SU-F-J-82: A Rapid Direct Method for Inverting Respiratory Deformation Fields

Purpose:To enable efficient and consistent registrationbetween source and target images, related bynonlinear but periodic deformation, with particular focus on 4D CTimages.Methods:We present a non-iterative method for inverting forward (or backward) deformation fields from a sequence of p CT images in arespiratory cycle. By exploiting the cyclic structure, the direct inversion methodeffectively factors the inverse transformation between any two frames inthe respiratory sequence into no more than p forward (or backward) transformations, which are available in the provided forward (or backward) sequence.Results:The direct method, inspired by a fixed-point iteration method, iscompared to the iterative method with an analytical phantom and a XCATlung phantom. With the analytic phantom, the new method renders the reversed deformation field in no more than p steps with satisfactory accuracy (RMSE is below 1E-10, for example), while the iterative method becomes slow, very slow or divergent under various conditions such as large deformation. The direct method is efficient and with the XCAT phantom as well. However, when interpolations are spatial resolution limited and by low-degree interpolant, the direct method suffers from the introduced perturbation due to the lack of self-correction capability. The direct method can be used as aprediction step, making large deformation small and followed bycorrection by an iterative method.Conclusion:A direct method is presented for inverting periodic motion fields with high efficiency. When interpolation is resolution limited, the method can be used in combination with an iterative method, especially, for the case where the deformation is large and the iterative method may not converge.NIH Grant No: R01-184173