QUADRATIC: Quality of Dice in Registration Circuits.

Image registration involves identification of a transformation to fit a target image to a reference image space. The success of the registration process is vital for correct interpretation of the results of many medical image-processing applications, including multi-atlas segmentation. While there are several validation metrics employed in rigid registration to examine the accuracy of the method, non-rigid registrations (NRR) are validated subjectively in most cases, validated in offline cases, or based on image similarity metrics, all of which have been shown to poorly correlate with true registration quality. In this paper, we model the error for each target scan by expanding on the idea of Assessing Quality Using Image Registration Circuits (AQUIRC), which created a model for error "quality" associated with NRR. In this paper, we model the Dice similarity coefficient (DSC) error in the network, for a more interpretable measure. We test four functional models using a leave-one-out strategy to evaluate the relationship between edge DSC and circuit DSC: linear, quadratic, third order, or multiplicative models. We found that the quadratic model most accurately learns the NRR-DSC, with a median correlation coefficient of 0.58 with the true NRR-DSC, we call this the QUADRATIC (QUAlity of Dice in RegistrATIon Circuits) model. The QUADRATIC model is used for multi-atlas segmentation based on majority vote. Choosing the four best atlases predicted from the QUDRATIC model resulted in a 7% increase in the DSC between segmented image and true labels.