Estimating a nonradial vignetting shape

Vignetting is a phenomenon characterized by a decrease in illumination towards the edges of an image. This effect is typically represented by a radially symmetrical model, however, this paper aims to demonstrate a non-radial model of vignetting and estimate its shape. To accomplish this, a synthetic image was created and the angular vignetting shape has been modeled as a sum of harmonics. The magnitudes and amplitudes of these harmonics were obtained and used to construct the desired angular vignetting shape. Once the synthetic image with the modeled vignetting shape and added noise was created, it was used as input into a function for vignetting estimation. Also, the inputs have been a fixed vignetting center and different initial values of harmonics’ magnitudes and phases. With that inputs, despite the level of the noise, we have successfully estimated vignetting function by non-linear optimization. The function has attempted to determine the original harmonics’ used to create the vignetting angular shape. When the vignetting model is calculated, we removed it in order to get a homogeneous image. While it may be difficult to obtain the exact original values of the harmonics’, the shape can be estimated with a high level of accuracy. The paper shows that highly accurate models can be estimated for a lower number of angular harmonics, with a residual gain error standard deviation of less than 0.03%. Even in the presence of 5dB noise in the images, the gain error standard deviation remains below 3%, as long as proper parameter initialization is performed prior to optimization.