• 호남수학학술지
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• 제45권4호
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• pp.585-597
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• 2023

We introduce the rotational hypersurface x = x(u, v, s, t) constructed by double rotation in five dimensional Euclidean space 𝔼⁵. We reveal the first and the second fundamental form matrices, Gauss map, shape operator matrix of x. Additionally, defining the i-th curvatures of any hypersurface via Cayley-Hamilton theorem, we compute the curvatures of the rotational hypersurface x. We give some relations of the mean and Gauss-Kronecker curvatures of x. In addition, we reveal Δx=𝓐x, where 𝓐 is the 5 × 5 matrix in 𝔼⁵.

• 전기학회논문지
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• 제66권8호
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• pp.1272-1277
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• 2017

To assist radiologists for the characterization of breast masses, Computer-aided Diagnosis(CADx) system has been studied. The CADx system can improve the diagnostic accuracy of radiologists by providing objective information about breast masses. Morphological and texture features were extracted from the breast ultrasound images. Based on extracted features, the CADx system retrieves masses that are similar to a query mass from a reference library using a k-nearest neighbor (k-NN) approach. Eight similarity measures of distance, Euclidean, Chebyshev(Minkowski family), Canberra, Lorentzian($F_2$ family), Wave Hedges, Motyka(Intersection family), and Cosine, Dice(Inner Product family) are evaluated by ROC(Receiver Operating Characteristic) analysis. The Inner Product family measure used with the k-NN classifier provided slightly higher performance for classification of malignant and benign masses than those with the Minkowski, $F_2$, and Intersection family measures.