A Closed-Form Focus Profile Model for Conventional Digital Cameras
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Abstract
According to the thin lens model, the classic depth of field (DOF) is defined as the distance range at which objects in front of a camera are in focus. However, the thin lens poses important practical limitations for modeling the camera focus due to its dependence on internal parameters, such as the focal length, numerical aperture and effective pixel size. In this paper, a new model for describing the focus of conventional digital cameras is proposed. The focus is modeled as the energy of the point-spread-function of the imaging system and describes the joint effect of defocus, diffraction and digitization. Experiments conducted on different acquisition devices show that the proposed model conforms accurately to the behavior of real systems and outperforms the most similar alternatives in the state-of-the-art. In addition, in contrast to the classic DOF model, the proposed approach can be used to predict the changes in the focus of conventional digital cameras when changing focus, zoom, and aperture by means of a simple calibration process.
Keywords
Focus measure Focus profile Camera model Camera calibration Depth of fieldSupplementary material
References
- Abramowitz, M., & Davidson, M. W. (2012). Numerical aperture and resolution. Accessed October 22, 2012.Google Scholar
- Aguet, F., Van De Ville, D., & Unser, M. (2008). Model-based 2.5-D deconvolution for extended depth of field in brightfield microscopy. IEEE Transactions on Image Processing, 17(7), 1144–1153.MathSciNetCrossRefGoogle Scholar
- Allen, E., & Triantaphillidou, S. (2011). The manual of photography (10th ed.). Waltham: Focal Press.Google Scholar
- Bass, M., Decusatis, C., Enoch, J. M., Lakshminarayanan, V., Li, G., McDonald, C., Mahajan, V. N. & van Stryland, E. (2009). Geometrical and physical optics, polarized light, components and instruments. In Handbook of optics (Vol. 1, 3rd ed.). OSA.Google Scholar
- Born, M., & Wolf, E. (1999). Principles of optics (7th ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
- Cao, G., Zhao, Y., & Ni, R. (2010). Edge-based blur metric for tamper detection. Journal of Information Hiding and Multimedia Signal Processing, 1(1), 20–27.Google Scholar
- Chen, S., & Li, Y. F. (2013). Finding optima focusing distance and edge blur distribution for weakly calibrated 3d vision. IEEE Transactions on Industrial Informatics, 9(3), 1680–1687.CrossRefGoogle Scholar
- Chern, N. N. K., Neow, P. A., & Ang, M. H. (2001). Practical issues in pixel-based autofocusing for machine vision. In Proceedings of IEEE international conference on robotics and automation (Vol. 3, pp. 2791–2796).Google Scholar
- Cody, W. J. (1969). Rational chebyshev approximations for the error function. Mathematics of Computation, 23(107), 631–637.MathSciNetCrossRefMATHGoogle Scholar
- de Angelis, M., Nicola, S. D., Ferraro, P., Finizio, A., Pierattini, G., & Hessler, T. (1999). An interferometric method for measuring short focal length refractive lenses and diffractive lenses. Optics Communications, 160(1–3), 5–9.CrossRefGoogle Scholar
- Ersoy, O. K. (2007). Diffraction, Fourier optics and imaging. New York: Wiley.CrossRefMATHGoogle Scholar
- Favaro, P. (2007). Shape from focus and defocus: Convexity, quasiconvexity and defocus-invariant textures. In Proceedings of international conference on computer vision (pp. 1–7).Google Scholar
- Favaro, P., & Soatto, S. (2005). A geometric approach to shape from defocus. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(3), 406–417.CrossRefGoogle Scholar
- FitzGerrell, A. R., Edward, R., Dowski, J., & Cathey, W. T. (1997). Defocus transfer function for circularly symmetric pupils. Applied Optics, 36(23), 5796–5804.CrossRefGoogle Scholar
- Goodman, J. W. (1996). Introduction to Fourier optics (2nd ed.). New York: McGraw-Hill.Google Scholar
- Hart, J. F. (1968). Computer approximations. New York: Willey.MATHGoogle Scholar
- Hasinoff, S., & Kutulakos, K. (2011). Light-efficient photography. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(11), 2203–2214.CrossRefGoogle Scholar
- He, J., Zhou, R., & Hong, Z. (2003). Modified fast climbing search auto-focus algorithm with adaptive step size searching technique for digital camera. IEEE Transactions on Consumer Electronics, 49(2), 257–262.CrossRefGoogle Scholar
- Healey, G., & Kondepudy, R. (1994). Radiometric CCD camera calibration and noise estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(3), 267–276.CrossRefGoogle Scholar
- Heikkila, J., & Silven, O. (1997). A four-step camera calibration procedure with implicit image correction. In Proceedings of conference on computer vision and pattern recognition (pp. 1106–1112).Google Scholar
- Hopkins, H. H. (1955). The frequency response of a defocused optical system. Proc. R. Soc. Lond., 231, 91–103.MathSciNetCrossRefMATHGoogle Scholar
- Horn, B. K. P. (1990). Robot vision (6th ed.). Cambridge: MIT Press.Google Scholar
- Ito, A., Tambe, S., Mitra, K., Sankaranarayanan, A. C., & Veeraraghavan, A. (2014). Compressive epsilon photography for post-capture control in digital imaging. ACM Transactions on Graphics, 33(4), 88:1–88:12.CrossRefGoogle Scholar
- Jeon, J., Lee, J., & Paik, J. (2011). Robust focus measure for unsupervised auto-focusing based on optimum discrete cosine transform coefficients. IEEE Transactions on Consumer Electronics, 57(1), 1–5.CrossRefGoogle Scholar
- Jeon, J., Yoon, I., Kim, D., Lee, J., & Paik, J. (2010). Fully digital auto-focusing system with automatic focusing region selection and point spread function estimation. IEEE Transactions on Consumer Electronics, 56(3), 1204–1210.CrossRefGoogle Scholar
- Joshi, N., Szeliski, R., & Kriegman, D. (2008). PSF estimation using sharp edge prediction. In Proceedings of computer vision and pattern recognition.Google Scholar
- Kehtarnavaz, N., & Oh, H. J. (2003). Development and real-time implementation of a rule-based auto-focus algorithm. Real-Time Imaging, 9, 197–203.CrossRefGoogle Scholar
- Lai, Y. C. (2011). PSO-based estimation for gaussian blur in blind image deconvolution problem. In Proceedings of IEEE international conference on fuzzy systems (pp. 1143–1148).Google Scholar
- Lei, F., & Dang, L. K. (1994). Measuring the focal length of optical systems by grating shearing interferometry. Applied Optics, 33(28), 6603–6608.CrossRefGoogle Scholar
- Liu, C., Szeliski, R., Kang, S. B., Zitnick, C., & Freeman, W. (2008). Automatic estimation and removal of noise from a single image. IEEE Transactions on Pattern Analysis and Machine Intelligence, 30(2), 299–314.CrossRefGoogle Scholar
- Mahmood, M., & Choi, T.-S. (2010). Focus measure based on the energy of high-frequency components in the s transform. Optics Letters, 35(8), 1272–1274.CrossRefGoogle Scholar
- Minhas, R., Mohammed, A. A., & Wu, Q. J. (2011). Shape from focus using fast discrete curvelet transform. Pattern Recognition, 44(4), 839–853.CrossRefGoogle Scholar
- Muhammad, M., & Choi, T.-S. (2012). Sampling for shape from focus in optical microscopy. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(3), 564–573.CrossRefGoogle Scholar
- Muhammad, M., Mutahira, H., Majid, A., & Choi, T.-S. (2009). Recovering 3d shape of weak textured surfaces. In Proceedings of international conference on computational science and its applications (pp. 191–197).Google Scholar
- Nayar, S. K., & Nakagawa, Y. (1994). Shape from focus. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(8), 824–831.CrossRefGoogle Scholar
- Oppenheim, R. W., Schafer, R. W., & Buck, J. R. (1999). Discrete-time digital signal processing. Englewood Cliffs: Prentice Hall.Google Scholar
- Orieux, F., Giovanelli, J. F., & Rodet, T. (2010). Deconvolution with gaussian blur parameter and hyperparameters estimation. In Proceedings of IEEE international conference on acoustics, speech and signal processing (pp. 1350–1353).Google Scholar
- Paramanand, C., & Rajagopalan, A. N. (2012). Depth from motion and optical blur with an unscented Kalman filter. IEEE Transactions on Image Processing, 21, 2798–2811.MathSciNetCrossRefGoogle Scholar
- Pertuz, S., Garcia, M. A., & Puig, D. (2015). Efficient focus sampling through depth-of-field calibration. International Journal of Computer Vision, 112(3), 342–353.CrossRefGoogle Scholar
- Pertuz, S., Puig, D., Garcia, M., & Fusiello, A. (2012a). Generation of all-in-focus images by noise-robust selective fusion of limited depth-of-field images. IEEE Transactions on Image Processing, 22(3), 1242–1251.MathSciNetCrossRefGoogle Scholar
- Pertuz, S., Puig, D., & Garcia, M. A. (2012b). Analysis of focus measure operators for shape-from-focus. Pattern Recognition, 45(5), 1415–1432.MATHGoogle Scholar
- Pollefeys, M., Koch, R., & Gool, L. V. (1999). Self-calibration and metric reconstruction inspite of varying and unknown intrinsic camera parameters. International Journal of Computational Vision, 32(1), 7–25.CrossRefGoogle Scholar
- Pratt, W. K. (2007). Digital image processing: PISK scientific inside (4th ed.). New York: Willey.CrossRefMATHGoogle Scholar
- Qin, F. Q. (2010). Blind image surper-resolution reconstruction based on PSF estimation. In Proceedings of international conference on information and automation (pp. 1200–1203).Google Scholar
- Rottenfusser, R., Wilson, E. E., & Davidson, M. W. (2012). Numerical aperture and resolution. Accessed February 11, 2016.Google Scholar
- Stokseth, P. A. (1969). Properties of a defocused optica-system. Journal of the Optical Society of America, 59, 1314–1321.CrossRefGoogle Scholar
- Subbarao, M., & Tian, J.-K. (1998). Selecting the optimal focus measure for autofocusing and depth-from-focus. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(8), 864–870.CrossRefGoogle Scholar
- Sundaram, H., & Nayar, S. (1997). Are textureless scenes recoverable? In Proceedings of IEEE conference on computer vision and pattern recognition (pp. 814–820).Google Scholar
- Tay, C., Thakur, M., Chen, L., & Shakher, C. (2005). Measurement of focal length of lens using phase shifting Lau phase interferometry. Optics Communications, 248(4–6), 339–345.CrossRefGoogle Scholar
- Taylor, J. R. (1997). An introduction to error analysis. The study of uncertainties in physical measurements (2nd ed.). Sausalito: University Science Books.Google Scholar
- Tenenbaum, J. M. (1971). Accommodation in computer vision. Ph.D. thesis, Stanford University.Google Scholar
- Tsai, D.-C., & Chen, H. (2016). Focus profile modeling. IEEE Transactions on Image Processing, 25(2), 818–828.MathSciNetCrossRefGoogle Scholar
- Tsai, D. C., & Chen, H. H. (2012). Reciprocal focus profile. IEEE Transactions on Image Processing, 21(2), 459–468.MathSciNetCrossRefGoogle Scholar
- Voeltz, D. G. (2010). Computational Fourier optics. Bellingham: SPIE Press.Google Scholar
- Yousefi, S., Rahman, M., & Kehtarnavaz, N. (2011). A new auto-focus sharpness function for digital and smart-phone cameras. IEEE Transactions on Consumer Electronics, 57(3), 1003–1009.CrossRefGoogle Scholar