Skip to main content

Robust Non-negative Tensor Factorization, Diffeomorphic Motion Correction, and Functional Statistics to Understand Fixation in Fluorescence Microscopy

Part of the Lecture Notes in Computer Science book series (LNIP,volume 11764)


Fixation is essential for preserving cellular morphology in biomedical research. However, it may also affect spectra captured in multispectral fluorescence microscopy, impacting molecular interpretations. To investigate fixation effects on tissue, multispectral fluorescence microscopy images of pairs of samples with and without fixation are captured. Each pixel might exhibit overlapping spectra, creating a blind source separation problem approachable with linear unmixing. With multiple excitation wavelengths, unmixing is intuitively extended to tensor factorizations. Yet these approaches are limited by nonlinear effects like attenuation. Further, light exposure during image acquisition introduces subtle Brownian motion between image channels of non-fixed tissue. Finally, hypothesis testing for spectral differences due to fixation is non-trivial as retrieved spectra are paired sequential samples. To these ends, we present three contributions, (1) a novel robust non-negative tensor factorization using the \(\beta \)-divergence and \(L_{2,1}\)-norm, which decomposes the data into a low-rank multilinear and group-sparse non-multilinear tensor without making any explicit nonlinear modeling choices or assumptions on noise statistics; (2) a diffeomorphic atlas-based strategy for motion correction; (3) a non-parametric hypothesis testing framework for paired sequential data using functional principal component analysis. PyTorch code for robust non-negative tensor factorization is available at

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-32239-7_73
  • Chapter length: 9 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
USD   99.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-32239-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   129.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.
Fig. 3.


  1. Avants, B.B., Epstein, C.L., Grossman, M., Gee, J.C.: Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain. Med. Image Anal. 12(1), 26–41 (2008)

    CrossRef  Google Scholar 

  2. Dey, N., et al.: Tensor decomposition of hyperspectral images to study autofluorescence in age-related macular degeneration. Med. Image Anal. 56, 96–109 (2019)

    CrossRef  Google Scholar 

  3. Févotte, C., Dobigeon, N.: Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization. IEEE Trans. Image Process. 24(12), 4810–4819 (2015)

    CrossRef  MathSciNet  Google Scholar 

  4. Hong, D., Kolda, T.G., Duersch, J.A.: Generalized canonical polyadic tensor decomposition. arXiv preprint arXiv:1808.07452 (2018)

  5. Huang, Z., et al.: Effect of formalin fixation on the near-infrared raman spectroscopy of normal and cancerous human bronchial tissues. Int. J. Oncol. 23(3), 649–655 (2003)

    Google Scholar 

  6. Ikoma, H., Heshmat, B., Wetzstein, G., Raskar, R.: Attenuation-corrected fluorescence spectra unmixing for spectroscopy and microscopy. Opt. Express 22(16), 19469–19483 (2014)

    CrossRef  Google Scholar 

  7. Joshi, S., Davis, B., Jomier, M., Gerig, G.: Unbiased diffeomorphic atlas construction for computational anatomy. NeuroImage 23, S151–S160 (2004)

    CrossRef  Google Scholar 

  8. Neher, R.A., Mitkovski, M., Kirchhoff, F., Neher, E., Theis, F.J., Zeug, A.: Blind source separation techniques for the decomposition of multiply labeled fluorescence images. Biophys. J. 96(9), 3791–3800 (2009)

    CrossRef  Google Scholar 

  9. Pomann, G.M., Staicu, A.M., Ghosh, S.: A two-sample distribution-free test for functional data with application to a diffusion tensor imaging study of multiple sclerosis. J. Roy. Stat. Soc.: Ser. C (Appl. Stat.) 65(3), 395–414 (2016)

    CrossRef  MathSciNet  Google Scholar 

  10. Ramsay, J.O.: Functional Data Analysis. Springer, New York (2005).

    CrossRef  MATH  Google Scholar 

  11. Smilde, A., Bro, R., Geladi, P.: Multi-way Analysis: Applications in the Chemical Sciences. Wiley, Hoboken (2005)

    Google Scholar 

  12. Waters, J.C.: Accuracy and precision in quantitative fluorescence microscopy. Rockefeller University Press (2009)

    Google Scholar 

  13. Zhou, P., Feng, J.: Outlier-robust tensor PCA. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2263–2271 (2017)

    Google Scholar 

Download references


Author support and HPC provided by NIH R01EY027948 and NSF MRI-1229185, respectively. Validation data provided by Hayato Ikoma.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Neel Dey .

Editor information

Editors and Affiliations

1 Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 2 (pdf 2103 KB)

Rights and permissions

Reprints and Permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Dey, N., Messinger, J., Smith, R.T., Curcio, C.A., Gerig, G. (2019). Robust Non-negative Tensor Factorization, Diffeomorphic Motion Correction, and Functional Statistics to Understand Fixation in Fluorescence Microscopy. In: , et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2019. MICCAI 2019. Lecture Notes in Computer Science(), vol 11764. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-32238-0

  • Online ISBN: 978-3-030-32239-7

  • eBook Packages: Computer ScienceComputer Science (R0)