Many algorithms for spatial color correction of digital images have been proposed in the past. Some of the most recently developed algorithms use stochastic sampling of the image in order to obtain maximum and minimum envelope functions. The envelopes are in turn used to guide the color adjustment of the entire image. In this paper, we propose to use a variational method instead of the stochastic sampling to compute the envelopes. A numerical scheme for solving the variational equations is outlined, and we conclude that the variational approach is computationally more efficient than using stochastic sampling. A perceptual experiment with 20 observers and 13 images is carried out in order to evaluate the quality of the resulting images with the two approaches. There is no significant difference between the variational approach and the stochastic sampling when it comes to overall image quality as judged by the observers. However, the observed level of noise in the images is significantly reduced by the variational approach.