Validation for 2D/3D registration II: The comparison of intensity‐ and gradient‐based merit functions using a new gold standard data set
Authors: Gendrin Christelle , Markelj Primož , Pawiro Supriyanto Ardjo , Spoerk Jakob , Bloch Christoph , Weber Christoph , Figl Michael , Bergmann Helmar , Birkfellner Wolfgang , Likar Boštjan , Pernuš Franjo 
Published: March 2011

Purpose:A new gold standard data set for validation of 2D/3D registration based on a porcine cadaver head with attached fiducial markers was presented in the first part of this article. The advantage of this new phantom is the large amount of soft tissue, which simulates realistic conditions for registration. This article tests the performance of intensity‐ and gradient‐based algorithms for 2D/3D registration using the new phantom data set.Methods:Intensity‐based methods with four merit functions, namely, cross correlation, rank correlation, correlation ratio, and mutual information (MI), and two gradient‐based algorithms, the backprojection gradient‐based (BGB) registration method and the reconstruction gradient‐based (RGB) registration method, were compared. Four volumes consisting of CBCT with two fields of view, 64 slice multidetector CT, and magnetic resonance‐T1 weighted images were registered to a pair of kV x‐ray images and a pair of MV images. A standardized evaluation methodology was employed. Targets were evenly spread over the volumes and 250 starting positions of the 3D volumes with initial displacements of up to 25 mm from the gold standard position were calculated. After the registration, the displacement from the gold standard was retrieved and the root mean square (RMS), mean, and standard deviation mean target registration errors (mTREs) over 250 registrations were derived. Additionally, the following merit properties were computed: Accuracy, capture range, number of minima, risk of nonconvergence, and distinctiveness of optimum for better comparison of the robustness of each merit.Results:Among the merit functions used for the intensity‐based method, MI reached the best accuracy with an RMS mTRE down to 1.30 mm. Furthermore, it was the only merit function that could accurately register the CT to the kV x rays with the presence of tissue deformation. As for the gradient‐based methods, BGB and RGB methods achieved subvoxel accuracy (RMS mTRE down to 0.56 and 0.70 mm, respectively). Overall, gradient‐based similarity measures were found to be substantially more accurate than intensity‐based methods and could cope with soft tissue deformation and enabled also accurate registrations of the MR‐T1 volume to the kV x‐ray image.Conclusions:In this article, the authors demonstrate the usefulness of a new phantom image data set for the evaluation of 2D/3D registration methods, which featured soft tissue deformation. The author's evaluation shows that gradient‐based methods are more accurate than intensity‐based methods, especially when soft tissue deformation is present. However, the current nonoptimized implementations make them prohibitively slow for practical applications. On the other hand, the speed of the intensity‐based method renders these more suitable for clinical use, while the accuracy is still competitive.