by Mauricio Delbracio, Andrés Almansa, Jean-Michel Morel, Pablo Musé
Abstract:
In most digital cameras, and even in high-end digital single lens reflex cameras, the acquired images are sampled at rates below the Nyquist critical rate, causing aliasing effects. This work introduces an algorithm for the subpixel estimation of the point spread function (PSF) of a digital camera from aliased photographs. The numerical procedure simply uses two fronto-parallel photographs of any planar textured scene at different distances. The mathematical theory developed herein proves that the camera PSF can be derived from these two images, under reasonable conditions. Mathematical proofs supplemented by experimental evidence show the well-posedness of the problem and the convergence of the proposed algorithm to the camera in-focus PSF. An experimental comparison of the resulting PSF estimates shows that the proposed algorithm reaches the accuracy levels of the best nonblind state-of-the-art methods.
Reference:
Subpixel Point Spread Function Estimation from Two Photographs at Different Distances (Mauricio Delbracio, Andrés Almansa, Jean-Michel Morel, Pablo Musé), In SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, volume 5, 2012.
Bibtex Entry:
@article{Delbracio2012,
Abstract = {In most digital cameras, and even in high-end digital single lens reflex cameras, the acquired images are sampled at rates below the Nyquist critical rate, causing aliasing effects. This work introduces an algorithm for the subpixel estimation of the point spread function (PSF) of a digital camera from aliased photographs. The numerical procedure simply uses two fronto-parallel photographs of any planar textured scene at different distances. The mathematical theory developed herein proves that the camera PSF can be derived from these two images, under reasonable conditions. Mathematical proofs supplemented by experimental evidence show the well-posedness of the problem and the convergence of the proposed algorithm to the camera in-focus PSF. An experimental comparison of the resulting PSF estimates shows that the proposed algorithm reaches the accuracy levels of the best nonblind state-of-the-art methods.},
Author = {Delbracio, Mauricio and Almansa, Andr{\'{e}}s and Morel, Jean-Michel and Mus{\'{e}}, Pablo},
Doi = {10.1137/110848335},
Issn = {1936-4954},
Journal = {SIAM Journal on Imaging Sciences},
Keywords = {42B35,65-04,65F22,65T40,68U10,aliasing,camera quality assessment,image blur,inverse problems,modulated transfer function,point spread function,subpixel convolution kernel estimation},
Language = {en},
Month = {nov},
Number = {4},
Pages = {1234--1260},
Publisher = {Society for Industrial and Applied Mathematics},
Title = {{Subpixel Point Spread Function Estimation from Two Photographs at Different Distances}},
Url = {http://hal.archives-ouvertes.fr/hal-00624757},
Volume = {5},
Year = {2012},
Bdsk-Url-1 = {http://hal.archives-ouvertes.fr/hal-00624757},
Bdsk-Url-2 = {https://doi.org/10.1137/110848335}}