Volumetric Image Pattern Recognition Using Three-Way Principal Component Analysis

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10126)

Abstract

The aim of the paper is to develop a relaxed closed form for tensor principal component analysis (PCA) for the recognition, classification, compression and retrieval of volumetric data. The 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. Furthermore, we numerically clarify that low-pass filtering after applying the multi-dimensional discrete cosine transform (DCT) efficiently approximates the data compression procedure based on tensor PCA. These orthogonal-projection-based data compression methods for three-way data is extracts outline shapes of biomedical objects such as organs and compressed expressions for the interior structures of cells.

References

  1. 1.
    Cichocki, A., Zdunek, R., Phan, A.-H., Amari, S.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley, Hoboken (2009)CrossRefGoogle Scholar
  2. 2.
    Itskov, M.: Tensor Algebra and Tensor Analysis for Engineers. Springer, Heidelberg (2013)CrossRefMATHGoogle Scholar
  3. 3.
    Mørup, M.: Applications of tensor (multiway array) factorizations and decompositions in data mining. Wiley Interdisc. Rev.: Data Mining Knowl. Discov. 1, 24–40 (2011)Google Scholar
  4. 4.
    Weber, G.W., Bookstein, F.L.: Virtual Anthropology: A Guide to a New Interdisciplinary Field. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Kroonenberg, P.M.: Applied Multiway Data Analysis. Wiley, Hoboken (2008)CrossRefMATHGoogle Scholar
  6. 6.
    Zelditch, M.L., Swiderski, D.L., Sheets, H.D.: Geometric Morphometrics for Biologists: A Primer, 2nd edn. Academic Press, Cambridge (2012)MATHGoogle Scholar
  7. 7.
    Younes, L.: Shapes and Diffeomorphisms. Springer, Heidelberg (2010)CrossRefMATHGoogle Scholar
  8. 8.
    Davies, R., Twining, C., Taylor, C.: Statistical Models of Shape Optimisation and Evaluation. Springer, Heidelberg (2008)MATHGoogle Scholar
  9. 9.
    Thompson, D.W.: On Growth and Form (The Complete Revised Edition). Dover, Minoela (1992)Google Scholar
  10. 10.
    Imiya, A., Eckhardt, U.: The Euler characteristics of discrete objects and discrete quasi-objects. CVIU 75, 307–318 (1999)Google Scholar
  11. 11.
    Sakai, T., Narita, M., Komazaki, T., Nishiguchi, H., Imiya, A.: Image hierarchy in Gaussian scale space. In: Advances in Imaging and Electron Physics, vol. 165, pp. 175–263. Academic Press (2013)Google Scholar
  12. 12.
    Inagaki, S., Itoh, H., Imiya, A.: Multiple alignment of spatiotemporal deformable objects for the average-organ computation. In: Agapito, L., Bronstein, M.M., Rother, C. (eds.) ECCV 2014. LNCS, vol. 8928, pp. 353–366. Springer, Cham (2015). doi:10.1007/978-3-319-16220-1_25 Google Scholar
  13. 13.
    Grenander, U., Miller, M.: Pattern Theory: From Representation to Inference. Oxford University Press, Oxford (2007)MATHGoogle Scholar
  14. 14.
    Hamidi, M., Pearl, J.: Comparison of the cosine Fourier transform of Markov-1 signals. IEEE ASSP 24, 428–429 (1976)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Oja, E.: Subspace Methods of Pattern Recognition. Research Studies Press, Baldock (1983)Google Scholar
  16. 16.
    Strang, G., Nguyen, T.: Wavelets and Filter Banks, 2nd edn. Wellesley-Cambridge Press, Wellesley (1996)MATHGoogle Scholar
  17. 17.
    Aubert-Broche, B., Griffin, M., Pike, G.B., Evans, A.C., Collins, D.L.: 20 new digital brain phantoms for creation of validation image data bases. IEEE TMI 25, 1410–1416 (2006)Google Scholar
  18. 18.

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.School of Advanced Integration ScienceChiba UniversityInage-kuJapan
  2. 2.Institute of Management and Information TechnologiesChiba UniversityInage-kuJapan
  3. 3.Graduate School of EngineeringNagasaki UniversityNagasakiJapan

Personalised recommendations