Cauchy Aperture and Perfect Reconstruction Filters for Extending Depth-of-Field from Focal Stack

Abstract

A pupil function of aperture in image capturing systems is theoretically derived such that one can perfectly reconstruct all-in-focus image through linear filtering of the focal stack. The perfect reconstruction filters are also designed based on the derived pupil function. The designed filters are space-invariant; hence the presented method does not require region segmentation. Simulation results using synthetic scenes shows effectiveness of the derived pupil function and the filters.

Filter Bank for Perfect Reconstruction of Light Field from Its Focal Stack

“…However, no method has been presented to solve the problem perfectly. In this paper * * , for Lambertian scenes with no occlusion, we show theoretically that the LF can be perfectly reconstructed from the FS that is captured by the camera with a Cauchy aperture [23]. Little attention has been paid to the design of the optimal aperture; conventional methods assume that the aperture is Gaussian or pillbox.…”

“…For the first time, we show here that the LF reconstruction problem can be made a well-posed problem by using a Cauchy aperture and then derive a filter bank that completely reconstructs the LF from the FS. Our previous work [23] showed that an allin-focus image can be perfectly reconstructed from the FS captured through the Cauchy aperture. This paper shows that LF can also be perfectly reconstructed.…”