Variational approach for multi-source image fusion

In this study, the authors propose a variational model for image fusion using a gradient field to describe the features of all input images. The authors´ model is based on energy minimisation and the fused image corresponds to the minimiser of the energy functional. The authors first construct the gradient of fused image by using a weighted sum of the input gradients. Next, to increase the contrast in the fused image, the authors subtract the norm of gradient in the fused image from the functional. Finally, for the purpose of visual uniformity, the authors integrate the inputs using a `gray world´ assumption. The authors implement the algorithm using the augmented Lagrangian method. Three sets of images are used to verify the proposed method. Comparisons with other state-of-the-art algorithms show that the proposed algorithm obtains remarkable results.