Image Segmentation Via Spectral Clustering and Diffusion Spectral Clustering

Import 22/07/2015Spektrální shlukování v posledních letech našlo svou pevnou pozici mezi obecnými datově segmentačními algoritmy. Použití spektrálního shlukování pro segmentaci, zejména reálných obrazů, otevírá široký prostor k dalším optimalizacím a modifikacím tohoto algoritmu. Tato práce představuje teoretický základ rozdílných konfigurací spektrálního shlukování včetně jeho difuzní varianty. Experimentální část práce se zabývá implementací difuzního spektrálního shlukování s použitím algoritmu \textit{Mean-shift}. Dále, na základě dosažených segmentací, poskytuje objektivní náhled možnosti reálného použití tohoto algoritmu pro segmentaci obrazu s ohledem na rozdílné případy použití.In recent years, spectral clustering has established itself as an robust segmentation algorithm. Using spectral clustering for, particularly real, image segmentation opens a wide scope to optimize and modify this algorithm further. This thesis introduces the theoretical background of spectral clustering algorithm focusing on its different modifications including diffuse spectral clustering. Experimental part of this thesis focuses on the implementation of spectral diffuse clustering using the Mean-shift algorithm and based on its outputs, using both real and synthetic inputs, it provides a sober perspective of possibilities of using spectral clustering for image segmentation concerning various use cases.460 - Katedra informatikyvýborn

Statistical Evidence for Three classes of Gamma-ray Bursts

Two different multivariate clustering techniques, the K-means partitioning method and the Dirichlet process of mixture modeling, have been applied to the BATSE Gamma-ray burst (GRB) catalog, to obtain the optimum number of coherent groups. In the standard paradigm, GRB are classified in only two groups, the long and short bursts. However, for both the clustering techniques, the optimal number of classes was found to be three, a result which is consistent with previous statistical analysis. In this classification, the long bursts are further divided into two groups which are primarily differentiated by their total fluence and duration and hence are named low and high fluence GRB. Analysis of GRB with known red-shifts and spectral parameters suggests that low fluence GRB have nearly constant isotropic energy output of 10^{52} ergs while for the high fluence ones, the energy output ranges from 10^{52} to 10^{54} ergs. It is speculated that the three kinds of GRBs reflect three different origins: mergers of neutron star systems, mergers between white dwarfs and neutron stars, and collapse of massive stars.Comment: 7 pages, accepted for publication in the Astrophysical Journal. Minor editorial change