Deriving Perfect Reconstruction Filter Bank for Focal Stack Refocusing

  • Asami Ito
  • Akira KubotaEmail author
  • Kazuya Kodama
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12047)


This paper presents a digital refocusing method that transforms the captured focal stack directly into a new focal stack under different focus settings. Assuming Lambertian scenes with no occlusions, this paper theoretically shows that there exist a set of filters that perfectly reconstructs focal stack under Gaussian aperture from that captured under Cauchy one. The perfect reconstruction filters are derived in linear and space-invariant using a layered scene representation. Numerical simulations using synthetic focal stacks showed that the root mean squared errors are quite small and less than \(10^{-9}\), indicating the derived filters allow perfect reconstruction.


Digital refocusing Focal stack Aperture Perfect reconstruction filters 


  1. 1.
    Ng, R., Levoy, M., Bredif, M., Duval, G., Horowitz, M., Hanrahan, P.: Light field photography with a hand-held plenoptic camera. Stanford University Computer Science Technical Report CSTR 2(11), pp. 1–11 (2005)Google Scholar
  2. 2.
    Levoy, M., Chen, B., Vaish, V., Horowitz, M., Mcdowall, I., Bolas, M.: Synthetic aperture confocal imaging. ACM Trans. Graph. 23(3), 822–831 (2004)CrossRefGoogle Scholar
  3. 3.
    Wu, G., et al.: Light field image processing: an overview. IEEE J. Sel. Topics Signal Process. 11(7), 926–954 (2017)CrossRefGoogle Scholar
  4. 4.
    Aizawa, K., Kodama, K., Kubota, A.: Producing object based special effects by fusing multiple differently focused images. IEEE Trans. Circuits Syst. Video Technol. 10(2), 323–330 (2000)CrossRefGoogle Scholar
  5. 5.
    Alonso, J.R., Fernandez, A., Ferrari, J.A.: Reconstruction of perspective shifts and refocusing of a three-dimensional scene from a multi-focus image stack. Appl. Opt. 55(9), 2380–2386 (2016)CrossRefGoogle Scholar
  6. 6.
    Pendu, M.L., Guillemot, C., Smolic, A.: A Fourier disparity layer representation for light fields. IEEE Trans. Image Process. (2019). Scholar
  7. 7.
    Kodama, K., Kubota, A.: Efficient reconstruction of all-in-focus images through shifted pinholes from multi-focus images for dense light field synthesis and rendering. IEEE Trans. Image Process. 22(11), 4407–4421 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Levin, A., Durand, F.: Linear view synthesis using a dimensionality gap light field prior. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 1831–1838 (2010)Google Scholar
  9. 9.
    Perez, F., Perez, A., Rodriguez, M., Magdaleno, E.: Lightfield recovery from its focal stack. Math. Imaging Vis. 56, 573–590 (2016)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Trujillo-Sevilla, J.M., et al.: Restoring integral images from focal stacks using compressed sensing techniques. Disp. Technol. 12, 701–706 (2016)CrossRefGoogle Scholar
  11. 11.
    Kubota, A., Ito, A., Kodama, K.: Deriving synthetic filter bank for perfect reconstruction of light field from its focal stack. In: Proceedings of 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (2018).
  12. 12.
    Ng, R.: Fourier slice photography. ACM Trans. Graph. 24(3), 735–744 (2005)CrossRefGoogle Scholar
  13. 13.
    Kubota, A.: Synthesis filter bank and pupil function for perfect reconstruction of all-in-focus image from focal stack. In: Proceedings of SPIE International Conference on Quality Control by Artificial Vision, p. 103380A (2017)Google Scholar
  14. 14.
    Kubota, A., Aizawa, K.: Arbitrary view and focus image generation: rendering object-based shifting and focussing effect by linear filtering. In: Proceedings of International Conference on Image Processing, pp. I-489–I-492 (2002)Google Scholar
  15. 15.
    Kubota, A., Aizawa, K.: Reconstructing arbitrarily focused images from two differently focused images using linear filters. IEEE Trans. Image Proces. 14(11), 1848–1859 (2005)CrossRefGoogle Scholar
  16. 16.
    Alonso, J.R.: Fourier domain post-acquisition aperture reshaping from a multi-focus stack. Appl. Opt. 56, D60–D65 (2017)CrossRefGoogle Scholar
  17. 17.
    Schechner, Y.Y., Kiryati, N., Basri, R.: Separation of transparent layers using focus. Int. J. Comput. Vis, 39(1), 25–39 (2000)CrossRefGoogle Scholar
  18. 18.
    Grenander, U., Szego, G.: Toeplitz Forms and Their Applications. University of California Press, Berkeley (1958)CrossRefGoogle Scholar
  19. 19.
    Kotz, S., Nadarajah, S.: Multivariate t Distributions and Their Applications. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Science and EngineeringChuo UniversityTokyoJapan
  2. 2.National Institute of InformaticsTokyoJapan

Personalised recommendations