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Adaptive Regularization for Image Reconstruction from Subsampled Data Read chapter Read first chapter

2018 | OriginalPaper | Chapter

8. Relaxed Optimisation for Tensor Principal Component Analysis and Applications to Recognition, Compression and Retrieval of Volumetric Shapes

Authors : Hayato Itoh, Atsushi Imiya, Tomoya Sakai

Published in: Imaging, Vision and Learning Based on Optimization and PDEs

Publisher: Springer International Publishing

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Abstract

The mathematical and computational backgrounds of pattern recognition are the geometries in Hilbert space used for functional analysis and the applied linear algebra used for numerical analysis, respectively. Organs, cells and microstructures in cells dealt with in biomedical image analysis are volumetric data. We are required to process and analyse these data as volumetric data without embedding into higher-dimensional vector spaces from the viewpoint of object-oriented data analysis. Therefore, sampled values of volumetric data are expressed as three-way array data. The aim of the paper is to develop relaxed closed forms for tensor principal component analysis (PCA) for the recognition, classification, compression and retrieval of volumetric data. Tensor PCA derives the tensor Karhunen-Loève transform, which compresses volumetric data, such as organs, cells in organs and microstructures in cells, preserving both the geometric and statistical properties of objects and spatial textures in the space.

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previous chapter Multi-Dimensional Regular Expressions for Object Detection with LiDAR Imaging
next chapter An Incremental Reseeding Strategy for Clustering
Appendix
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Footnotes
1
The project “Computational Anatomy for Computer-aided Diagnosis and Therapy: Frontiers of Medical Image Sciences” funded by Grant-in-Aid for Scientific Research on Innovative Areas, MEXT, Japan. http://​www.​comp-anatomy.​org/​wiki/​index.​php?​Computational.
 
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Metadata
Title
Relaxed Optimisation for Tensor Principal Component Analysis and Applications to Recognition, Compression and Retrieval of Volumetric Shapes
Authors
Hayato Itoh
Atsushi Imiya
Tomoya Sakai
Copyright Year
2018
Book
Imaging, Vision and Learning Based on Optimization and PDEs

Print ISBN: 978-3-319-91273-8

Electronic ISBN: 978-3-319-91274-5

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91274-5_8

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