2D and 3D Optical Flow Based Interpolation of the 4DCT ImageSequences in the External Beam Radiotherapy

Abstract

Purpose: Although in the external beam radiotherapy tumor motionis a crucial and challenging issue due to respiration  motion, temporal changes in anatomy during imaging cause considerable problems. Moreover, the Four Dimensional Computed Tomography (4DCT) imaging has been proposed to track these changes at the different breathing phases. Also at real time tumor tracking, the accuracy of motion tracking models that are necessary can be increased by constructing virtual images due to obtaining additional motion data.
Methods: In this study, the 4DCT data set of five real patients who have had lung cancer were provided by DIR-lab site in addition to deformable image registration algorithms presented in MATLAB software and DIRART software respectively to calculate 2D and 3D vector felids between two respiratory volumes. Moreover, the 2D and 3D displacement vector were calculated by optical flow based on Horn-Schunck method, these vector fields were used to generate an interpolated image at the desired time by 2D and 3D interpolation methods. Although 2D interpolation methods included nearest, cubic, linear, and B-spline, the 3D interpolation method was based on the 3D spatial interpolation. In this study, the reconstructed image at the desired time by two methods was compared with real image at the same time. Considering Roots Mean Square Error (RMSE) between actual and interpolated imageis used to measure the accuracy of interpolated images. Also the accuracy of our reconstruction images depends on the accuracy of displacement field. 
Results: All of the methods are able to generate images at the desired time with less RMSE and high correlation coefficient. While the 2D interpolation methods that include nearest, cubic, linear, and B-spline were able to generate an image with less errors, the performance of the 2D interpolation method is less efficient than other methods.
Conclusion: The behavior and capability of the algorithmsare demonstrated by synthetic image examples. Furthermore, to compare 2D and 3D optical flow based interpolation methods, the RMSE quantitative measures are calculated. Results indicate that both 2D and 3D interpolation presented methods are outperformed significantly, and the patient is kept away from re-scanning for getting new images.