In this paper, we propose a method for 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 frequency characteristics and physical properties of vignetting to distinguish it from other sources of intensity variation. The vignetting data acquired from regions are weighted according to a presented reliability measure to promote robustness in estimation. Comprehensive experiments demonstrate the effectiveness of this technique on a broad range of images.