Stopping Criteria for Log-Domain Diffeomorphic Demons Registration: An Experimental Survey for Radiotherapy...

A crucial issue in deformable image registration is achieving a robust registration algorithm at a reasonable computational cost. Given the iterative nature of the optimization procedure an algorithm must automatically detect convergence, and stop the iterative process when most appropriate. This paper ranks the performances of three stopping criteria and six stopping value computation strategies for a Log-Domain Demons Deformable registration method simulating both a coarse and a fine registration. The analyzed stopping criteria are: (a) velocity field update magnitude, (b) mean squared error, and (c) harmonic energy. Each stoping condition is formulated so that the user defines a threshold ∊, which quantifies the residual error that is acceptable for the particular problem and calculation strategy. In this work, we did not aim at assigning a value to e, but to give insights in how to evaluate and to set the threshold on a given exit strategy in a very popular registration scheme. Experiments on phantom and patient data demonstrate that comparing the optimization metric minimum over the most recent three iterations with the minimum over the fourth to sixth most recent iterations can be an appropriate algorithm stopping strategy. The harmonic energy was found to provide best trade-off between robustness and speed of convergence for the analyzed registration method at coarse registration, but was outperformed by mean squared error when all the original pixel information is used. This suggests the need of developing mathematically sound new convergence criteria in which both image and vector field information could be used to detect the actual convergence, which could be especially useful when considering multi-resolution registrations. Further work should be also dedicated to study same strategies performances in other deformable registration methods and body districts.