A Modified Demons Algorithm for Cone-Beam CT-Guided Surgery

S. Nithiananthan et al.

Incorporating Tissue Excision in Deformable Image Registration: A Modified Demons Algorithm for Cone-Beam CT-Guided Surgery S.Nithiananthan,a D. Mirota,b A. Uneri,b S. Schafer,a Y. Otake,b J.W. Stayman,a and J. H. Siewerdsena,b a Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21205 b Department of Computer Science, Johns Hopkins University, Baltimore MD 21218 ABSTRACT The ability to perform fast, accurate, deformable registration with intraoperative images featuring surgical excisions was investigated for use in cone-beam CT (CBCT) guided head and neck surgery. Existing deformable registration methods generally fail to account for tissue excised between image acquisitions and typically simply “move” voxels within the images with no ability to account for tissue that is removed (or introduced) between scans. We have thus developed an approach in which an extra dimension is added during the registration process to act as a sink for voxels removed during the course of the procedure. A series of cadaveric images acquired using a prototype CBCT-capable C-arm were used to model tissue deformation and excision occurring during a surgical procedure, and the ability of deformable registration to correctly account for anatomical changes under these conditions was investigated. Using a previously developed version of the Demons deformable registration algorithm, we identify the difficulties that traditional registration algorithms encounter when faced with excised tissue and present a modified version of the algorithm better suited for use in intraoperative image-guided procedures. Studies were performed for different deformation and tissue excision tasks, and registration performance was quantified in terms of the ability to accurately account for tissue excision while avoiding spurious deformations arising around the excision. Keywords: image-guided interventions, cone-beam CT, flat-panel detector, C-arm, 3D imaging, surgical navigation, image registration, head and neck surgery

1. INTRODUCTION It is becoming increasingly clear that the introduction of high-quality 3D intraoperative imaging systems will advance surgical management of complicated head and neck cases.[1] During such complex cases patient anatomy changes over time due to deformation and surgical excisions. Image-guidance relative to preoperative imaging can thus be rendered insufficiently accurate for precise localization of critical anatomy. One technology developed to address such limitations is intraoperative cone-beam CT (CBCT) imaging implemented on a surgical C-Arm.[2] Illustrated in Figure 1 is a prototype CBCT-capable C-arm which can acquire high quality intraoperative 3D images at doses sufficiently low that multiple high-quality 3D images can be acquired during the course of the procedure.[3] The availability of up-to-date intraoperative CBCT images augments the array of preoperative imaging studies typically available. Ideally, the latest CBCT image may be studied relative to previous CBCT images, preoperative imaging studies, and perhaps most importantly, surgical planning information delineated on any previous imaging sets. As outlined in Figure 1b), the use of deformable registration allows all available imaging and planning information to be integrated into the same frame of reference while accounting for anatomical changes which have occurred during the procedure. We previously investigated the use of a variant of the Demons deformable registration algorithm[4] as a fast, efficient, and accurate means of performing deformable registration within the time constraints of a surgical procedure.[5,6] This algorithm has demonstrated registration accuracy at the level of CBCT voxel size in head and neck procedures, and a modification that includes an iterative intensity match[7,8] permits accurate registration of preoperative CT to intraoperative CBCT despite image intensity differences. In this way, as illustrated in Fig. 1b), multimodality image and planning data that is registered to preoperative CT may be similarly transformed to intraoperative CBCT. One particular difficulty with applying deformable registration for surgical guidance is that tissue is purposely excised during the course of a surgical procedure, as opposed to being solely deformed. Previous work has identified that tissue excision should be explicitly identified and handled as part of the registration process.[9] Proposed solutions tend to involve segmentation of excisions sites performed simultaneously with spatial registration. The location of excision areas has then been used for subsequent mitigation steps such as updating preoperative models,[10] or modified

Volume 7964

SPIE Medical Imaging 2011, Proc. Visualization, Image-Guided Procedures, and Display

(IN PRESS)

S. Nithiananthan et al.

deformation field smoothing.[11,12] In this work, we introduce a registration method featuring “extra-dimensional” deformations in order to explicitly model tissue excision in addition to deformation. We quantify the ability of this extradimensional component to accurately model tissue excision when solved for simultaneously with the normal deformation components and investigate the ability to mitigate erroneous deformations arising due to the presence of tissue excisions.

Figure 1. a) Experimental setup showing prototype CBCT capable C-arm and cadaver model with surgically induced deformations. b) Schematic illustration of imaging and planning information available in CBCT-guided surgical procedure and role of deformable registration in linking preoperative and intraoperative frames of reference.

2. REGISTRATION METHOD 2.1 Demons Deformable Registration Deformable registration is performed using a variant of the popular Demons algorithm previously optimized and evaluated for use in CBCT-guidance of head and neck surgical procedures.[6] Demons type algorithms consist of multiple simple steps repeated iteratively: calculation of an update field with a displacement vector calculated independently at each voxel location, addition of the update field to the previous solution, and Gaussian smoothing of the newly constructed field to yield a regularized deformation field.[4,13] For CBCT-guided head and neck procedures we find that a symmetric version of the Demons force equation considering the gradients of both the preoperative image, I0, and the intraoperative image, I1, yields the best registration result in terms of registration performance;[5] results supported by other theoretical and experimental work. [14,15] The displacement d at every voxel location x is thus computed

[

]

v v v 2[I 0 ( x ) − I1 ( x )] ∇I1 ( x ) + ∇I 0 ( x ) d (x ) = v v 2 2 ∇I1 ( x ) + ∇I 0 ( x ) + [I 0 ( x ) − I1 ( x )] / K

(1)

where the normalization factor K is taken as the mean squared value of the image voxel sizes.[16] The field computed by applying (1) at every voxel in the image is added to the existing solution and the result is smoothed by convolution with a Gaussian kernel.

Volume 7964

SPIE Medical Imaging 2011, Proc. Visualization, Image-Guided Procedures, and Display

(IN PRESS)

S. Nithiananthan et al.

2.1.1 Multi-Resolution Strategy and Convergence Criterion The steps described above are implemented in a multi-resolution strategy in order to increase registration performance in terms of overall speed and robustness. Registration is performed on a series of images created by downsampling the input images by a factor 8, 4, 2, and (optionally) 1. Registration starts at the coarsest level with the result at one level being used to initialize the subsequent level. Registration is halted at each level, and overall, by a convergence criterion based upon the difference between successive deformation fields (after smoothing). When a sufficiently large percentage of the deformation field is changing by less than 1/10 the average voxel size at the current pyramid level, registration at that level is considered convergent. Use of such a multi-resolution strategy coupled with the convergence criterion above has been measured to give registration accuracy on the order of the image voxel sizes with less than a minute of computation (on a CPU implementation) for CBCT-CBCT head and neck registration tasks featuring only tissue deformation.[6] 2.1.2 Iterative Intensity Matching for CT-CBCT Registration The Demons algorithm was originally designed for fast, monomodality registration. Without reformulation, the traditional mean-square-based force equation and its variants such as given in Equation (1) cannot be used for multimodality registration. In order to exploit the strong assumptions about intensity similarity that can be made for monomodality registration, we work within the paradigm shown in Figure 1b) where complementary sources of diagnostic imaging information such as MRI and PET are assumed to have been registered preoperatively to a planning CT. The preoperative CT can then be registered to intraoperative CBCT images using fast, intensity based methods. Unfortunately, naïve Demons registration cannot be applied for CT-CBCT registration in every case due to the possibility of intensity deviations arising either due to physical factors such as the large scatter fraction in CBCT imaging,[17] or due to other sources such as inaccurate reconstruction algorithms or insufficient Hounsfield Unit calibration. To accommodate such intensity deviations in CT-CBCT registration, we have investigated the use of an iterative tissue specific intensity match performed simultaneously with the registration procedure and found this method able to handle a range of intensity deviations while improving mean target registration error by 3 mm and 0.3 mm compared to Demons registration performed with no intensity match or with a preliminary intensity histogram matching, respectively.[7,8]

Figure 2. Illustration of problems occurring when applying Demons registration to images featuring excised tissue. (a) The pre-excision (moving) image with a region to be excised highlighted in turquoise. (b) The post-excision (fixed) image showing (simulated) removal of tissue within the specified region. (c) The deformed image (i.e., image (a) registered to (b)) using the conventional Demons algorithm. The true extent of simulated excision is highlighted in turquoise in all images. The warped, bowl-like shape of the clivus and increased curvature of posterior wall evident in (c) is an artifact of conventional Demons registration in the presence of tissue excision.

2.2 Registration in the Presence of Excised Tissue Figure 2 illustrates a sample of the problems that can occur when tissue is removed between acquisition of two images that are to be registered. In this case, voxels within the excision volume in the fixed image are matched to voxels in the moving image located in a nearby air-filled region. This false “excision” (actually computed as a deformation) leads to erroneous reshaping of the clivus into a bowl like shape, both within and nearby the excision volume. Previous

Volume 7964

SPIE Medical Imaging 2011, Proc. Visualization, Image-Guided Procedures, and Display

(IN PRESS)

S. Nithiananthan et al.

investigation into the effects of excised tissue on Demons registration performance have identified large erroneous deformation vectors being computed at the tissue excision site which can ultimately degrade registration accuracy throughout the volume due to the propagative nature of the Gaussian smoothing step. This observation led to the development of an algorithm where uniform Gaussian smoothing is replaced by filtering which is “uni-directional” through an excision.[11,12] The approach presented in this work extends ideas present in previously proposed methods, namely that excision must be handled differently from deformation and that the site of excisions can be estimated simultaneously with the registration process, and goes further by proposing an explicit method of representing excisions within the registration process. 2.2.1 Modeling Excisions as Higher Dimensional Extension of Deformations We present a modified version of the Demons algorithm which for an N-dimensional registration problem outputs an Ndimensional deformation field populated with N+1 dimensional vectors (i.e., for two 2D images the output deformation field is a 2D grid of 3D vectors, similarly, for two 3D images the deformation field is represented as a 3D volume of 4D vectors). Thus, excisions are represented as voxels displaced “into” the (N+1)th dimension while tissue deformations are handled by the first N dimensional components. Illustrated in Figure 3 is an example illustrating the 2D case where the extra-dimensional deformation field represents both deformations and excisions by “in-plane” and “out-of-plane” deformation/excision vectors, respectively. We note that all subsequent results presented in this work were performed using 3D volumetric images and 2D slices are extracted for illustration of results only. Thus, for simplicity of notation and for consistency with experiments described below, only the case of 3D-3D registration is discussed below, where excisions are represented by “deformations” into the 4th dimension. In our initial implementation, segmentation of excision areas is based upon comparison of intensity values of matched voxels to an air-tissue threshold value. While not without its limitations, this simple approach to identifying excisions can be performed independently (and thus in parallel) at each location where a deformation vector must be calculated. The simple case of an air-tissue boundary corresponds to drillout or removal of tissue (e.g., bone) in air, as in a clival drillout in skull base surgery. At every registration iteration, the intensity value of each pair of currently overlapping voxels is compared to the air-tissue threshold value to identify voxels where the moving (preoperative) intensity value is above the threshold and the fixed (intraoperative) intensity value is below. Where this condition is not met, the update displacement vector is computed as normal for the first three components by Equation (1). Voxels where this condition is true are considered candidate locations for an excision and the update vector at this voxel is computed proportional to Equation (1) but with a non-zero magnitude only in the fourth component. The newly computed update field is then added to the existing deformation field.

Figure 3. Illustration of an “extra-dimensional” deformation field representing both deformations and excisions. (a) Pre-deformation moving image overlaid with “in-plane” deformation vectors. (b) Oblique view of the moving image with “out-of-plane” excision vectors. (c) Oblique view of the moving image with both deformation and excision vectors overlaid.

Volume 7964

SPIE Medical Imaging 2011, Proc. Visualization, Image-Guided Procedures, and Display

(IN PRESS)

S. Nithiananthan et al.

As detailed above, the subsequent step is deformation field smoothing. Uniform Gaussian smoothing is applied as in normal Demons registration to the first three deformation components of the field. For the excision components, we have experimented with various smoothing parameters & methods and found a trade-off between the ability to completely recreate excision volumes and the risk of introducing erroneous excisions in other areas of the image. Currently, we have found the best results (given below) with no smoothing of the excision dimension (as may be expected given that there is little reason to believe that an excision volume or boundary would be smooth). Future work will investigate more sophisticated methods to better integrate excision smoothing with deformation smoothing. Finally, a warped version of the preoperative image is created by applying the current estimate of the 4Ddeformation field to the original preoperative image. For deformations represented by the first three components of the deformation field, linear interpolation of the intensity values within the preoperative image is carried out. The 4th dimension is assumed to be comprised of air and a form of nearest-neighbor interpolation is performed along this dimension, reflecting the fact that tissue is either excised or not, but not a mixture of both. The “voxel size” in the fourth dimension is taken to be the same as the isotropic voxel size in the normal spatial dimensions. This new warped version of the preoperative image is then used for the subsequent registration iteration.

3. EXPERIMENTAL METHODS 3.1 Cadaver model and simulated excisions To measure the accuracy of deformable registration in the presence of missing tissue and to evaluate the effect of the proposed algorithm in a controlled manner, a cadaver study was performed using a series of CBCT images acquired before and after manually introduced deformations. The images were subsequently digitally altered to introduce simulated excisions – viz., regions of voxels “erased” in a controlled manner to simulate tissue removal. This allowed measurement of the effect of excisions on registration accuracy in comparison to known “truth” and quantitative comparison of algorithm performance. The experimental setup featuring the mobile CBCT-capable C-arm is shown in Figure 1a). CBCT images were acquired before and after a series of real tissue deformations were introduced, including jaw flexion and displacement of internal sinus anatomy as shown in Figures 2(a) and 2(b). Based upon the post-deformation CBCT image, two subsequent volumes where created featuring simulated excisions representing partial clivus drillout and total clearing of the ethmoid sinuses, respectively, as shown in Figures 4(b) and 4(d). These images allowed investigation of the performance of Demons registration in the presence of excisions of differing size and surrounding anatomy with both real deformations and ground truth knowledge of the true excision volume. 3.2 Registration Tasks Registration was performed with both the “standard” Demons algorithm and the “Extra-Dimensional Demons” (XDDemons) approach described in 2.2.1. For each simulated excision described above, registration was performed with two different moving images representing distinct registration tasks: excision only, and excision + deformation. For the first task, the preoperative moving image differed from the intraoperative fixed image only by the simulated excision. For the second task, the fixed and moving images differed by both the simulated excision and the real deformations. 3.3 Analysis Registration performance was analyzed both in terms of the ability of the registration methods to cope with the presence of excisions without introducing erroneous deformations, and the success of the algorithms in representing real excisions where appropriate without introducing false excisions in nearby surrounding tissue. For both types of analysis, we used knowledge of the true excision volume which was known completely in these experiments. For more in-depth analysis, a second region of interest was created by dilating the true excision volume to create a structure representing the surrounding normal volume in which analysis of the effects of registration on tissue surrounding excisions was analyzed. Illustration of these analysis areas is given in Figure 4. For the excision only registration tasks, any computed deformation was considered erroneous. To aid analysis of the deformation + excision registration task, Demons registration was performed using the original versions of the pre and post deformation CBCT image with no simulated excision. This deformation field computed when no excision was present was compared to the deformation fields computed in the presence of excisions, and differences between the two fields were counted as erroneous deformations. For the purpose of analysis of erroneous deformations, all three

Volume 7964

SPIE Medical Imaging 2011, Proc. Visualization, Image-Guided Procedures, and Display

(IN PRESS)

S. Nithiananthan et al.

components of the deformations vectors produced by the Demons method were included, whereas the first three “involume” components of the XDDemons deformation field (which represent deformations) were included in the erroneous deformation analysis. The quality of registration (including the ability of the algorithm to effectively “eject” voxels into the extra dimension while preserving normal, non-excised tissues) was quantified in terms of excision sensitivity (# of voxels correctly removed from true excision volume ÷ size of true excision volume) and specificity (1 – # of voxels incorrectly removed from surrounding normal volume ÷ size of normal surrounding volume). A value of 1.0 for these metrics represents total accuracy in accounting for excised tissue and no erroneous removal of surrounding normal anatomy. On the other hand, a value of 0.0 represents total inability to recreate the true excision volume and incorrect removal of all anatomy in the surrounding normal volume.

Figure 4. Example slices from CBCT volumes showing images before and after (a,b) simulated clival drillout and (c,d) simulated ethmoid sinus ablation. In each “pre-operative” image the total excision volume in the slice is shown in turquoise. In each “post-operative” image the surrounding normal volume is highlighted in blue.

Mean (Max) Erroneous Deformation Magnitude (mm) Registration Task Excision Only Excision Only Deformation & Excision Deformation & Excision

Excision Location Clivus Ethmoid Clivus Ethmoid

Conventional Demons 0.5 (5.2) 0.2 (1.2) 0.7 (5.1) 0.2 (1.5)

XDDemons 0.3 (1.7) 0.2 (1.1) 0.4 (2.5) 0.2 (1.3)

Excision Sensitivity Conventional Demons XDDemons 0.31 0.97 0.44 0.64 0.31 0.97 0.42 0.68

Excision Specificity Conventional Demons XDDemons 0.99 0.996 0.98 0.98 0.99 0.99 0.97 0.97

Table 1. Quantification of registration performance in the presence of excision as measured in terms of mean and max erroneous deformation introduced into the surrounding normal volume as well as excision sensitivity (fraction of voxels correctly removed from excision site in the process of registration) and specificity (fraction of voxels correctly maintained [i.e., not removed] from surrounding normal tissue in the process of registration).

Volume 7964

SPIE Medical Imaging 2011, Proc. Visualization, Image-Guided Procedures, and Display

(IN PRESS)

S. Nithiananthan et al.

4. RESULTS Figure 5 illustrates the inability of conventional Demons registration to represent both tissue deformation and excision. While the majority of tissue deformations are accounted for and partial excavation of the excision site is seen at the clivus, being forced to accommodate excisions in terms of deformation leads to erroneous deformations around the site of the excision. For the ethmoid excision site, local “stretching” of tissue is seen within the excision site after Demons registration. The proposed extra-dimensional Demons algorithm offers a visible improvement in the ability to account for tissue excision in the cases considered while maintaining the ability to perform tissue deformation. It is noted that XDDemons performed better for the images featuring a clivus excision as opposed to an ethmoid ablation. This may be due to the finer structures present in the latter area and partial volume effects confounding the simple threshold approach used for excision identification in the current implementation

Figure 5. Illustration of registration results for conventional Demons and XDDemons registration. Each row represents a registration case: the first column is the moving image while the last column is the fixed image; the moving image after being warped with the deformation field computed by conventional and proposed Demons registration is shown in the second and third column. The first two rows show results for simulated clival drillouts while the last two rows feature simulated total ethmoid ablation. Note that the proposed registration approach attempts to reproduces the excision area, “ejecting” voxels in the region of missing tissue, while simultaneously matching the moving and fixed images.

Volume 7964

SPIE Medical Imaging 2011, Proc. Visualization, Image-Guided Procedures, and Display

(IN PRESS)

S. Nithiananthan et al.

These results are quantified in Table 1 where we see that XDDemons reduces the measured amount of erroneous deformations introduced into the surrounding normal volume by tissue excision for all the cases considered. Consistent with the qualitative results in Figure 4, we see that XDDemons performed better than conventional Demons in terms of excision sensitivity without sacrificing specificity. Once again, results in the ethmoids are not as good as in the clivus and highlight areas for future work.

5. CONCLUSIONS AND FUTURE WORK The introduction of intra-operative 3D imaging systems such as CBCT-capable C-arms promises to overcome the reliance of image-guidance systems upon preoperative image data which can be rendered inaccurate as the procedure progresses. Fast, accurate, deformable registration could combine the advantages of intraoperative imaging with important preoperative imaging and surgical planning information in the correct anatomical frame of reference. Conventional deformable registration algorithms fail to model tissue excision, a fundamental shortfall when used in surgical guidance scenarios – e.g., tumor surgery, where the primary task is usually excision of the target volume. In this work, we presented a version of the Demons registration algorithm modified to account for tissue excision and showed in a cadaveric model that both tissue deformation and excision could be handled accurately during CBCT-guided head and neck procedures. By addition of additional dimensions to the (normally 3D) registration problem, the XDDemons algorithm allows voxels to be ejected from (or introduced to) the image in order to account for excision simultaneous to registration. Explicit modeling of tissue excision serves not only to recreate the excision area, but also reduces errors in other parts of the volume introduced by the presence of excisions. The initial implementation presented in this work showed that registration performance could be improved by adding an extra spatial dimension to the registration problem to alleviate the burden of attempting to represent excision in a deformation only framework. Conventional Demons resulted in erroneous deformation in regions of tissue excision, whereas XDDemons demonstrated a comparably accurate removal of voxels from the image. Future work will investigate improvements to the tissue segmentation step and smoothing of identified segmentation areas. Explicitly modeling tissue excision within the registration step is anticipated to yield overall improvements in registration for intraoperative guidance.

ACKNLOWDGEMENTS This research was supported by the National Institutes of Health (R01-CA-127944) and collaboration with Siemens Healthcare (Erlangen, Germany) for the prototype C-arm. This work benefited from the use of the Insight Segmentation and Registration Toolkit (ITK, U.S. National Library of Medicine).

REFERENCES [1] [2] [3] [4] [5]

[6]

R. Sindwani and R. D. Bucholz, “The Next Generation of Navigational Technology,” Otolaryngologic Clinics of North America 38, 551-562 (2005) [doi:10.1016/j.otc.2004.11.003]. J. H. Siewerdsen, D. J. Moseley, S. Burch, S. K. Bisland, A. Bogaards, B. C. Wilson, and D. A. Jaffray, “Volume CT with a flat-panel detector on a mobile, isocentric C-arm: pre-clinical investigation in guidance of minimally invasive surgery,” Med Phys 32, 241-254 (2005). M. J. Daly, J. H. Siewerdsen, D. J. Moseley, D. A. Jaffray, and J. C. Irish, “Intraoperative cone-beam CT for guidance of head and neck surgery: Assessment of dose and image quality using a C-arm prototype,” Med Phys 33, 3767-80 (2006). J. P. Thirion, “Image matching as a diffusion process: an analogy with Maxwell's demons,” Med Image Anal 2, 243-260 (1998). S. Nithiananthan, K. K. Brock, J. C. Irish, and J. H. Siewerdsen, “Deformable registration for intra-operative conebeam CT guidance of head and neck surgery,” in Engineering in Medicine and Biology Society, 2008. EMBS 2008. 30th Annual International Conference of the IEEE, pp. 3634-3637 (2008) [doi:10.1109/IEMBS.2008.4649995]. S. Nithiananthan, K. K. Brock, M. J. Daly, H. Chan, J. C. Irish, and J. H. Siewerdsen, “Demons deformable registration for CBCT-guided procedures in the head and neck: Convergence and accuracy,” Med. Phys. 36, 4755-

Volume 7964

SPIE Medical Imaging 2011, Proc. Visualization, Image-Guided Procedures, and Display

(IN PRESS)

S. Nithiananthan et al.

[7] [8]

[9] [10] [11] [12] [13] [14] [15] [16] [17]

4764 (2009) [doi:10.1118/1.3223631]. S. Nithiananthan, S. Schafer, A. Uneri, D. J. Mirota, J. W. Stayman, W. Zbijewski, K. K. Brock, M. J. Daly, H. Chan, et al., “Demons Deformable Registration of CT and Cone-Beam CT Using an Iterative Intensity Matching Approach,” Medical Physics (2011). S. Nithiananthan, K. K. Brock, M. J. Daly, H. Chan, J. C. Irish, and J. H. Siewerdsen, “Demons deformable registration for cone-beam CT guidance: registration of pre- and intra-operative images,” in Medical Imaging 2010: Visualization, Image-Guided Procedures, and Modeling 7625, K. H. Wong and M. I. Miga, Eds., pp. 76250L-7, SPIE, San Diego, California, USA (2010). M. Ferrant, A. Nabavi, B. Macq, P. M. Black, F. A. Jolesz, R. Kikinis, and S. K. Warfield, “Serial registration of intraoperative MR images of the brain,” Medical Image Analysis 6, 337-359 (2002) [doi:10.1016/S13618415(02)00060-9]. M. I. Miga, D. W. Roberts, F. E. Kennedy, L. A. Platenik, A. Hartov, K. E. Lunn, and K. D. Paulsen, “Modeling of retraction and resection for intraoperative updating of images,” Neurosurgery 49, 75-84; discussion 84-5 (2001). P. Risholm, E. Samsett, I. Talos, and W. Wells, “A non-rigid registration framework that accommodates resection and retraction,” Inf Process Med Imaging 21, 447-458 (2009). P. Risholm, E. Samset, and W. Wells III, “Validation of a nonrigid registration framework that accommodates tissue resection,” presented at Medical Imaging 2010: Image Processing, 2010, San Diego, California, USA, 762319-762319-11 [doi:10.1117/12.844302]. J. Thirion, “Fast non-rigid matching of 3D medical images,” Research Report RR-2547, INRIA, France (1995). H. Wang, L. Dong, J. O'Daniel, R. Mohan, A. S. Garden, K. K. Ang, D. A. Kuban, M. Bonnen, J. Y. Chang, et al., “Validation of an accelerated 'demons' algorithm for deformable image registration in radiation therapy,” Phys Med Biol 50, 2887-2905 (2005) [doi:10.1088/0031-9155/50/12/011]. T. Vercauteren, X. Pennec, A. Perchant, and N. Ayache, “Diffeomorphic demons: Efficient non-parametric image registration,” NeuroImage 45, S61-S72 (2009) [doi:doi: DOI: 10.1016/j.neuroimage.2008.10.040]. X. Pennec, P. Cachier, and N. Ayache, “Understanding the "Demon's Algorithm": 3D Non-rigid Registration by Gradient Descent,” in Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 597-605, Springer-Verlag (1999). J. H. Siewerdsen and D. A. Jaffray, “Cone-beam computed tomography with a flat-panel imager: Magnitude and effects of x-ray scatter,” Med. Phys. 28, 220-231 (2001) [doi:10.1118/1.1339879].

Volume 7964

SPIE Medical Imaging 2011, Proc. Visualization, Image-Guided Procedures, and Display

(IN PRESS)