Purpose: Conventional deformable image registration is often challenged by regularization design: (1) regularization functional needs to be hand crafted; (2) balancing hyper-parameters need to be tuned, often on a per-case basis; (3) single tradeoff can be insufficient for spatially heterogeneous scales across the domain; and (4) slow iterative solvers. In this study, we propose a registration network with a novel deformation representation model to perform intrinsic regularization that could be spatially variant on displacement vector field (DVF).
Methods: We introduce a representation model in the form of convolutional auto-encoder (CAE) which is trained with a set of rich DVFs as a feasibility descriptor. Then the auto-encoding discrepancy of a candidate DVF, reflecting its deviation from the learned feasible deformation manifold, is combined with fidelity in training the overall registration network. The trained network generates DVF estimates from paired images with a single forward inference evaluation run. The proposed method was tested on analytically simulated images and 2D cardiac MRI.
Results: Simulation study shows that the network reduced registration error from 1.88 to 0.39 pixels (p=2.33Ã—10â?»â?µÂ¹) compared to conventional method. Evaluation with 2D cardiac MRI sequences demonstrates the methodâ€™s capability of generating physically and physiologically feasible deformations. One notable observation is that the deformations better localized in myocardia. Incorporation of the deformation representation model yielded a registration error significantly lower than its counterpart without such model. The inference run takes 5.01 ms, compared to 5633 ms in SimpleElastix on the same platform, providing three orders of magnitude speedup over conventional method.
Conclusion: The proposed method is simple and efficient, and addresses the critical deficiency of regularization flexibility in scale and heterogeneity in existing approaches. It demonstrates the strength of combining model driven rationale in penalized objective and deep learning infrastructure (for both CAE and overall optimization).