A fast inverse consistent deformable image registration method based on symmetric optical flow computation

Abstract

Deformable image registration is widely used in various radiation therapy applications including daily treatment planning adaptation to map planned tissue or dose to changing anatomy. In this work, a simple and efficient inverse consistency deformable registration method is proposed with aims of higher registration accuracy and faster convergence speed. Instead of registering image I to a second image J, the two images are symmetrically deformed toward one another in multiple passes, until both deformed images are matched and correct registration is therefore achieved. In each pass, a delta motion field is computed by minimizing a symmetric optical flow system cost function using modified optical flow algorithms. The images are then further deformed with the delta motion field in the positive and negative directions respectively, and then used for the next pass. The magnitude of the delta motion field is forced to be less than 0.4 voxel for every pass in order to guarantee smoothness and invertibility for the two overall motion fields that are accumulating the delta motion fields in both positive and negative directions, respectively. The final motion fields to register the original images I and J, in either direction, are calculated by inverting one overall motion field and combining the inversion result with the other overall motion field. The final motion fields are inversely consistent and this is ensured by the symmetric way that registration is carried out. The proposed method is demonstrated with phantom images, artificially deformed patient images and 4D-CT images. Our results suggest that the proposed method is able to improve the overall accuracy (reducing registration error by 30% or more, compared to the original and inversely inconsistent optical flow algorithms), reduce the inverse consistency error (by 95% or more) and increase the convergence rate (by 100% or more). The overall computation speed may slightly decrease, or increase in most cases because the new method converges faster. Compared to previously reported inverse consistency algorithms, the proposed method is simpler, easier to implement and more efficient.

Quantitative evaluation of the performance of different deformable image registration algorithms in helical, axial, and cone‐beam CT images using a mobile phantom

“…It includes a variety of DIR algorithms coded in the MATLAB software (MathWorks, Inc., Natick, MA, USA) and has software tools to perform important functions in implementing adaptive radiation therapy 3. Four DIR algorithms: Demons,18, 19 Fast‐Demons,20, 21 Horn‐Schunck,22 and Lucas‐Kanade23, 24 were used to register the CT images of a mobile phantom along with CT images of the stationary phantom. These algorithms represent a variety of autonomous intensity‐based algorithms DIR to solve the optical flow equation.…”

“…The optical flow is calculated in two steps: (a) the instantaneous optical flow is computed for every point within the static image, and (b) the deformation field is regularized by smoothing with a Gaussian filter 18. The Fast‐Demons algorithm explicitly takes into account Newton's third law of motion in combination with the diffusing model used by the Demons algorithm 20, 21. In Fast‐Demons, the demons forces allow additionally the moving object to diffuse through the static or reference image 21.…”

“…In Fast‐Demons, the demons forces allow additionally the moving object to diffuse through the static or reference image 21. This active force in the Fast‐Demons algorithm serves as an amplifying factor in the overall force applied in the Demons algorithm 20, 21…”

“…Four DIR algorithms: Demons,18, 19 Fast‐Demons,20, 21 Horn‐Schunk,22 and Lucas‐Kanade23, 24 from the DIRART software were selected to register CT images of a phantom which moved with controlled motion patterns. The variations in the volumes and CT‐number values of the mobile targets obtained from deformed images were quantified.…”

Efficient symmetric and inverse-consistent deformable registration through interleaved optimization

“…Unfortunately, most contributions remain largely academic with few work focussing on practical aspects such as achieving similar numerical accuracy in clinically affordable time-frames. Yang et al [5] present an inverse-consistent registration algorithm that is similar to Avants et al diffeomorphic mapping, but focusses on simplicity and computational efficiency. Nevertheless, their reported results are still costly for clinical applications.…”