Fourier slice photography

ABSTRACT

This paper contributes to the theory of photograph formation from light fields. The main result is a theorem that, in the Fourier domain, a photograph formed by a full lens aperture is a 2D slice in the 4D light field. Photographs focused at different depths correspond to slices at different trajectories in the 4D space. The paper demonstrates the utility of this theorem in two different ways. First, the theorem is used to analyze the performance of digital refocusing, where one computes photographs focused at different depths from a single light field. The analysis shows in closed form that the sharpness of refocused photographs increases linearly with directional resolution. Second, the theorem yields a Fourier-domain algorithm for digital refocusing, where we extract the appropriate 2D slice of the light field's Fourier transform, and perform an inverse 2D Fourier transform. This method is faster than previous approaches.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.4 IMAGE PROCESSING AND COMPUTER VISION
      I.4.5 Reconstruction
          Subjects: Transform methods

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computation of transforms (e.g., fast Fourier transform)

  I. Computing Methodologies
  I.4 IMAGE PROCESSING AND COMPUTER VISION
      I.4.1 Digitization and Image Capture
          Subjects: Imaging geometry

General Terms:
Algorithms, Performance

Keywords:
digital photography, digital refocusing, fourier transform, plenoptic camera, projection-slice theorem