Abstract
Most medium to high quality digital cameras (dslrs) acquire images at a spatial rate which is several times below the ideal Nyquist rate. For this reason only aliased versions of the cameral point-spread function (psf) can be directly observed. Yet, it can be recovered, at a sub-pixel resolution, by a numerical method. Since the acquisition system is only locally stationary, this psf estimation must be local. This paper presents a theoretical study proving that the sub-pixel psf estimation problem is well-posed even with a single well chosen observation. Indeed, theoretical bounds show that a near-optimal accuracy can be achieved with a calibration pattern mimicking a Bernoulli(0.5) random noise. The physical realization of this psf estimation method is demonstrated in many comparative experiments. We use an algorithm to accurately estimate the pattern position and its illumination conditions. Once this accurate registration is obtained, the local psf can be directly computed by inverting a well conditioned linear system. The psf estimates reach stringent accuracy levels with a relative error of the order of 2% to 5%. To the best of our knowledge, such a regularization-free and model-free sub-pixel psf estimation scheme is the first of its kind.
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Backman, S., Maekynen, A. J., Kolehmainen, T. T., & Ojala, K. M. (2003). Fast lens testing using random targets. Optics and Photonics Technologies and Applications, 4876(1), 1100–1109. Opto-Ireland 2002.
Backman, S., Makynen, A., Kolehmainen, T., & Ojala, K. (2004). Random target method for fast MTF inspection. Optics Express, 12, 2610–2615.
Bookstein, F. L. (1989). Principal warps: thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis & Machine Intelligence, 11(6), 567–585.
Bouguet, J. Y. (2008). Camera calibration toolbox for Matlab. URL: http://www.vision.caltech.edu/bouguetj/calib_doc/.
Brauers, J., Seiler, C., & Aach, T. (2010). Direct PSF estimation using a random noise target. In Proceedings of SPIE—The International Society for Optical Engineering (Vol. 7537, pp. 75,370B–75,370B-10).
Capel, D. (2004). Image mosaicing and super-resolution. Distinguished Dissertation Series, Springer.
Chalmond, B. (1991). PSF estimation for image deblurring. CVGIP: Graphical Models and Image Processing, 53(4), 364–372.
Cheng, O., Guangzhi, W., Quan, Z., Wei, K., & Hui, D. (2005). Evaluating Harris method in camera calibration. In Conference proceedings of the International Conference of IEEE Engineering in Medicine and Biology Society (Vol. 6, pp. 6383–6386).
Claxton, C. D., & Staunton, R. C. (2008). Measurement of the point-spread function of a noisy imaging system. Journal of the Optical Society of America A, 25(1), 159–170. doi:10.1364/JOSAA.25.000159.
Daniels, A., Boreman, G., Ducharme, A., & Sapir, E. (1995). Random transparency targets for modulation transfer function measurement in the visible and infrared regions. Optical Engineering, 34(3), 860–868.
Delbracio, M., Musé, P., & Almansa, A. (2011). Non-parametric sub-pixel local point spread function estimation. In Image Processing On Line (IPOL) workshop, algorithmic description. Online demo and source code accessible at http://www.ipol.im/pub/algo/admm_non_blind_psf_estimation.
Goodman, J. W. (1996). Introduction to Fourier optics. New York: McGraw-Hill Science.
Grant, M., & Boyd, S. (2009) CVX: Matlab software for disciplined convex programming (web page and software). URL: http://stanford.edu/boyd/cvx. Online; accessed 19-July-2009.
Harris, C., & Stephens, M. (1988). A combined corner and edge detector. In Proceedings of the fourth Alvey vision conference (pp. 147–151).
Healey, G., & Kondepudy, R. (1994). Radiometric CCD camera calibration and noise estimation. IEEE Transactions on Pattern Analysis & Machine Intelligence, 16(3), 267–276.
ISO (2000). ISO 12233:2000: Photography—electronic still-picture cameras—resolution measurements.
Joshi, N. (2008). Enhancing photographs using content-specific image priors. PhD thesis, Department of Computer Science and Engineering, University of California, San Diego.
Joshi, N., Szeliski, R., & Kriegman, D. J. (2008). PSF estimation using sharp edge prediction. In IEEE conference on Computer Vision and Pattern Recognition (CVPR) (pp. 1–8). Los Alamitos: IEEE Computer Society.
Ladjal, S. (2005). Flou et quantification dans les images numériques. PhD thesis, Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan.
Levy, E., Peles, D., Opher-Lipson, M., & Lipson, S. (1999). Modulation transfer function of a lens measured with a random target method. Applied Optics, 38(4), 679–683.
LLC I (2010). Imatest 3.6. http://www.imatest.com/.
Lucchese, L., & Mitra, S. K. (2002). Using saddle points for subpixel feature detection in camera calibration targets. In APCCAS (2) (pp. 191–195). Bellingham: IEEE.
Luxen, M., & Förstner, W. (2002). Characterizing image quality: Blind estimation of the point spread function from a single image. In Proceedings of Photogrammetric Computer Vision 2002 (pp. 205–210).
Marion, A. (1997). Acquisition et visualisation des images. Paris: Eyrolles.
Portugal, L. F., Júdice, J. J., & Vicente, L. N. (1994). A comparison of block pivoting and interior-point algorithms for linear least squares problems with nonnegative variables. Mathematics of Computation, 63(208), 625–643.
Reichenbach, S. E., Park, S. K., & Narayanswamy, R. (1991). Characterizing digital image acquisition devices. Optical Engineering, 30(2), 170–177.
Rooms, F., Philips, W., & Portilla, J. (2004). Parametric PSF estimation via sparseness maximization in the wavelet domain. In F. Truchetet & O. Laligand (Eds.), Proceedings of the SPIE—Wavelet Applications in Industrial Processing II (Vol. 5607, pp. 26–33).
Smith, E. H. B. (2006). PSF estimation by gradient descent fit to the ESF. In Proceedings of SPIE—Image Quality and System Performance III (Vol. 6059, p. 60590E). Bellingham: SPIE. doi:10.1117/12.643071.
Sprengel, R., Rohr, K., & Stiehl, H. (1996). Thin-plate spline approximation for image registration. In Engineering in Medicine and Biology Society 1996. Bridging disciplines for biomedicine. Proceedings of the 18th Annual International Conference of the IEEE (Vol. 3, pp. 1190–1191). doi:10.1109/IEMBS.1996.652767.
Tian, H., Fowler, B., & Gamal, A. E. (2001). Analysis of temporal noise in CMOS photodiode active pixel sensor. IEEE Journal of Solid-State Circuits, 36(1), 92–101.
Šroubek, F., Cristóbal, G., & Flusser, J. (2007). A unified approach to superresolution and multichannel blind deconvolution. IEEE Transactions on Image Processing, 16(9), 2322–2332.
Williams, C. S., & Becklund, O. A. (2002). SPIE press monograph: Vol. PM112. Introduction to the optical transfer function. Bellingham: SPIE Publications.
Yadid-Pecht, O. (2000). Geometrical modulation transfer function for different pixel active area shapes. Optical Engineering, 39(4), 859–865.
Zandhuis, J., Pycock, D., Quigley, S., & Webb, P. (1997). Sub-pixel non-parametric psf estimation for image enhancement. IEE Proceedings. Vision, Image and Signal Processing, 144(5), 285–292.
Zhang, W., & Cham, W. K. (2008). A single image based blind super-resolution approach. In IEEE International Conference on Image Processing (ICIP) (pp. 329–332).
Zhang, Z. (2000). A flexible new technique for camera calibration. IEEE Transactions on Pattern Analysis & Machine Intelligence, 22(11), 1330–1334.
Zhao, T., Wang, R., Liu, Y., & Yu, F. (2006). Characteristic-analysis of optical low pass filter used in digital camera. In Proceedings of SPIE—The International Society for Optical Engineering (Vol. 6034, pp. 60,340N.1–60,340N.9). Bellingham: SPIE.
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Delbracio, M., Musé, P., Almansa, A. et al. The Non-parametric Sub-pixel Local Point Spread Function Estimation Is a Well Posed Problem. Int J Comput Vis 96, 175–194 (2012). https://doi.org/10.1007/s11263-011-0460-0
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DOI: https://doi.org/10.1007/s11263-011-0460-0