Total variation based variational model for the uneven illumination correction

It is well known that an image is the pixel-wise multiplication of two components (illumination and reflectance) that are described as intrinsic images. To enhance the visual quality of a degraded image with uneven illumination and low local contrast, it is an effective way to extract the illumination or reflectance from the image and correct the unevenness of illumination. In this paper, we propose a variational model to estimate the illumination and reflectance from the degraded image for the uneven illumination correction. The proposed model is solved by the alternating minimization scheme and the augmented Lagrange method. We give some theoretic analysis of our model and convergence analysis of the algorithm. Experimental results show that the proposed model can achieve excellent performance in the correction of the uneven illumination.