A phantom study to evaluate three different registration platform of 3D/3D, 2D/3D, and 3D surface match with 6D alignment for precise image‐guided radiotherapy

Abstract Purpose To evaluate two three‐dimensional (3D)/3D registration platforms, one two‐dimensional (2D)/3D registration method, and one 3D surface registration method (3DS). These three technologies are available to perform six‐dimensional (6D) registrations for image‐guided radiotherapy treatment. Methods Fiducial markers were asymmetrically placed on the surfaces of an anthropomorphic head phantom (n = 13) and a body phantom (n = 8), respectively. The point match (PM) solution to the six‐dimensional (6D) transformation between the two image sets [planning computed tomography (CT) and cone beam CT (CBCT)] was determined through least‐square fitting of the fiducial positions using singular value decomposition (SVD). The transformation result from SVD was verified and was used as the gold standard to evaluate the 6D accuracy of 3D/3D registration in Varian’s platform (3D3DV), 3D/3D and 2D/3D registration in the BrainLab ExacTrac system (3D3DE and 2D3D), as well as 3DS in the AlignRT system. Image registration accuracy from each method was quantitatively evaluated by root mean square of target registration error (rmsTRE) on fiducial markers and by isocenter registration error (IRE). The Wilcoxon signed‐rank test was utilized to compare the difference of each registration method with PM. A P < 0.05 was considered significant. Results rmsTRE was in the range of 0.4 mm/0.7 mm (cranial/body), 0.5 mm/1 mm, 1.0 mm/1.5 mm, and 1.0 mm/1.2 mm for PM, 3D3D, 2D3D, and 3DS, respectively. Comparing to PM, the mean errors of IRE were 0.3 mm/1 mm for 3D3D, 0.5 mm/1.4 mm for 2D3D, and 1.6 mm/1.35 mm for 3DS for the cranial and body phantoms respectively. Both of 3D3D and 2D3D methods differed significantly in the roll direction as compared to the PM method for the cranial phantom. The 3DS method was significantly different from the PM method in all three translation dimensions for both the cranial (P = 0.003–P = 0.03) and body (P < 0.001–P = 0.008) phantoms. Conclusion 3D3D using CBCT had the best image registration accuracy among all the tested methods. 2D3D method was slightly inferior to the 3D3D method but was still acceptable as a treatment position verification device. 3DS is comparable to 2D3D technique and could be a substitute for X‐ray or CBCT for pretreatment verification for treatment of anatomical sites that are rigid.

was still acceptable as a treatment position verification device. 3DS is comparable to 2D3D technique and could be a substitute for X-ray or CBCT for pretreatment verification for treatment of anatomical sites that are rigid. All registration methods discussed here result in rigid body transformations. There are different approach of 2D3D registration. 2 The most popular one is the intensity-based method which is the one compared in this study. The (2D3D) 2,3 registration process compares the intensity of the paired planar kV X-ray images with the intensity of digitally reconstructed radiographs (DRRs) created from the planning CT. A similarity metric is minimized iteratively to optimize the translations and rotations used to generate the DRRs by minimizing the geometrical difference between the paired DRRs and the paired X-ray image. 3D3D method directly compare two volumetric data set (KV-CBCT and planning CT in this study) and compute the geometric transformation of the two volumetric images by minimizing the similarity metric (intensity difference, mutual information, etc.) in three dimensions. Optical surface imaging renders the object surface in image space. The geometric transformation is determined by minimizing the distance of the correspondence (most popularly using Integrative Closet Point method) in the two threedimensional point set sampled from in-room active illuminated projector/receiver (typically, structured-light/camera) and the planning CT surface (3DS). The principle of structured-light 3D surface imaging techniques is to extract the 3D surface shape based on the information from the distortion of the projected structured-light pattern. 4 To keep a reasonable frame rate for real-time monitoring, the point cloud is restricted to a limited and predefined region of interest (ROI).
All these modalities have large numbers of points, pixels, or voxels to be matched and rely on an iterative optimization procedure to search for the geometrical transformation. In addition to the uncertainties due to the spatial resolution of both image sets, image artifacts, noise, and possible effects due to preprocessing alterations to correct for the nonuniform intensity distribution between two images, iterative methods normally cannot guarantee that a solution converges to a global minimum and are not as robust as analytical methods.
Image registration based on extrinsic markers is straightforward and does not require complex optimization algorithms. For rigid bodies, the point match (PM) problem is typically defined to be the problem of finding the translation vector and the rotation matrix that produces the least-square fit of the corresponding fiducial points.
The problem of determining the rotation matrix can be reduced to the "Orthogonal Procrustes Problem," 5 which has many closed form solutions. 6 Assuming the points are not colinear, the limitation of PM is the localization error of the individual markers. 7 Increasing the number of fiducial points reduces the localization uncertainty. One-millimeter target registration error is theoretically possible when using four extrinsic fiducials with 2-mm CT scan slice thickness. 8 PM-based registration using extrinsic markers is accurate and is therefore often used as a ground truth for validation of other registration methods under rigid conditions. It is the aim of this study to compare the accuracy of several image guidance systems used in RT using PM as a baseline.

2.A | Data acquired
Registration accuracy was studied in two clinical cases: the cranium and the torso. Thirteen external markers were asymmetrically placed around the surface of a cranial phantom (STEEV) (CIRS Inc., Norfolk, VA). Eight of the markers (the "C" group) were used to compute the PM transformation (using the singular value decomposition -SVD- | 189 based root mean square scheme in the following section) between two set of images. The remaining five markers (the "V" group) were used to validate and compare the registration accuracy of all from different registration methods. Similarly, eight markers were asymmetrically placed around the surface of a body phantom (ET verification phantom, BrainLab, Munich, Germany). Five of the markers ("C" group) were used to compute the transformation for PM method.
The remaining three markers ("V" group) were used to validate and compare all the registration methods in this study.  Table 1.

2.B | Rigid body transformation: Least-square solution using SVD
Assume there exist two corresponding point sets represented by Matrices A and B. The question is to determine a rotation matrix R and a translation vector T using a least-squares scheme: where A t and B t denote the transpose of the matrix A and B, respectively, and Ω is a set of 3 × 3 orthogonal rotation matrices such that where R t denotes the transpose of the matrix R.
Using the SVD solution developed by Arun et al. in 1987, 8 Soderkvist 6 outlined the algorithm in the following steps:

Re-center A points and B points to the centroids,
4. Compute SVD of B', B'=UΛV t , the optimal rotation matrix, R, that maximizes the desired trace is R = VU t , where VV t = UU t = I 3 , The following image registration techniques were investigated and validated using the extrinsic fiducial makers: (a) an in-house PM image registration program using the above SVD scheme applied to the fidu-  Table 2.

2.C | Validation and evaluation
Image guidance system based on fiducial registration usually display the measure of registration accuracy based on the goodness of fit of the fiducials. Using fiducial markers with rigid geometry, the true transformation from one CT image set to another CT image set should register the two image sets with a residual error of zero. Fiducial registration error (FRE), which is a common measure of goodness of fit, is the distance between corresponding fiducial points after registration. The problem of registration reduces to finding a rotation and translation that minimizes FRE. For C group with n fiducial markers, where a i ∈ A and b i ∈ B.
T A B L E 1 Number of registration and resolution of the images taken for the technique applied in this study.
where < .> means "expected value of." To assess the accuracy of all registration techniques, an independent group (V) of fiducial markers was used to compute the target registration error (TRE), which is the distance between corresponding markers not used in generating the registrations. For the V group with m fiducial markers, where a j ∉ A and b j ∉ B.
A root mean square target registration error (rmsTRE) was calculated for each setup observation to compare the accuracy of the registration techniques applied in this study.
where R and T are the values calculated by PM, 3D3DV, 3D3DE, 2D3D, and 3DS methods, respectively.
The extrinsic markers were easy to place and to study the known transformation from one image to another image. However, they were placed outside of the phantom and were distant from the treatment target. The centroid of the extrinsic makers is typically close to the treatment target (as in this study) such that the mea-

2.D | Statistics
Wilcoxon signed-rank test was utilized to compare the difference of each registration method with the PM method. A P < 0.05 was considered significant. Using rmsTRE as evaluation metric, the accuracy of each image registration method in this study was summarized in Table 3. Overall, the PM method applied in this study had the smallest mean and standard deviation (STD) and was considered the most accurate. The mean value of rmsTRE using 3D3D was approximately 0.1-0.5 mm higher than the PM method and was close to half of the maximum pixel dimension. The mean value of rmsTRE using 2D3D and 3DS was found to be 0.3-0.8 mm higher than the PM method.  Unlike FRE, which does not depend on the configuration of the fiducial markers, the accuracy of PM method evaluated independently by rmsTRE is optimal when N (number of markers used to compute transformation) increases and the distance between makers is large. 10,12 The rmsTRE values of the PM method were slightly (0.1 mm) larger than the mean FRE, which was compatible with the results from literature. 13  Many studies have compared 2D3D-paired X-ray images to 3D3D CBCT in phantom or in patients. [14][15][16][17][18] The typical improvements in 3D3D to 2D3D were at the order of millimeter. Our study showed that the intensity-based 2D3D registrations had rmsTRE of 0.9 and 1.5 mm at cranial and body site, respectively. They were 100% larger than the PM method and were about 50% larger than the 3D3D method. The IREs were reduced to 0.5 and 0. sensing ROI is limited to the sharply varying slopes in the nasal area.

| RESULTS
Another result from this study showed that the rmsTRE was less than the IRE in both cranial and body sites. These results were different from the intensity-based registration which performed evaluation based on the entire image. 3DS uses ROI to optimize 3D alignment, ROI normally is partially limited to the anterior surface and has its centroid distance away from ISO. An optimal match at the surface may not necessarily be an optimal match at deeper locations due to the limitations of iterative optimization. A minimal rotational mismatch will introduce translation error of point distance away from the rotation center. 6 This may explain why a larger registration error (especially the translation) was observed at the ISO than at the maker points on surface.   This study implemented a robust PM registration using extrinsic fiducial markers as a gold standard to assess the accuracy of image registrations applied in modern IGRT techniques. Studies were done under rigid phantom with the clinical application limited to treatment site which is rigid, for example, cranial, paraspinal, and pelvis bone. All the three IGRT platforms discussed in this study using auto-registration process is optimal under rigid condition. Treatment sites with shape or position (relative to nearby bone) varies from day to day, their treatment accuracies can be enhanced by using different way, for example, using fiducial makers (prostate in 2D3D match), 28 using a soft tissue mode by limiting a smaller ROI to the target (lung lesion in 3D3D match), 29 using OSI to align setup (arm, breast, H&N) followed with X-ray or CBCT, or using nonrigid registration followed with adapted plan (Adaptive Radiation Therapy). 30 The accuracy of the nonrigid condition using the methods listed above is beyond the scope of this study. Although the PM results in this study were limited by the pixel size and the number of markers, the achieved TREs were small and the evaluation of the commercial image registration methods can be used as a guideline in clinical IGRT implementation.

| CONCLUSIONS
The accuracy of the image registrations utilized in modern IGRT techniques has been evaluated using a PM method. 3D3D using

CONF LICT OF I NTEREST
The authors have no conflict of interest to disclose.