IEEE Transactions on Image Processing, 10(2):XXX-XXX 2001. Blind Inverse Gamma Correction Hany Farid † The luminance non-linearity introduced by many imaging devices can often be described by a simple point-wise operation (gamma correction). This paper presents a technique for blindly estimating the amount of gamma correction in the absence of any calibration infor- mation or knowledge of the imaging device. The basic approach exploits the fact that gamma correction introduces specific higher-order correlations in the frequency domain. These cor- relations can be detected using tools from polyspectral analysis. The amount of gamma correction is then estimated by minimizing these correlations. Keywords: higher-order statistics, image processing, image restoration, blind inverse gamma correction 1 Introduction The luminance non-linearity introduced by many imaging devices can often be described with a simple point-wise operation (gamma correction) of the form: g (u) = u γ , (1) where u ∈ [0, 1] denotes the image pixel intensity. If the value of γ is known then inverting this process is trivial: g −1 (u) = u 1/γ . (2) The value of γ is typically determined experimentally by passing a calibration target with a full range of known luminance values through the imaging system (e.g., a Macbeth chart [1]). But often such calibration is not available or direct access to the imaging device is not possible, for example when downloading an image from the web. In addition, most commercial digital cameras dynamically vary the amount of gamma. For many applications in digital photography, image processing, and computer vision it would be advantageous to remove these non-linearities prior to subsequent processing stages. In this paper a technique is presented for estimating the amount of gamma correction in the absence of any calibration information or knowledge of the imaging device. We term this technique blind in- verse gamma correction. The basic approach exploits the fact that gamma correction introduces specific higher-order correlations in the frequency domain. These correlations can be detected using tools from polyspectral analysis. The amount of gamma correction is then determined by minimizing these corre- lations. Higher-order statistics have previously been used for various forms of image restoration: noise re- moval [2], deblurring [3, 4], and speckle removal [5]. See also [6, 7, 8] for general discussions on the use of higher-order statistics in image processing. Previous work in this area however has not addressed the issue of inverting the effects from gamma correction. † 6211 Sudikoff Laboratory, Computer Science Department, Dartmouth College, Hanover, NH 03755.3510. tel: 603.646.2761 fax: 603.646.1672 email: farid@cs.dartmouth.edu. 1