Image vignetting reduction via a maximization of fuzzy entropy

Variational-Bayesian Single-Image Devignetting

“…In addition, we examined the recent method proposed by Lopez-Fuentes et al [5], which is based on minimization of a certain type of image entropy. While Lopez-Fuentes et al proposed several entropies and found that the best-performing entropy depends on images [6], we used the basic version [5] because they did not detail the implementation of alternative entropies. For the parameters of these previous methods, we used the default values suggested in their respective papers [2], [5].…”

“…Cho et al [2] proposed a more effective method based on the radial bright channel of an image (i.e., a one-dimensional function composed of maximum values at each radius around an optical center), which is nearly constant for vignetting-free images but decreasing for vignetted images. Meanwhile, Lopez-Fuentes et al proposed methods that minimize different kinds of image entropies, i.e., log-entropy [5] and negative fuzzy entropy [6] to distinguish vignetted and vignetting-free images. However, these methods have limited ability to improve the quality of noisy images with vignetting because they simply invert vignetting by näive pixelwise division of a vignetted image using an estimated vignetting function [2], [5], which does not remove noise.…”

“…However, these methods have limited ability to improve the quality of noisy images with vignetting because they simply invert vignetting by näive pixelwise division of a vignetted image using an estimated vignetting function [2], [5], which does not remove noise. Furthermore, noise can also make vignetting estimation unstable, thereby leading to poor performance of subsequent vignetting removal, particularly in methods that ignore noise in vignetting estimation [5], [6]. Although some methods incorporate simple noise models in their cost functions for vignetting estimation [2], [4], these methods require additional parameters that depend on noise distributions, whose optimal values can differ between inputs, and their performance in the presence of noise has not been examined experimentally.…”

“…The Kang-Weiss model [10], which is based on the physical properties of vignetting, is a standard parameterization scheme used in various methods [2], [4]. Another common scheme is the polynomial model [1], whose parameters can be adjusted via näive hill-climbing optimization [5], [6]. In contrast, we do not employ any explicit parameterization.…”

“…In devignetting, it is essential to estimate this function accurately. Previous work on single-image devignetting [2]- [6] basically assumed a rather ideal imaging condition, i.e., degradation other than vignetting is absent or negligible. In this case, we can often determine a correct vignetting function from a vignetted image, and then obtain a desired vignetting-free image by inverting the vignetting process of that function.…”