Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
Levoy, M., Chen, B., Vaish, V., Horowitz, M., Mcdowall, I., Bolas, M.: Synthetic aperture confocal imaging. ACM Trans. Graph. 23(3), 822–831 (2004)
Wu, G., et al.: Light field image processing: an overview. IEEE J. Sel. Topics Signal Process. 11(7), 926–954 (2017)
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)
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)
Pendu, M.L., Guillemot, C., Smolic, A.: A Fourier disparity layer representation for light fields. IEEE Trans. Image Process. (2019). https://doi.org/10.1109/TIP.2019.2922099
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)
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)
Perez, F., Perez, A., Rodriguez, M., Magdaleno, E.: Lightfield recovery from its focal stack. Math. Imaging Vis. 56, 573–590 (2016)
Trujillo-Sevilla, J.M., et al.: Restoring integral images from focal stacks using compressed sensing techniques. Disp. Technol. 12, 701–706 (2016)
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). https://doi.org/10.23919/APSIPA.2018.8659454
Ng, R.: Fourier slice photography. ACM Trans. Graph. 24(3), 735–744 (2005)
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)
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)
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)
Alonso, J.R.: Fourier domain post-acquisition aperture reshaping from a multi-focus stack. Appl. Opt. 56, D60–D65 (2017)
Schechner, Y.Y., Kiryati, N., Basri, R.: Separation of transparent layers using focus. Int. J. Comput. Vis, 39(1), 25–39 (2000)
Grenander, U., Szego, G.: Toeplitz Forms and Their Applications. University of California Press, Berkeley (1958)
Kotz, S., Nadarajah, S.: Multivariate t Distributions and Their Applications. Cambridge University Press, Cambridge (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Ito, A., Kubota, A., Kodama, K. (2020). Deriving Perfect Reconstruction Filter Bank for Focal Stack Refocusing. In: Palaiahnakote, S., Sanniti di Baja, G., Wang, L., Yan, W. (eds) Pattern Recognition. ACPR 2019. Lecture Notes in Computer Science(), vol 12047. Springer, Cham. https://doi.org/10.1007/978-3-030-41299-9_42
Download citation
DOI: https://doi.org/10.1007/978-3-030-41299-9_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41298-2
Online ISBN: 978-3-030-41299-9
eBook Packages: Computer ScienceComputer Science (R0)