A Nash game based variational model for joint image intensity correction and registration to deal with varying illumination

Abstract

Registration aligns features of two related images so that information can be compared and/or fused in order to highlight differences and complement information. In real life images where bias field is present, this undesirable artefact causes inhomogeneity of image intensities and hence leads to failure or loss of accuracy of registration models based on minimization of the differences of the two image intensities. Here, we propose a non-linear variational model for joint image intensity correction (illumination and translation) and registration and reformulate it in a game framework. While a non-potential game offers flexible reformulation and can lead to better fitting errors, proving the solution existence for a non-convex model is nontrivial. Here we establish an existence result using the Schauder's fixed point theorem. To solve the model numerically, we use an alternating minimization algorithm in the discrete setting. Finally numerical results can show that the new model outperforms existing models.

Image retinex based on the nonconvex TV-type regularization

“…One is of trying on some values for providing satisfactory results and then keeping it to be the fixed outputting. The second way is by using Game theory to reformulate the optimization problem so that the dimension of the parameters' space is much reduced, as is done in [48]. The third approach is of choosing them by using some rules based on the prior statistical characteristic such as the L-curve method [19], the generalized cross validation (GCV) [14,49], the discrepancy principle [41,45], or the variational Bayes approach [44].…”

Diffeomorphic unsupervised deep learning model for mono- and multi-modality registration

“…There exist various deformable variational models for image registration where the unknown displacement field u is sought in a properly chosen functional space. [6][7][8][9][10][11] Generally speaking, the variational problem consists in solving the optimisation problem…”

“…There exist various deformable variational models for image registration where the unknown displacement field u is sought in a properly chosen functional space. 6–11 Generally speaking, the variational problem consists in solving the optimisation problem where φ(x)=x+u(x). In (1), S(u) is a regularisation term which controls the smoothness of u and reflects our expectations by penalising unlikely transformations.…”