Topology, homogeneity and scale factors for object detection: application of eCognition software for urban mapping using multispectral satellite image

The research scope of this paper is to apply spatial object based image analysis (OBIA) method for processing panchromatic multispectral image covering study area of Brussels for urban mapping. The aim is to map different land cover types and more specifically, built-up areas from the very high resolution (VHR) satellite image using OBIA approach. A case study covers urban landscapes in the eastern areas of the city of Brussels, Belgium. Technically, this research was performed in eCognition raster processing software demonstrating excellent results of image segmentation and classification. The tools embedded in eCognition enabled to perform image segmentation and objects classification processes in a semi-automated regime, which is useful for the city planning, spatial analysis and urban growth analysis. The combination of the OBIA method together with technical tools of the eCognition demonstrated applicability of this method for urban mapping in densely populated areas, e.g. in megapolis and capital cities. The methodology included multiresolution segmentation and classification of the created objects.Comment: 6 pages, 12 figures, INSO2015, Ed. by A. Girgvliani et al. Akaki Tsereteli State University, Kutaisi (Imereti), Georgi

Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing

Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets or curvelets have also been proposed for the detection of anisotropic features such cosmic strings in the cosmic microwave background. We review in this paper a range of methods based on sparsity that have been proposed for astronomical data analysis. We also discuss what is the impact of Compressed Sensing, the new sampling theory, in astronomy for collecting the data, transferring them to the earth or reconstructing an image from incomplete measurements.Comment: Submitted. Full paper will figures available at http://jstarck.free.fr/IEEE09_SparseAstro.pd

Topological Homogeneity for Electron Microscopy Images

In this paper, the concept of homogeneity is defined, from a topological perspective, in order to analyze how uniform is the material composition in 2D electron microscopy images. Topological multiresolution parameters are taken into account to obtain better results than classical techniques.Ministerio de Economía y Competitividad MTM2016-81030-PMinisterio de Economía y Competitividad TEC2012-37868-C04-0

Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions

We attach to each finite bipartite separated graph (E,C) a partial dynamical system (\Omega(E,C), F, \theta), where \Omega(E,C) is a zero-dimensional metrizable compact space, F is a finitely generated free group, and {\theta} is a continuous partial action of F on \Omega(E,C). The full crossed product C*-algebra O(E,C) = C(\Omega(E,C)) \rtimes_{\theta} F is shown to be a canonical quotient of the graph C*-algebra C^*(E,C) of the separated graph (E,C). Similarly, we prove that, for any *-field K, the algebraic crossed product L^{ab}_K(E,C) = C_K(\Omega(E,C)) \rtimes_\theta^{alg} F is a canonical quotient of the Leavitt path algebra L_K(E,C) of (E,C). The monoid V(L^{ab}_K(E,C)) of isomorphism classes of finitely generated projective modules over L^{ab}_K(E,C) is explicitly computed in terms of monoids associated to a canonical sequence of separated graphs. Using this, we are able to construct an action of a finitely generated free group F on a zero-dimensional metrizable compact space Z such that the type semigroup S(Z, F, K) is not almost unperforated, where K denotes the algebra of clopen subsets of Z. Finally we obtain a characterization of the separated graphs (E,C) such that the canonical partial action of F on \Omega(E,C) is topologically free.Comment: Final version to appear in Advances in Mathematic