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In this paper, we propose a method for robustly determining the vignetting function given only a single image. Our method is designed to handle both textured and untextured regions in order to maximize the use of available information. To extract vignetting information from an image, we present adaptations of segmentation techniques that locate image regions with reliable data for vignetting estimation. Within each image region, our method capitalizes on the frequency characteristics and physical properties of vignetting to distinguish it from other sources of intensity variation. Rejection of outlier pixels is applied to improve the robustness of vignetting estimation. Comprehensive experiments demonstrate the effectiveness of this technique on a broad range of images with both simulated and natural vignetting effects. Causes of failures using the proposed algorithm are also analyzed.