Browsing by Subject "Radial basis functions"

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Open Access
Carcinoma cell line discrimination in microscopic images using unbalanced wavelets
(IEEE, 2012-03) Keskin, Furkan; Suhre, Alexander; Erşahin, Tüli,; Çetin Atalay, Rengül; Çetin, A. Enis
Cancer cell lines are widely used for research purposes in laboratories all over the world. In this paper, we present a novel method for cancer cell line image classification, which is very costly by conventional methods. The aim is to automatically classify 14 different classes of cell lines including 7 classes of breast and 7 classes of liver cancer cells. Microscopic images containing irregular carcinoma cell patterns are represented by randomly selected subwindows which possibly correspond to foreground pixels. For each subwindow, a correlation descriptor utilizing the fractional unbalanced wavelet transform coefficients and several morphological attributes as pixel features is computed. Directionally selective textural features are preferred primarily because of their ability to characterize singularities at multiple orientations, which often arise in carcinoma cell lines. A Support Vector Machine (SVM) classifier with Radial Basis Function (RBF) kernel is employed for final classification. Over a dataset of 280 images, we achieved an accuracy of 88.2%, which outperforms the classical correlation based methods. © 2012 IEEE.
Open Access
Finite-rank multivariate-basis expansions of the resolvent operator as a means of solving the multivariable lippmann-schwinger equation for two-particle scattering
(Springer Verlag, 2014-11) Kuruoglu, Z. C.
Finite-rank expansions of the two-body resolvent operator are explored as a tool for calculating the full three-dimensional two-body T-matrix without invoking the partial-wave decomposition. The separable expansions of the full resolvent that follow from finite-rank approximations of the free resolvent are employed in the Low equation to calculate the T-matrix elements. The finite-rank expansions of the free resolvent are generated via projections onto certain finite-dimensional approximation subspaces. Types of operator approximations considered include one-sided projections (right or left projections), tensor-product (or outer) projection and inner projection. Boolean combination of projections is explored as a means of going beyond tensor-product projection. Two types of multivariate basis functions are employed to construct the finite-dimensional approximation spaces and their projectors: (i) Tensor-product bases built from univariate local piecewise polynomials, and (ii) multivariate radial functions. Various combinations of approximation schemes and expansion bases are applied to the nucleon-nucleon scattering employing a model two-nucleon potential. The inner-projection approximation to the free resolvent is found to exhibit the best convergence with respect to the basis size. Our calculations indicate that radial function bases are very promising in the context of multivariable integral equations.