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New Approaches for Hierarchical Image Decomposition, Based on IDP, SVD, PCA and KPCA

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New Approaches in Intelligent Image Analysis

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 108))

Abstract

The contemporary forms of image representation vary depending on the application. There are well-known mathematical methods for image representation, which comprise: matrices, vectors, determined orthogonal transforms, multi-resolution pyramids, Principal Component Analysis (PCA) and Independent Component Analysis (ICA), Singular Value Decomposition (SVD), wavelet sub-band decompositions, hierarchical tensor transformations, nonlinear decompositions through hierarchical neural networks, polynomial and multiscale hierarchical decompositions, multidimensional tree-like structures, multi-layer perceptual and cognitive models, statistical models, etc. In this chapter are analyzed the basic methods for hierarchical decomposition of grayscale and color images, and of sequences of correlated images of the kind: medical, multispectral, multi-view, etc. Here is also added one expansion and generalization of the ideas of the authors from their previous publications, regarding the possibilities for the development of new, efficient algorithms for hierarchical image decompositions with various purposes. In this chapter are presented and analyzed the following four new approaches for hierarchical image decomposition: the Branched Inverse Difference Pyramid (BIDP), based on the Inverse Difference Pyramid (IDP); the Hierarchical Singular Value Decomposition (HSVD) with tree-like computational structure; the Hierarchical Adaptive Principle Component Analysis (HAPCA) for groups of correlated images; and the Hierarchical Adaptive Kernel Principal Component Analysis (HAKPCA) for color images. In the chapter are given the algorithms, used for the implementation of these decompositions, and their computational complexity is evaluated. Some experimental results, related to selected applications are also given, and various possibilities for the creation of new hybrid algorithms for hierarchical decomposition of multidimensional images are specified. On the basis of the results obtained from the executed analysis, the basic application areas for efficient image processing are specified, such as: reduction of the information surplus; noise filtration; color segmentation; image retrieval; image fusion; dimensionality reduction for objects classification; search enhancement in large scale image databases, etc.

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  1. Department of Radio Communications and Video Technologies, Technical University of Sofia, 8 Kl. Ohridski Blvd., 1000, Sofia, Bulgaria

    Roumen Kountchev

  2. T&K Engineering Co., Drujba 2, Bl. 404/2, 1582, Sofia, Bulgaria

    Roumiana Kountcheva

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  1. Roumen Kountchev
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  1. Technical University of Sofia, Sofia, Bulgaria

    Roumen Kountchev

  2. University of Hyogo, Chuo-ku, Japan

    Kazumi Nakamatsu

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Kountchev, R., Kountcheva, R. (2016). New Approaches for Hierarchical Image Decomposition, Based on IDP, SVD, PCA and KPCA. In: Kountchev, R., Nakamatsu, K. (eds) New Approaches in Intelligent Image Analysis. Intelligent Systems Reference Library, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-319-32192-9_1

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