Journal of Mathematical Imaging and Vision

, Volume 56, Issue 3, pp 573–590 | Cite as

Lightfield Recovery from Its Focal Stack

  • F. Pérez
  • A. Pérez
  • M. Rodríguez
  • E. Magdaleno


The Focal Stack Transform integrates a 4D lightfield over a set of appropriately chosen 2D planes. The result of such integration is an image focused on a determined depth in 3D space. The set of such images is the Focal Stack of the lightfield. This paper studies the existence of an inverse for this transform. Such inverse could be used to obtain a 4D lightfield from a set of images focused on several depths of the scene. In this paper, we show that this inversion cannot be obtained for a general lightfield and introduce a subset of lightfields where this inversion can be computed exactly. We examine the numerical properties of such inversion process for general lightfields and examine several regularization approaches to stabilize the transform. Experimental results are provided for focal stacks obtained from several plenoptic cameras. From a practical point of view, results show how this inversion procedure can be used to recover, compress, and denoise the original 4D lightfield.


Lightfield Focal Stack Plenoptic Inverse problems Regularization 



The authors would like to thank R. Ng and Heidelberg University for lightfields that were used in the experimental results. This work has been partially supported by “Ayudas al Fomento de Nuevos Proyectos de Investigación” (Project 2013/0001339) of the University of La Laguna.

Supplementary material

10851_2016_658_MOESM1_ESM.docx (34 kb)
Supplementary material 1 (docx 34 KB)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • F. Pérez
    • 1
  • A. Pérez
    • 1
  • M. Rodríguez
    • 2
  • E. Magdaleno
    • 2
  1. 1.Departamento de Estadística, Investigación Operativa y ComputaciónUniversity of La LagunaSan Cristóbal de La LagunaSpain
  2. 2.Departamento de Física Fundamental, Experimental, Electrónica y SistemasUniversity of La LagunaSan Cristóbal de La LagunaSpain

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