Graph loss function for unsupervised learning-based deformable medical image registration

Establishing accurate spatial correspondences is the main purpose for deformable medical image registration. Although many unsupervised learning-based methods have been proposed in this field and achieved fairly good results, because of their strong feature extraction ability and no need of the ground truth, they are often limited by relying on similarity of the spatially adjacent pixels which could not fully utilize geometrical feature for robust registration. To address this limitation, we propose a new graph loss function to represent the nonadjacent geometrical similarity. We divide the algorithm into two branches. The first branch takes pairs of medical images as input directly and obtains the loss term LcNN by typical convolution operation. In the second branch, we convert the images to forms of graph represents, and then obtain the loss term LGcN by graph convolution operation. Finally, the sum of the two loss terms constitute the total loss function. We verify our method on two datasets including LPBA40 and ADNI, and the experimental results demonstrate a marked improvement, with higher average Dice and lower registration errors of MSE compared with state-of-the-art methods.