiveness of the treatment of breast cancer depends on its timely detection. An early step in the diagnosis is the cytological examination of breast material obtained directly from the tumor. This work reports on advances in computer-aided breast cancer diagnosis based on the analysis of cytological images of fine needle biopsies to characterize these biopsies as either benign or malignant. Instead of relying on the accurate segmentation of cell nuclei, the nuclei are estimated by circles using the circular Hough transform. The resulting circles are then filtered to keep only high-quality estimations for further analysis by a support vector machine which classifies detected circles as correct or incorrect on the basis of texture features and the percentage of nuclei pixels according to a nuclei mask obtained using Otsu's thresholding method. A set of 25 features of the nuclei is used in the classification of the biopsies by four different classifiers. The complete diagnostic procedure was tested on 737 microscopic images of fine needle biopsies obtained from patients and achieved 98.51% effectiveness. The results presented in this paper demonstrate that a computerized medical diagnosis system based on our method would be effective, providing valuable, accurate diagnostic information.
A large number of differential equation problems which admit traveling waves are usually defined on very large or infinite domains. To numerically solve these problems on smaller subdomains of the original domain, artificial boundary conditions must be defined for these subdomains. One type of artificial boundary condition which can minimize the size of such subdomains is the absorbing boundary condition. The imposition of absorbing boundary conditions is a technique used to reduce the necessary spatial domain when numerically solving partial differential equations that admit traveling waves. Such absorbing boundary conditions have been extensively studied in the context of hyperbolic wave equations. In this paper, general absorbing boundary conditions will be developed for the Schrödinger equation with one spatial dimension, using group velocity considerations. Previously published absorbing boundary conditions will be shown to reduce to special cases of this absorbing boundary condition. The well-posedness of the initial boundary value problem of the absorbing boundary condition, coupled to the interior Schrödinger equation, will also be discussed. Extension of the general absorbing boundary condition to higher spatial dimensions will be demonstrated. Numerical simulations using initial single Gaussian, double Gaussian, and a narrow Gaussian pulse distributions will be given, with comparision to exact solutions, to demonstrate the reflectivity properties of various orders of the absorbing boundary condition.
According to the World Health Organization (WHO), breast cancer (BC) is one of the most deadly cancers diagnosed among middle-aged women. Precise diagnosis and prognosis are crucial to reduce the high death rate. In this paper we present a framework for automatic malignancy grading of fine needle aspiration biopsy tissue. The malignancy grade is one of the most important factors taken into consideration during the prediction of cancer behavior after the treatment. Our framework is based on a classification using Support Vector Machines (SVM). The SVMs presented here are able to assign a malignancy grade based on preextracted features with the accuracy up to 94.24%. We also show that SVMs performed best out of four tested classifiers.
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