Distance-based discretization of parametric signal manifolds

The characterization of signals and images in manifolds often lead to efficient dimensionality reduction algorithms based on manifold distance computation for analysis or classification tasks. We propose in this paper a method for the discretization of signal manifolds given in a parametric form. We present an iterative algorithm for the selection of samples on the manifold that permits to minimize the average error in the manifold distance computation. Experimental results with image appearance manifolds demonstrate that the proposed discretization algorithm outperforms baseline solutions based on random or regular sampling, both in terms of projection accuracy and image registrati


Learning Smooth Pattern Transformation Manifolds
Vural, Elif (2013-04-01)
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that represent observations of geometrically transformed signals. To construct a manifold, we build a representative pattern whose transformations accurately fit various input images. We examine two objectives of the manifold-building problem, namely, approximation a...
Approximation of pattern transformation manifolds with parametric dictionaries
Vural, Elif (2011-07-12)
The construction of low-dimensional models explaining high-dimensional signal observations provides concise and efficient data representations. In this paper, we focus on pattern transformation manifold models generated by in-plane geometric transformations of 2D visual patterns. We propose a method for computing a manifold by building a representative pattern such that its transformation manifold accurately fits a set of given observations. We present a solution for the progressive construction of the repr...
Invariant manifolds and Grobman-Hartman theorem for equations with degenerate operator at the derivative
Karasözen, Bülent; Loginov, B (2003-01-01)
Analog of Grobman-Hartman theorem about stable and unstable manifolds solutions for differential equations in Banach spaces with degenerate Fredholm operator at the derivative are proved. In contrast to usual evolution equation here central manifold arises even in the case of spectrum absence on the imaginary axis. Jordan chains tools and implicit operator theorem are used. The obtained results allow to develop center manifold methods for computation of bifurcation solution asymptotics and their stability i...
Waveguide multiplexer: miniaturized contiguous-band six-channel multiplexer structure
Sevinc, Y.; Demir, Şimşek (2017-08-24)
Efficient design procedure is introduced for the design of miniaturized contiguous band manifold-coupled multiplexer using the combination of the circuit-full-wave-based optimization in this study. Systematic methodology is based on the design of miniaturized channel filters using circuit model extraction and H-plane manifold network with hybrid optimization. The multiplexer is firstly analyzed in circuit level, and relevant lengths between channel filters and the lengths between each channel filters to man...
Learning pattern transformation manifolds for classification
Vural, Elif (2013-02-21)
Manifold models provide low-dimensional representations that are useful for analyzing and classifying data in a transformation-invariant way. In this paper we study the problem of jointly building multiple pattern transformation manifolds from a collection of image sets, where each set consists of observations from a class of geometrically transformed signals. We build the manifolds such that each manifold approximates a different signal class. Each manifold is characterized by a representative pattern that...
Citation Formats
E. Vural, “Distance-based discretization of parametric signal manifolds,” 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48062.