Henri Bouma, Judith Dijk and Adam W. M. van Eekeren, “Precise local blur estimation based on the first-order derivative”, Proc. SPIE, Vol. 8399, 839904 (2012); http://dx.doi.org/10.1117/12.918600 Copyright 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. Precise local blur estimation based on the first-order derivative Henri Bouma * , Judith Dijk and Adam W.M. van Eekeren; TNO, PO Box 96864, 2509 JG The Hague, The Netherlands. ABSTRACT Blur estimation is an important technique for super resolution, image restoration, turbulence mitigation, deblurring and autofocus. Low-cost methods have been proposed for blur estimation. However, they can have large stochastic errors when computed close to the edge location and biased estimates at other locations. In this paper, we define an efficient, accurate and precise estimate that can be computed at the edge location based on the first-order derivative. Our method is compared and benchmarked against previous state-of-the-art. The results show that the proposed method is fast, unbiased and with low stochastic error. Keywords: Blur estimation, PSF, autofocus, image restoration, image enhancement, turbulence, super resolution. 1. INTRODUCTION Blur estimation is a technique that can be used for many practical applications, such as super resolution [10], image restoration, turbulence mitigation [8][9], quantification [3], deblurring and autofocus [16]. Many algorithms have been proposed to perform blur estimation in images and video. In a short survey, we show that some are computationally inefficient, and some require higher-order polynomials. Some seem very efficient and robust, but have large stochastic errors when computed close to the edge location and systematic errors at other locations, as will be shown and analyzed. In this paper, we present an efficient, accurate and precise blur estimator that can be computed at the edge location. Furthermore, it is robust against small variations due to dislocation or noise. The novel estimator is based on the first- order derivative. Our method is compared and benchmarked against previous state-of-the-art methods under different levels of blur, dislocations and noise to gain insight in the robustness. The capabilities and limitations of both state-of- the-art and our methods are analyzed and described. The experimental results show that the presented method is fast, unbiased and with low stochastic error. *henri.bouma@tno.nl; phone +31 888 66 4054; http://www.tno.nl