Developmental hip dysplasia (DDH) is a congenital condition which may cause greater contact pressures between the femoral head and acetabular cartilage due to a deformed acetabulum or femoral head. These conditions may cause pain and limit the amount of physical activity an individual may perform. When DDH is not addressed, severe arthritis by age 30 is typical, and requires surgical intervention .
In 1984, the periacetabular osteotomy (PAO) was developed by Ganz for the purpose of treating DDH. Standing AP and false profile radiographs are used to preoperatively assess the condition and develop an initial surgical plan. Osteotomies along the pubis, ilium, ischium, and posterior column of the pelvis are performed, typically with fluoroscopic guidance . The ischial and posterior cuts present significant challenges, including using difficult to interpret fluoroscopic views, potentially affecting the Sciatic nerve, and risking joint breakage due to the osteotome’s proximity to the acetabulum. After completing the osteotomies, the acetabular fragment is freed from the pelvis and repositioned to increase femoral coverage and improve joint contact pressure [2, 3, 4, 5, 6] (Fig. 1).
Mentally resolving the 3D pose of the acetabular fragment using intraoperative fluroscopy is challenging, especially for novice surgeons . An acceptable repositioning is often determined using the lateral center edge (LCE) angle , which estimates the amount of lateral femoral head coverage provided by the acetabulum. In order to achieve long-term survivability of the joint, a LCE angle between is desired 
. Mentally resolving the LCE angle from 2D radiographs, without any other tools, was shown to have a large variance.
To address the challenges with performing PAO, several computer assisted systems using optical tracking technology have been developed; e.g. [11, 12, 13, 14, 15, 16]. However, intraoperative optical tracking systems are not yet standard equipment in most operating rooms, and have several technical disadvantages, such as a sensitivity to occlusion and a limited workspace. Moreover, the need to digitize points on the ilium and iliac crest for registration of the patient’s pelvis to a preoperative model, requires more invasive incisions than typically needed for a PAO [12, 17, 18]. These reasons, and the universal availability of intraoperative fluoroscopic imaging, provide motivation for the use of an X-Ray based navigation system. In place of specialized 3D tracking devices, computer-assisted X-Ray navigation systems use the fluoroscopic or radiographic imagers already present during many interventions [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32]. Since the acetabular fragment is created intraoperatively, an accurate model of the fragment shape is not available, and invalidates the assumptions used in existing multiple-object registration methods [22, 24, 28].
We propose a fiducialess approach that performs multiple-object, multiple-view, 2D/3D X-Ray to CT registration to resolve the pose of an acetabular fragment with respect to the anterior pelvic plane (APP). After the clinician performs a repositioning of the fragment, the pelvis and fragment are registered using several fluoroscopic images, and the fragment’s pose and LCE angle are reported. The fragment shape is estimated after registering the patient’s non-acetabular portion of the pelvis. Cut lines present in the 2D images are used to approximate the ilium and pubis osteotomies, while the ischial and posterior osteotomies remain set according to a preoperative plan. The pose and LCE values may be interpreted by the clinician to determine whether the fragment is in an acceptable pose, or whether further adjustment is needed. When the fragment needs to be moved, the current pose estimate may help determine the direction in which the fragment should next be adjusted. Additionally, but beyond the scope of this work, biomechanical indicators may also be computed once the fragment’s relative pose is known [3, 4, 5, 6]. The high-level workflow of our proposal is shown in Fig. 2.
We believe this is the first computer assisted system for intraoperatively tracking an acetabular fragment with X-Ray navigation without the use of artificial fiducial objects. Compared to other multiple-view registration approaches in literature, our approach does not require a tracked, encoded, or motorized, C-Arm. Unlike existing multiple-object registration solutions, an inaccurate model of the fractured shape is allowed and a prior distribution over fragment shapes is not required. Moreover, non-standard equipment is not required to perform the surgery and no burdensome steps are added to the operating workflow.
We have evaluated the proposed method with a large simulation study and six cadaver surgeries. In both experiments we report fragment pose and LCE errors when knowing the true fragment shape, a preoperatively planned shape, and an intraoperatively estimated shape. To evaluate the performance of our method, we examine rotation and translation components of the pose differences from ground truth, as well as the error in LCE angle measurement. Since it is expected that fragment pose and LCE angle errors will increase as the shapes used for registration match intraoperative shapes less, analysis of the simulation and cadaver experiments will determine if the proposed methods are sufficiently accurate to assist with intraoperative evaluation of dysplasia.
2 Related Work
Initial work on computer aided systems for pelvic osteotomy focused on performing the actual osteotomies, rather than tracking the mobilized acetabular fragment. Langlotz demonstrated the use of preoperative CT and optically tracked surgical instruments to assist with PAOs, but did not provide estimates on the relocated pose of the acetabular fragment [11, 33]. Mayman used optical tracking to intraoperatively place guiding screws on the patient’s pelvis and matching osteotomies from a preoperative plan, but did not provide intraoperative tracking of the fragment . Akiyama also tracked osteotomes during a curved periacetabular osteotomy (CPO)  using optical tracking . In , Radermacher constructed patient specific cutting guides for use in a triple osteotomy , however the pose of the fragment was not reported during the procedure. Similarly, Otsuki developed patient specific cutting guides to perform CPO and did not track the pose of the acetabular fragment .
Also using preoperative CT and optical tracking devices, Murphy did not track the ostoetomes, but instead tracked the acetabular movements and computed intraoperative biomechanics [38, 12]. Through repeated digitizations of points on the acetabular fragment body, the fragment was tracked and the appropriate biomechanical properties were presented to the clinician . Fragment pose errors of and mm were reported. The process of manually digitizing the bone bur points during each fragment reposition adds a small amount of time to the overall procedure and may be subject to some error . Liu also developed a system for preoperative PAO planning and intraoperative tracking of the fragment using optical tracking and a separate rigid body attached to the fragment [14, 39]. However, fixing a separate rigid body to the fragment is not necessarily practical when using a state-of-the-art, minimally invasive, approach such as  and . For rotational acetabular osteotomies (RAO) , Takao used an optically tracked system to monitor the osteotomes and fragment movement . The fragment pose was intraoperatively estimated by digitizing the anterior edge of the acetabulum, which resulted in some difficulty distinguishing between rotation and translation.
X-Ray navigation has been used to assist with the reduction of traumatic bone fractures, by providing real-time 3D visualizations of relocated bone fragments  and feedback corresponding to a 3D preoperative plan . Methods to automatically annotate intraoperative images have been used to avoid wrong-level spinal surgery  and mitigate the malpositioning of surgical implants . Using intraoperative X-Ray imaging, a surgical robot may be guided into an optimal location for the milling [23, 31], or drilling , of bone. Automatic 3D visualization and kinematic analysis of the wrist  and knee [25, 21] have also been demonstrated with X-Ray navigation. To our knowledge, no existing method based on X-Ray navigation, without fiducials, is able to localize a bone fragment without accurate preoperative knowledge or a statistical prior of the fragment shape.
At the core of an X-Ray based navigation system is a 2D/3D registration algorithm 
. The goal of 2D/3D registration is to determine the pose of 3D objects with respect to a 3D coordinate frame using a series of 2D X-Ray images. Typically, a preoperative 3D model, such as a CT scan is used to represent the patient, and the information contained in the X-Ray image is used to determine the pose of the patient with respect to the intraoperative X-Ray imager. The majority of 2D/3D X-Ray registration methods may be classified as either “intensity-based” or “feature-based,” however we limit discussion to intensity-based methods in this paper.
Intensity-based registration performs an optimization over the relevant pose parameters, using an objective function that compares simulated radiographs, commonly referred to as digitally reconstructed radiographs (DRRs), with the intraoperative image . The comparison is performed using a mathematical construct known as a similarity measure . Due to the differences in X-Ray energy between preoperative CT and intraoperative fluoroscopy, the most effective similarity metrics compare the 2D gradients of a measured radiograph and a DRR, such as normalized cross-correlation between the Sobel gradient images (Grad-NCC) . Robustness to metallic objects and bone fractures may be improved by taking a weighted sum of similarity measures computed in local regions of interest [41, 42]. Registration with multiple 2D views, and known relative poses between each view, is accomplished by creating DRRs at each view and summing the similarity scores for each view . In order to register multiple objects with known shape, each object may be treated as a separate volume, and DRRs for each object are summed together to create a single DRR . The registration problem for object poses: , with intraoperative views: , a pre-operative CT: , a DRR operator: , similarity metric: , and regularizer over plausible poses: , is concisely stated in (1).
With the advent of general purpose GPU programming resources, Otake was able to efficiently form many DRRs simultaneously and use a state of the art “Covariance Matrix Adaptation: Evolutionary Search” (CMA-ES) optimization strategy  to carry out registration of a single femur using three views in under 22 seconds . Relative pose information was computed using an external fiducial for a non-motorized C-Arm and was preoperatively calibrated when using a motorized C-Arm.
Several groups have demonstrated registration of multiple objects with intensity-based objective functions and accurate shape models, or with a statistical prior of the shape distributions.
In , Otake’s framework was extended to multiple objects for the knee joint (distal femur, patella, proximal tibia) tracking with bi-plane fluoroscopy. Initial registration times at the start of each sequence for the femur, tibia, and patella bones were between 2 and 5 minutes. All femur and tibia poses were estimated within and mm, and 74% of patella poses were estimated within the same thresholds.
Gong proposed to use intensity-based registration to intraoperatively estimate the position of bone fragments resulting from a distal radius fracture . The approach requires preoperative knowledge of the bone fragment shapes and uses a preoperative, but post-trauma, CT scan . Two 3D printed phantoms with synthetic fractures were used to test the method with four fluoroscopic views from a tracked C-Arm. Target registration errors (TREs) smaller than 3 mm were achieved when using a manual, interactive, initialization of the registration. Execution times of 3-9 minutes were reported using modest hardware.
In order to localize and determine the shape of carpal bones in the hand, Chen, et al. use a 2D/3D registration of a single fluoroscopic view to 3D statistical shape and pose models of the carpal bones, radius, and ulna . TREs of mm were reported in simulation, and TREs from were reported in the flouroscopic experiments. Registration times were approximately 3 minutes per frame.
Although related by the motivation to track multiple objects with intensity-based registration, the aforementioned works do not provide a complete solution for the localization of an acetabular fragment. Most importantly, the fragment shape is not completely known pre-operatively and, to our knowledge, no statistical priors of pelvic osteotomies exist. In contrast to the fluoroscopic data collected of the phantom in , the fluoroscopic images of a human have more heterogeneous hard and soft tissue distributions, usually resulting in a more challenging registration. Additionally, objects such as metallic screws, wires, or tools may confound a registration strategy, and were not present in the fluoroscopic views used by [28, 22, 20].
Without any external fiducial objects or optical tracking systems, the methods proposed in this paper intraoperatively estimate an acetabular fragment’s pose using X-Ray navigation. The pose estimation problem is solved by extending previous 2D/3D X-Ray registration techniques to partially estimate the acetabular fragment shape during surgery, and then localize the pelvis and fragment without a tracked, motorized, or encoded, X-Ray imager. Furthermore, our method aims to provide intraoperative feedback in a reasonable timeframe, with computation times on the order of seconds.
3 Materials and Methods
3.1 Preoperative Processing and Planning
Lower torso preoperative CT images were acquired and resampled to have 1 mm isotropic voxel spacing. Segmentation of the pelvis, and left and right femurs was performed using an automatic method , followed by manual touch up. The manual touch up was occasionally necessary to distinguish between the acetabulum of a pelvis and the corresponding femoral head. Using manually annotated landmarks, the APP was computed as described by  and the origin was relocated to the ipsilateral femoral head. The APP coordinate axes are aligned with the left/right (LR), inferior/superior (IS), and anterior/posterior (AP) anatomical axes. An example of the APP axis orientations is shown in Fig. 1. In order to report LCE angles intraoperatively, the most lateral points of the acetabulum are digitized from coronal slices of the preoperative CT volume.
Other landmarks identified for registration purposes were the medial and inferior points of maximal curvature on the obturator foramen, the greater sciatic notch, and inferior symphysis. To allow for accurate initialization of full pelvis registration in the presence of a mobilized fragment, the registration landmarks should not be located on portions of the pelvis that may become fragment.
A preoperative plan of the osteotomies is created by manual selection of several landmarks on the pelvis surface and cutting planes are fit to pass through the landmarks. Next, a label map is computed that indicates whether a voxel represents the acetabular bone fragment, the non-fragment pelvis, a portion of bone removed due to the chiseling action, left femur, or right femur. The osteotomy action is simulated by moving a virtual chisel, of width 1 mm, along the virtual cutting planes defined by the preoperative plan. Starting from the original segmentation, all pelvis labels contained within the convex hull defined by the virtual cutting planes are marked as a candidate fragment voxel. Furthermore, if a candidate fragment voxel is within a chisel width of any virtual cut plane, it is also marked as a candidate “cut” voxel. The set of candidate fragment voxels is divided into connected components, with the largest component kept as candidate fragment voxels, and the others reverted to pelvis labels. Of the remaining candidate fragment voxels, any marked as candidate cut voxels are labeled as cuts, and are otherwise labeled as fragment. Tight bounding boxes are computed about the pelvis labels, fragment labels, and femur labels to create sub-volumes for each object.
3.2 Intraoperative Registration Strategy
Our registration strategy is based on the methods described in  and . However, the methods proposed here do not rely on external information to recover the multiple-view geometry, provide a quick single-landmark initialization, use a similarity metric robust to mismatches between the preoperative models and intraoperative reality, perform a faster local search at higher resolution levels, and attempt to recover the shape of intraoperatively created bone fragments without an additional CT.
DRRs are formed by ray casting through each object’s attenuation volume with a ray step size of 1 mm and trilinear interpolation. Grad-NCC scores are computed throughout image patches, with the mean value used as the similarity measure for all intensity-based registrations in this work. Ray casting and similarity metric computation are computed on a GPU through the use of OpenCL , while optimization logic is conducted on the CPU. Image parameters and the projection geometry are derived from a Siemens CIOS Fusion C-Arm with 30 cm flat panel detector. Using DICOM metadata populated by a CIOS Fusion, we created a naïve set of intrinsic parameters for the C-Arm: image dimensions of , isotropic pixel spacing of mm/pixel, a source-to-detector distance of 1020 mm, no distortion, and a principal point at the center of the image.
We use two 2D image resolution levels in this work, starting from coarse ( downsampling in each 2D dimension) and moving to a finer resolution ( downsampling). At the coarsest resolution level, all optimizations are conducted with the CMA-ES strategy, and the Bounded Optimization by Quadratic Approximation (BOBYQA) strategy  is used at the second level. The CMA-ES search strategy is a derivative free method which requires a large number of objective function evaluations per iteration, but approximates a traditional second-order algorithm while maintaining robustness to local minima . Since the BOBYQA strategy requires only a single objective function evaluation per iteration, it has significantly faster runtimes compared to CMA-ES for this work. Even though BOBYQA does not provide the same robustness to local minima as CMA-ES, we justify its use at the second resolution level due to its efficiency, and because we assume that pose estimates after the first resolution level lie within a smooth, convex, region about the true minima.
The C-Arm is not required to be motorized, encoded, or capable of reporting relative pose information. In order to obtain the relative pose information required by the multi-object fragment registration, we treat the patient’s anatomy as a “fiducial” object. Single-view registrations of the pelvis are performed for each view and the pelvis coordinate frame is then used as the C-Arm world frame.
Assuming the first fluoroscopic view is approximately AP, a single landmark is manually annotated in 2D to initialize pelvis registration. The 3D landmark location, with respect to the C-Arm, is estimated by traversing the source-to-detector ray of this landmark of the source-to-detector distance. Orientation of the pelvis is computed using the APP coordinate frame described in section 3.1. Translation is recovered by aligning the landmark points in the two coordinate frames. The point of maximal curvature on the medial portion of the ipsilateral obturator foramen was chosen as the initialization landmark used in this work, and an example annotation is shown in the top left of Fig. 3. If the first view is not approximately AP, an initial pose estimate of the pelvis may be obtained by annotating more landmarks in 2D and solving the PnP problem . Once the initial pose is estimated, a single-view intensity-based registration of the pelvis is performed.
By restricting the possible movements of the C-Arm for subsequent views, initial pelvis pose estimates for the remaining views are automatically obtained through an exhaustive search starting from the registered pose of the pelvis in the first view. More precisely, we limit the geometries of the remaining views to only differ from the first view by a rotation along the C-Arm’s orbit. DRRs are computed by adjusting the registered pelvis pose of the initial view by C-Arm orbital rotations of in increments, for a total of 181 DRRs. Similarity computations are made between the second and third fluoroscopic views, and the poses corresponding to the best similarity scores are used to initialize intensity-based registrations. An offline calibration process was conducted to determine center of orbital rotation and rotation axis for the CIOS Fusion.
Prior to any further registrations, the preoperative plan of the fragment may be refined as described in section 3.3.
Once the single view pelvis registrations are complete, the multiple-view geometry is recovered using the pelvis coordinate frame and the multiple-object registration is conducted. Specifically, we attempt to solve problem (1) through successive optimizations of individual objects, followed by a simultaneous optimization. At each resolution level, the pelvis pose estimate is refined starting from its current estimate. The pose of the pelvis is kept fixed, while an optimization over the pose of the femur is performed. Keeping the poses of the pelvis and femur fixed, the pose of the acetabular fragment is estimated. At the coarse level, the femur and fragment poses are initialized with the current estimate of the pelvis pose, while previous poses are used for initialization at the second level. At the second level, a “simultaneous” optimization is performed after the “sequential” optimizations; which optimizes over all object poses simultaneously. An example of three views used for a fragment localization is shown in Fig 3.
The registration process produces pose estimates of the extrinsic C-Arm frame () with respect to the pelvis () and fragment () volumes: and . The relative pose of the fragment with respect to the APP is computed as:
is obtained when estimating the APP from preoperative landmarks and maps points in the APP to the preoperative pelvis and fragment volumes. Using , the intraoperative fragment movement may be visualized in 3D (see Fig. 1) and shown to the clinician. Additional information useful for the assessment of dysplasia may also be displayed, such as the LCE angle and a decomposition of the pose with respect to each anatomical axis. Similar to the approach in , the LCE angle is computed by applying the fragment’s relative pose to transform the 3D preoperative lateral trace of the acetabulum.
Given initial estimates for poses of each object, the optimization for each object is performed over the Lie Algebra , with the reference point set from the initialization point. For a single view registration, an intermediate coordinate frame that is axis aligned with the camera projection frame, with origin at the initial estimate of the femoral head, is used. For multiple view registrations, the APP with origin at ipsilateral femoral head is used as an intermediate frame during the optimization. To discourage implausible poses, regularization is applied when using the CMA-ES optimization strategy. For single view registrations, regularization is applied separately to each translation component and the Euler decompositions of the rotation matrix, whereas the total rotation and translation magnitudes are used for multiple view registrations. Box constraints are used for all optimizations using the BOBYQA optimization strategy. Since the pelvis is initially registered with single-views, the optimization parameters used during the multi-view/multi-object registration for the pelvis are set for quicker execution time and tighter constraints in comparison to those used to register the femur and fragment.
Exact parameter values are listed in supplementary section .1.2.
3.3 Fragment Shape Estimation
Since the fracture line introduced during bone chiseling is dependent on bone quality, the cut does not always follow a planned path. Therefore, it is not realistic for a clinician to exactly reproduce the planned cuts, even when the osteotome is guided by a navigation system. To account for the potential uncertainties associated with the osteotomies, we have developed a method to estimate the fragment shape; starting from a preoperative plan and refined from intraoperative fluoroscopic images.
For each osteotomy to be estimated, a post-osteotomy fluoroscopic view clearly showing the cut lines is required. The full pelvis shape is registered to this view and a user manually annotates 2D pixels along the cut lines visible on the main pelvis object. For each 2D label, a ray is cast from the C-Arm detector towards the X-Ray source, and the 3D intersection points with the pelvis surface are computed. The osteotomy is estimated by fitting a plane to the recovered 3D points. When looking approximately down the cut line, the ray is nearly tangent to the entire cut and 3D intersection points entering and leaving the pelvis surface are used. Otherwise, a label must indicate whether the ray intersects the 3D osteotomy when entering or exiting the pelvis surface; in this case only the entry or exit intersection point is used. Fig. 4 shows an example of the 2D labeling of ilium and pubis cut pixels.
If an appropriate view and corresponding pelvis registration is not available, then the preoperative plan for that osteotomy is used for shape estimation. For the ischial and posterior osteotomies, it is challenging to obtain a view that clearly shows the cut lines, and for which a pelvis registration may be successfully performed. Therefore, only the ilium and pubis osteotomies will be estimated in the following experiments, and the ischium and posterior osteotomies will be set at the planned values.
3.4 Simulation Study
In order to determine the feasibility of this registration strategy, we conducted a large simulation study using the CT scans of 6 non-dysplastic cadaveric specimens. The group of specimens consisted of 4 male and 2 female subjects, with ages ranging from 57 to 94 years (). For the left and right sides of each specimen, we created simulated acetabular fragments, simulated fragment movements, and simulated intraoperative fluoroscopic images.
All PAOs were performed bilaterally by a single surgeon (B.A.M.). In order to create nominal fragment shapes, planes were fit to the osteotomy contours in postoperative CT volumes and then mapped into preoperative CT coordinates. Random surgeries were simulated by applying random rigid transformations to the cutting planes associated with each nominal osteotomy. The random adjustments were manually verified to create plausible PAO fragments and any invalid fragments were rejected. This resulted in 15 simulated fragments for each side of each patient and 180 for the entire study.
Random movements of each fragment and ipsilateral femur were sampled. Random rotations of the fragment and femur were sampled along with a random translation component for both the fragment and femur. The translation component is shared, since the fragment and femur tend to move together. To mimic clinically relevant movements of the fragment and femur, Euler angles and translations about each anatomical axis were sampled. All transformations are with respect to the APP with appropriate femoral head origin. Collision detection was performed to ensure that different bones did not overlap in 3D space. When a collision occurred, the set of transformations was rejected, and another set was sampled. A total of 20 movements for each fragment were sampled, with a mean rotation of and mean translation of . This yields a total of fragment movements for this study.
Three views are used for each repositioned fragment: a perturbed AP view, followed by two views offset at random rotations about the C-Arm’s orbit. The simulated fluoroscopy incorporates soft-tissues by piece-wise rigidly warping the original CT volume according to the pelvis, femur, and fragment labels as described in . A temporary fixation of the fragment is simulated by inserting two random K-wires into the volume, each at a random pose intersecting the ilium and fragment. Using a protocol similar to , fluoroscopic images are created from this new volume and view geometries. An example set of simulated fluoroscopic images is shown in the bottom row of Fig. 3.
The registration process proceeds according to the strategy described in 3.2. Registrations are initialized by simulating a 2D and 3D point picking process for the single landmark strategy. Using the registration point manually identified in each CT, the corresponding 2D pixel location is computed for each set of fluoroscopic views. Random noise is added to the 2D and 3D points to simulate variation in human point picking behavior. The landmarks are offset by a random distance along a random direction. The offset directions are drawn uniformly from the appropriate (2D or 3D) sphere. The 3D offset magnitudes are sampled, in mm, from , and the 2D magnitudes are sampled, in pixels, from . Five different initializations are estimated for each set of fluoroscopic views.
These simulations result in a total of multiple-object/multiple-view registrations that need to be evaluated. Each registration is run over four scenarios; each with a different fragment shape used during the registration. The first case considered is when the fragment shape in the fluoroscopic views exactly matches the preoperative plan. We also considered the case of tracking a fragment with an unknown, or uncertain shape. To achieve this we assumed that the nominal fragments represent preoperative plans for the randomly adjusted fragments present in the simulated fluoroscopic images. The remaining two cases examined the effect of using intraoperative information to update the planned cut model. For the first case of incorporating intraoperative knowledge, it was assumed that the ilium and pubis osteotomies would be perfectly recovered; the planned ilium and pubis cuts were replaced with the actual values. In the second case, synthetic 2D cut annotations were used to simulate the fragment shape estimation described in section 3.3.
Further details regarding the simulated datasets are described in supplementary section .1.4.
3.5 Cadaver Study
In order to further evaluate the proposed methods, intraoperative fluoroscopy was collected during six of the PAOs previously used for simulation studies. Four specimens, three male and one female, were used. Each surgery was performed under fluoroscopic guidance with a Siemens CIOS Fusion C-Arm with 30 cm flat panel detector. Fig. 5 shows a photograph of the operating theater. Each fluoroscopy image of the repositioned fragments contains screws, K-wires, or a combination of the two.
Fragment registrations were evaluated using the true fragment shape, preoperative planned fragments, and intraoperatively estimated fragment shapes. Postoperative CT scans were taken, and the fragment shape was manually segmented, to obtain the true fragment shape. Fifteen preoperative plans for each surgery were created by fitting cutting planes to the manually segmented fragment, followed by random adjustments. Each preoperative plan was manually verified to be a valid PAO, with any invalid plan rejected and resampled. The 2D cut lines of the ilium and pubis osteotomies were manually annotated in the fluoroscopic images, and were used to compute the ilium and pubis cutting planes of the estimated fragment shape. Each estimated shape is completed with the planned ischium and posterior osteotomies.
Included with this paper is a supplementary video111https://youtu.be/pXmVa3-MJXo, which illustrates the workflow used to perform the fragment shape and pose estimation for the left side of the specimen shown in Figures 1, 3, 4, and 5. This will be available at http://ieeexplore.ieee.org.
Ground truth poses of each fragment were obtained using metallic BBs implanted into the pelves. The postoperative CT volumes contain the relocated fragment which had been intraoperatively fixed in place using screws and K-wire. Prior to osteotomy, BBs were implanted onto the interior ilium surface in a region expected to lie on the fragment, and additional BBs were implanted onto the interior ilium surface in a region expected to not lie on the fragment. The ground truth fragment poses are calculated with 3D/3D paired-point registrations  between the 3D locations of the fragment BBs before osteotomy, and the 3D locations after osteotomy. For two specimens, and three PAOs, the fragment BB locations were computed using 3D CT imaging only. Eight BBs were placed on the ilium region and another eight placed on the fragment, with each eight BB constellation made of four mm diameter BBs and four mm diameter BBs. A Halifax Biomedical Inc. injection device was used to insert the mm diameter BBs. One of our clinical co-authors, C.P.A., inserted these BBs after performing soft-tissue dissections. An additional preoperative CT of the specimens was obtained to recover the pre-osteotomy BB locations. For the remaining two specimens, and remaining three PAOs, four BBs ( mm diameter) were inserted on the ilium region and four BBs ( mm diameter) inserted on the fragment region. No additional preoperative CT was obtained, however a series of fluoroscopic images were taken prior to osteotomy. Using the BB constellations obtained from the postoperative CT, the pre and post-osteotomy 3D locations of the BBs were obtained through a series of 2D/3D landmark registrations on the fluoroscopic images. A similar approach, using a plastic pelvis phantom with injected BBs and three views from CBCT projections, showed that the fragment pose may be recovered within / mm of CBCT ground truth [53, 54]. Details of BB insertion and the methods used to obtain ground truth poses are described in supplementary section .1.5. The BBs were not present in the preoperative CTs used to drive the intensity-based registrations and did not aid the proposed methods in any way.
4.1 Simulation Study
Fragment pose estimation was most accurate when the exact fragment shape was used during registration, and accuracy monotonically decreased as knowledge of the shape decreased. For each simulation in which the osteotomies were at least partially known or estimated, the mean rotation and translation errors were less than and mm, respectively. Mean fragment pose errors of and mm were obtained from the simulation using preoperatively planned shapes. For all fragment shapes, mean LCE errors were less than . Table 1
lists the mean and standard deviations of the fragment pose and LCE errors for each simulation study. Fig.6 shows the joint histograms for the fragment pose estimation errors. The shape of the error distribution “widens” as the amount of uncertainty associated with the fragment shape increases, particularly with respect to rotation error. The percentages of registrations with rotation errors below were , , , and , for the cases of all cuts known, no cuts known (preoperatively planned), known ilium and pubis cuts, and estimated ilium and pubis cuts, respectively. Similarly, the corresponding percentages of trials with LCE errors below were , , , and .
Single-tailed Mann-Whitney U-Tests were performed to determine any statistical significance between the errors obtained when running registration with different fragment shapes. The p-values are shown in Table 2, and indicate that pose and LCE estimation errors associated with the various categories of fragment shape are statistically different. Moreover, the single-tailed test indicates that the errors associated with fragment shapes using less intraoperative osteotomy information are statistically larger than errors determined by fragment shapes incorporating more knowledge of the intraoperative cuts.
|Study||Rotation ()||Translation (mm)||LCE ()|
|All Cuts Known|
|No Cuts Known|
|Ilium & Pubis Known|
|Ilium & Pubis Est.|
|Means and standard deviations of the fragment pose errors and lateral center edge (LCE) angle errors for each simulation study. The errors are organized by the type of fragment shape used for pose estimation, the total rotation and translation error magnitudes, the decompositions of the errors about each anatomical axis, and the LCE angle. Small LCE errors for all fragment shapes indicate that any shape is reliable for reporting lateral coverage of the femoral head.|
|All Cuts Known||No Cuts Known|
|All Cuts Known||Ilium & Pubis Known|
|All Cuts Known||Ilium & Pubis Est.|
|Ilium & Pubis Known||Ilium & Pubis Est.|
|Ilium & Pubis Est.||No Cuts Known|
Results of the Mann-Whitney U-Tests on fragment pose errors for the simulation studies. The total rotation and translation magnitudes of the pose errors, along with the error of the lateral center edge (LCE) angle are examined. The null hypothesis indicates that both sets of errors are drawn from the same distribution with identical medians and the alternative hypothesis indicates that the errors are drawn from different distributions with the second distribution (fragment shape with label 2) having larger median. Applying a threshold ofto the above p-values results in a rejection of the null-hypothesis for all but one of the tests. This implies that errors associated with fragment shapes incorporating less information of the true cuts are statistically larger than the errors associated with cuts that more closely match intraoperative cuts, except when comparing translation errors when ilium and pubis cuts are known versus estimated.
4.2 Cadaver Study
A summary of the fragment pose and LCE error statistics is provided in Table 3. Two results, one corresponding to a planned fragment shape and another to an estimated shape, produced fragment rotation errors above and were discarded from analysis. The pose estimations with manual segmented fragments, planned fragments, and estimated fragments resulted in mean rotation/translation errors of / mm, / mm, and / mm, respectively. Mean LCE errors were below for all fragment shapes. Additionally, the standard deviations of all rotation and LCE errors strictly increased as knowledge of the fragment’s 3D shape decreased. Rotation errors were less than for , , and of the registration trials when using a manual segmentation of the fragment, a planned fragment, and an estimated fragment, respectively. The corresponding proportions of LCE errors less than were , , and .
Table 4 shows p-values from statistical tests of significance conducted on the rotation, translation, and LCE errors. The protocol was identical to that used for evaluating the simulation study results. Using a threshold of , no statistical differences are indicated between the rotation, translation, or LCE errors when comparing the various fragment shapes.
The single-landmark initialization strategy was used for four of the six cases, and multiple-landmark initialization was used for the remaining two. In the two cases requiring multiple-landmark initialization, the initial views were taken with the detector parallel to the operating table and did not match a typical AP view due to the pelvic tilt of the specimens.
An expected runtime of seconds was obtained by re-running the estimated-fragment pose estimation pipeline 20 times for each surgery. The expected time required to manually choose a single 2D landmark, required for registration initialization, was seconds; the expected time for manual annotation of 2D cut lines, required for fragment shape estimation, was seconds.
The ground truth fragment poses from each surgery, the error statistics for each individual surgery, violin plots of the error distributions, and a breakdown of timings across the individual components of the registration pipeline are provided in supplementary section .2.2.
|Study||Rotation Errors ()||Translation Error (mm)||LCE ()|
|Means and standard deviations of fragment pose and lateral center edge angle (LCE) errors for the cadaver surgeries. For each type of fragment shape used during registration, the total rotation and translation error magnitudes are reported, along with the errors about each anatomical axis and the LCE angle error. The manual segmented fragment shape, planned fragment shape, and estimated fragment shapes roughly correspond to the simulation cases of a fragment shape with all cuts known, a preoperatively planned fragment shape with no cuts known, and a shape with ilium and pubis cuts estimated, respectively, as shown in Table 1.|
|Man. Seg.||Ilium & Pubis Cuts Est.|
|Ilium & Pubis Cuts Est.||Planned|
|Results of the Mann-Whitney U-Tests on fragment pose and lateral center edge (LCE) angle errors for the cadaver experiments. See Table 2 for a discussion of the hypotheses. Using a threshold of , no significant difference is reported for any of the errors and for each comparison of shapes.|
The simulation study yielded promising results for the localization of the acetabular fragment. As one would expect, the pose errors were smallest on average when the exact shape of each bone was known during registration, and degraded as less information about the osteotomies was known. This increase in average error was consistent across total rotation and translation magnitudes, the decompositions about anatomical axes, and for the LCE angle estimates. The increases in rotation error magnitudes and LCE angle errors were statistically significant for all comparisons and highlight the impact of preoperative/intraoperative fragment shape mismatch on registration accuracy. Increases in the translation error magnitudes were statistically significant in all but one comparison: using true pubis and ilium osteotomies, mixed with planned ischial and posterior osteotomies, compared with estimating the pubis and ilium osteotomies. This also indicates that the fragment localization is partially robust to differences between the planned and intraoperative osteotomies for the ischial and posterior cuts.
To our knowledge, no bounds on the accuracy of fragment pose or LCE angle have been identified in previous literature, therefore we consider to be an acceptable upper bound on LCE angle error. This threshold allows the clinician to target LCE angles between , while having confidence that the true LCE angle is within the criteria put forth by . At this threshold, the lowest success rate of corresponds to a preoperatively planned fragment shape, and indicates that an arbitrary preoperative plan is sufficient to obtain a successful registration. However, if the LCE error threshold is lowered to , successful pose estimates were found in , , , and of trials, for the cases of the fragment shape with all cuts known, the preoperatively planned fragment shape, the shape with known ilium and pubis cuts, and the shape with estimated ilium and pubis cuts, respectively. Therefore, a clinician may attach more confidence to pose estimates obtained after estimating the fragment’s ilium and pubis cuts.
In cadaver surgeries, registrations using each fragment shape yielded average LCE errors less than . This indicates that the proposed pipeline is capable of producing clinically usable estimates on real fluoroscopic imagery. In terms of average rotational and LCE error, registrations using the manually segmented fragment shape outperformed registrations using preoperatively planned shapes and intraoperatively refined shapes. However, when examining translation dimensions, the manually segmented fragment did not offer a noticeable advantage over the remaining two shapes. The performance across all error metrics was roughly equivalent when comparing the registrations using the preoperative plan and estimated fragments. Moreover, when comparing the errors produced through registrations using differing shape types, no statistically significant differences were found. This is in stark contrast to the simulation study results, which imply that an estimated shape should perform statistically better than a preoperatively planned fragment.
We believe this is primarily caused by low bone qualities from two specimens used for three surgeries. Prior to any osteotomies made to free the acetabular fragment, a small osteotomy of the anterior superior iliac spine (ASIS) is performed in order to provide sufficient access to the ilium. At the conclusion of the surgery, the ASIS is reattached in its original location. The ASIS osteotomy was excessively large for two specimens, resulting in a fragment shape with an additional osteotomy not representable by our four-cut model. When these three surgeries are removed from the results, of the registrations using manually segmented fragment shapes, using preoperatively planned fragment shapes, and using estimated shapes produce LCE errors less than . Furthermore, mean rotation errors of the fragment pose were , , and when using a manually segmented fragment shape, a preoperative plan, and estimated shape, respectively. Although no statistical difference was found between these error distributions, the results are more consistent with the trend established by the simulation study of increasing errors, corresponding to registrations using more mismatched fragment shapes. Since most patients undergoing PAO are young adults, bone quality is not expected to be an issue in clinical use. Considering these factors, we can say that the fragment pose estimation using an estimated shape provided clinically relevant results to determine femoral head coverage, with LCE errors less than .
The mean rotation error of , when using the estimated fragment shape during the cadaver surgeries, is noticeably larger than the error reported by a state-of-the-art optically tracked solution . Translation errors found with the proposed system are roughly equivalent to the mm identified by the optically tracked method. Although the X-Ray navigation approach has inferior rotation performance compared to the optically tracked method, the previous analysis of LCE angle errors indicate it is capable of providing clinically appropriate pose estimates.
The amount of femoral head coverage is primarily derived from the series of rotations applied to the acetabular fragment about the femoral head. For this reason, we report errors using rotation and translation components of the pose differences between registered estimates and ground truth poses. Furthermore, large TREs at regions distant from the cartilage surface, such as the ilium osteotomy, do not imply an incorrect estimate of the femoral head coverage.
Given the promising results in cadaveric experiments, and the diversity of data used in simulation, we believe this method should perform well on human subjects. Although we did not evaluate the proposed methods on dysplastic hips, our method should not suffer any performance degradation when run on dysplastic hips of younger patients. We have not made any assumptions in our processing specific to normal hip anatomy, and we only require an intensity volume of the pelvis that we may compute DRRs from. Some dysplastic hips may be subject to severe arthritis, which would likely cause difficulty during preoperative segmentation and also create a less-smooth registration similarity metric, however these patients would most likely undergo a total hip replacement (THR) instead of pelvic osteotomy.
The expected computation time of approximately
seconds is reasonable for intraoperative operation, however this does not include the time required to perform any manual annotations. Since the fragment will not change shape after the osteotomies are completed, annotation of the cut lines only needs to be performed once. It is likely that several adjustments to the fragment’s pose will be required, therefore we believe that the cut annotation time is amortized over each of these adjustments. A similar amortization is not applicable to registration re-initialization via landmark identification. However, other techniques using neural networks for recognizing fluoroscopic landmarks, or for approximate pose regression , could be applied to avoid this bottleneck.
Although implicitly penalized by the image similarity metric, the proposed registration method does not penalize 3D collision or overlap of bones. It is possible that the method’s performance may improve by including collision and overlap information into the regularization term of (1). When the fragment shape used during registration does not match the true fragment shape, it is possible for collisions to occur, particularly about the ischial and posterior osteotomies. Therefore, it may be possible to recover more accurate shapes by updating the volumetric segmentation to remove collisions after registration. Shapes could be refined by iteratively switching between registration and shape updates.
The six cadaver surgeries have served as proof-of-concept for the methods proposed in this work, however we believe further efforts should include clinical PAO cases. This would include the acquisition of clinical PAO fluoroscopic data used for further validation, and move towards a comparison of patient outcomes and operative times of non-navigated, optically navigated, and X-Ray navigated cases. The system could also integrate a preoperative plan of the biomechanically optimal fragment reposition, and intraoperatively provide feedback consisting of adjustments that would maximize the likelihood of achieving the plan.
Although the experiments in this paper were restricted to PAO, we have not made any assumptions that would preclude application to other pelvic osteotomies, such as RAO, CPO, or triple osteotomy. Forty percent of THR surgeries result in a mal-positioned (with respect to the “safe zone”) acetabular component , therefore we believe that our fragment tracking approach would also be useful for the intraoperative visualization, and guidance, of the THR acetabular implant.
Although the use of a preoperative CT scan is an increasingly common practice, it is not considered the current standard of care at all centers. When CT scans are used for diagnosis or preoperative planning, slice spacings are typically in the range of mm . It is not clear what effect lower resolution CT data will have on the accuracy of the proposed system and remains an important topic to be investigated. Furthermore, higher resolution preoperative CT scans may add additional cost and expose the patient to, potentially hazardous, radiation. In the future, a “CT free” approach could be implemented using a statistical deformation model (SDM) created from a database of existing pelvic CTs . The SDM would be used in a deformable 2D/3D registration to recover the patient’s 3D anatomy from standard preoperative standing radiographs and several pre-osteotomy fluoroscopic images . However, the SDM would most likely be unable to recover a sufficiently accurate cartilage model required for biomechanical measures and analysis. This could be overcome through the use of a partial preoperative CT, scanning only the acetabulum and extrapolating the remaining anatomy with the SDM, similar to the methods proposed in  and .
The proposed method for intraoperative localization of a mobilized acetabular fragment, with uncertain shape, has been demonstrated to report LCE angles within clinical tolerance in simulated cases and also in cadaveric cases for PAO. Less common equipment used in other approaches, such as an encoded or motorized CBCT C-Arm or an optical tracking device, is not required by this method. Additionally, the processing runs in an amount of time which is reasonable for incorporation into an intraoperative workflow. As entry-level flat panel imaging technology becomes more common in operating theaters, our method should be directly applicable to pelvic osteotomies or other similar fragment tracking tasks. The proposed X-Ray navigation could make pelvic osteotomies more accessible to novice surgeons, reduce the number of times a fragment needs to be adjusted during a procedure, and possibly reduce the radiation exposure to the surgical team by reducing the number of fluoroscopic images used.
The authors would like to thank Mr. Demetries Boston for his assistance during cadaveric testing. Professor Yoshinobu Sato provided productive and insightful discourse during the algorithmic development of this work, for which we are very grateful. Additionally, we are indebted to Dr. Masaki Takao and Dr. Nobuhiko Sugano for allowing us to observe an RAO procedure and become aware of the challenges involved. We also thank Professor Mathias Unberath for helpful discussions. Finally, we are appreciative of the constructive comments and critiques provided by the anonymous reviewers, which have resulted in an improved paper. This feedback led to the single-landmark registration initialization strategy, and has greatly improved the system’s ease of use. This research was supported by NIH/NIBIB grants R01EB006839, R21EB020113, Johns Hopkins University Internal Funds, and a Johns Hopkins University Applied Physics Laboratory Graduate Student Fellowship. Part of this research project was conducted using computational resources at the Maryland Advanced Research Computing Center (MARCC).
-  S. B. Murphy, R. Ganz, and M. Müller, “The prognosis in untreated dysplasia of the hip. A study of radiographic factors that predict the outcome.” J Bone Joint Surg Am, vol. 77, no. 7, pp. 985–989, 1995.
-  R. Ganz et al., “A new periacetabular osteotomy for the treatment of hip dysplasias technique and preliminary results.” Clin. Orthop. Relat. Res., vol. 232, pp. 26–36, 1988.
-  M. Armand et al., “Outcome of periacetabular osteotomy: joint contact pressure calculation using standing AP radiographs, 12 patients followed for average 2 years,” Acta Orthop, vol. 76, no. 3, pp. 303–313, 2005.
-  R. S. Armiger et al., “Three-dimensional mechanical evaluation of joint contact pressure in 12 periacetabular osteotomy patients with 10-year follow-up,” Acta Orthop, vol. 80, no. 2, pp. 155–161, 2009.
-  N. Niknafs et al., “Biomechanical factors in planning of periacetabular osteotomy,” Front Bioeng Biotechnol, vol. 1, 2013.
-  J. A. Hipp et al., “Planning acetabular redirection osteotomies based on joint contact pressures.” Clin. Orthop. Relat. Res., vol. 364, pp. 134–143, 1999.
-  A. Troelsen, “Surgical advances in periacetabular osteotomy for treatment of hip dysplasia in adults,” Acta Orthop, vol. 80, no. sup332, pp. 1–33, 2009.
-  G. Wiberg, “Studies on dysplastic acetabulum and congenital subluxation of the hip joint with special reference to the complications of osteoarthritis,” Acta Chir Scand, vol. 83, no. 58, 1939.
-  C. Hartig-Andreasen et al., “What factors predict failure 4 to 12 years after periacetabular osteotomy?” Clin. Orthop. Relat. Res., vol. 470, no. 11, pp. 2978–2987, 2012.
-  A. Troelsen et al., “Assessment of hip dysplasia and osteoarthritis: Variability of different methods,” Acta Radiol, vol. 51, no. 2, pp. 187–193, 2010.
-  F. Langlotz et al., “Computer assistance for pelvic osteotomies.” Clin. Orthop. Relat. Res., vol. 354, pp. 92–102, 1998.
-  R. J. Murphy et al., “Development of a biomechanical guidance system for periacetabular osteotomy,” Int J Comput Assist Radiol Surg, vol. 10, no. 4, pp. 497–508, 2015.
-  D. J. Mayman et al., “The kingston periacetabular osteotomy utilizing computer enhancement: a new technique,” Comput Aided Surg, vol. 7, no. 3, pp. 179–186, 2002.
-  L. Liu et al., “Computer assisted planning and navigation of periacetabular osteotomy with range of motion optimization,” in Proc. Med. Image Comput. Comput.-Assist. Interv, 2014, pp. 643–650.
-  H. Akiyama et al., “Computed tomography-based navigation for curved periacetabular osteotomy,” J Orthop Sci, vol. 15, no. 6, pp. 829–833, 2010.
-  M. Takao et al., “Comparison of rotational acetabular osteotomy performed with navigation by surgeons with different levels of experience of osteotomies,” Int J Comput Assist Radiol Surg, vol. 12, no. 5, pp. 841–853, 2017.
-  A. Troelsen, B. Elmengaard, and K. Søballe, “A new minimally invasive transsartorial approach for periacetabular osteotomy,” J Bone Joint Surg Am, vol. 90, no. 3, pp. 493–498, 2008.
-  A. Troelsen, B. Elmengaard, and K. Søballe, “Comparison of the minimally invasive and ilioinguinal approaches for periacetabular osteotomy 263 single-surgeon procedures in well-defined study groups,” Acta Orthop, vol. 79, no. 6, pp. 777–784, 2008.
-  P. Belei et al., “Fluoroscopic navigation system for hip surface replacement,” Comput. Aided Surg., vol. 12, no. 3, pp. 160–167, 2007.
-  X. Chen et al., “Automatic inference and measurement of 3D carpal bone kinematics from single view fluoroscopic sequences,” IEEE Trans. Med. Imag., vol. 32, no. 2, pp. 317–328, 2013.
-  D. A. Dennis et al., “In vivo determination of normal and anterior cruciate ligament-deficient knee kinematics,” J Biomechan, vol. 38, no. 2, pp. 241–253, 2005.
-  R. H. Gong, J. Stewart, and P. Abolmaesumi, “Multiple-object 2-D–3-D registration for noninvasive pose identification of fracture fragments,” IEEE Trans. Biomed. Eng., vol. 58, no. 6, pp. 1592–1601, 2011.
-  A. Guéziec et al., “Anatomy-based registration of CT-scan and intraoperative X-ray images for guiding a surgical robot,” IEEE Trans. Med. Imag., vol. 17, no. 5, pp. 715–728, 1998.
-  L. Joskowicz et al., “FRACAS: a system for computer-aided image-guided long bone fracture surgery,” Comput. Aided Surg., vol. 3, no. 6, pp. 271–288, 1998.
-  M. R. Mahfouz et al., “A robust method for registration of three-dimensional knee implant models to two-dimensional fluoroscopy images,” IEEE Trans. Med. Imag., vol. 22, no. 12, pp. 1561–1574, 2003.
-  P. Markelj et al., “A review of 3D/2D registration methods for image-guided interventions,” Med Image Anal, vol. 16, no. 3, pp. 642–661, 2012.
-  Y. Otake et al., “Intraoperative image-based multi-view 2D/3D registration for image-guided orthopaedic surgery: Incorporation of fiducial-based C-arm tracking and GPU-acceleration,” IEEE Trans. Med. Imag., vol. 31, no. 4, pp. 948–962, 2012.
-  Y. Otake et al., “Robust patella motion tracking using intensity-based 2D-3D registration on dynamic bi-plane fluoroscopy: toward quantitative assessment in MPFL reconstruction surgery,” in Proc. SPIE, 2016, pp. 97 860B–97 860B.
-  G. P. Penney et al., “A comparison of similarity measures for use in 2-D-3-D medical image registration,” IEEE Trans. Med. Imag., vol. 17, no. 4, pp. 586–595, 1998.
-  L. L. Sheng-fu et al., “Automatic localization of target vertebrae in spine surgery: clinical evaluation of the LevelCheck registration algorithm,” Spine, vol. 40, no. 8, p. E476, 2015.
-  J. Yao et al., “A C-arm fluoroscopy-guided progressive cut refinement strategy using a surgical robot,” Comput. Aided Surg., vol. 5, no. 6, pp. 373–390, 2000.
-  T. Yi et al., “Robotic drill guide positioning using known-component 3D–2D image registration,” J Med Imag, vol. 5, no. 2, p. 021212, 2018.
-  F. Langlotz et al., “The first twelve cases of computer assisted periacetabular osteotomy,” Comput. Aided Surg., vol. 2, no. 6, pp. 317–326, 1997.
-  M. Naito et al., “Curved periacetabular osteotomy for treatment of dysplastic hip.” Clin. Orthop. Relat. Res., vol. 433, pp. 129–135, 2005.
-  K. Radermacher et al., “Computer assisted orthopaedic surgery with image based individual templates.” Clin. Orthop. Relat. Res., vol. 354, pp. 28–38, 1998.
-  D. Tönnis et al., “Triple pelvic osteotomy.” J Pediatr Orthop B, vol. 3, no. 1, pp. 54–67, 1994.
-  B. Otsuki et al., “Developing a novel custom cutting guide for curved peri-acetabular osteotomy,” Int Orthop, vol. 37, no. 6, pp. 1033–1038, 2013.
-  R. J. Murphy et al., “Clinical evaluation of a biomechanical guidance system for periacetabular osteotomy,” J Orthop Surg Res, vol. 11, no. 1, p. 1, 2016.
-  L. Liu et al., “Periacetabular osteotomy through the pararectus approach: technical feasibility and control of fragment mobility by a validated surgical navigation system in a cadaver experiment,” Int Orthop, vol. 40, no. 7, pp. 1389–1396, 2016.
-  S. Ninomiya and H. Tagawa, “Rotational acetabular osteotomy for the dysplastic hip.” J Bone Joint Surg Am, vol. 66, no. 3, pp. 430–436, 1984.
-  D. Knaan and L. Joskowicz, “Effective intensity-based 2D/3D rigid registration between fluoroscopic X-ray and CT,” in Proc. Med. Image Comput. Comput.-Assist. Interv. Springer, 2003, pp. 351–358.
-  R. B. Grupp, M. Armand, and R. H. Taylor, “Patch-based image similarity for intraoperative 2D/3D pelvis registration during periacetabular osteotomy,” in Proc. Int. Workshop Clin. Image-Based Procedures. Springer, 2018, pp. 153–163.
-  N. Hansen and A. Ostermeier, “Completely derandomized self-adaptation in evolution strategies,” Evol Comput, vol. 9, no. 2, pp. 159–195, 2001.
-  M. Krčah, G. Székely, and R. Blanc, “Fully automatic and fast segmentation of the femur bone from 3D-CT images with no shape prior,” in Proc. IEEE Intl. Symp. Biomed. Imag, 2011, pp. 2087–2090.
-  C. Nikou et al., “Description of anatomic coordinate systems and rationale for use in an image-guided total hip replacement system,” in Proc. Med. Image Comput. Comput.-Assist. Interv, 2000, pp. 1188–1194.
-  J. E. Stone, D. Gohara, and G. Shi, “OpenCL: A parallel programming standard for heterogeneous computing systems,” Computing in science & engineering, vol. 12, no. 3, pp. 66–73, 2010.
-  M. J. Powell, “The BOBYQA algorithm for bound constrained optimization without derivatives,” Cambridge NA Report NA2009/06, University of Cambridge, Cambridge, 2009.
R. Hartley and A. Zisserman,
Multiple view geometry in computer vision. Cambridge university press, 2003.
-  R. S. Armiger et al., “Evaluation of a computerized measurement technique for joint alignment before and during periacetabular osteotomy,” Comput Aided Surg, vol. 12, no. 4, pp. 215–224, 2007.
-  R. M. Murray et al., A mathematical introduction to robotic manipulation. CRC press, 1994.
-  P. Markelj, B. Likar, and F. Pernuš, “Standardized evaluation methodology for 3D/2D registration based on the visible human data set,” Med Phys, vol. 37, no. 9, pp. 4643–4647, 2010.
-  B. K. Horn, “Closed-form solution of absolute orientation using unit quaternions,” J Opt Soc Am A, vol. 4, no. 4, pp. 629–642, 1987.
-  M. Armand et al., “Biomechanical guidance system for periacetabular osteotomy,” in Intelligent Orthopaedics. Springer, 2018, pp. 169–179.
-  R. Murphy et al., “Computer-assisted X-ray image-based navigation of periacetabular osteotomy with fiducial based 3D acetabular fragment tracking,” in Orthop. Proc., vol. 95, no. SUPP_28. The British Editorial Society of Bone & Joint Surgery, 2013, pp. 84–84.
-  B. Bier et al., “X-ray-transform invariant anatomical landmark detection for pelvic trauma surgery,” in Proc. Med. Image Comput. Comput.-Assist. Interv. Springer, 2018, pp. 55–63.
-  A. Kendall, M. Grimes, and R. Cipolla, “PoseNet: A convolutional network for real-time 6-DOF camera relocalization,” in Proc. IEEE Int. Conf. Comput Vis, 2015, pp. 2938–2946.
-  M. C. Callanan et al., “The John Charnley Award: risk factors for cup malpositioning: quality improvement through a joint registry at a tertiary hospital,” Clin. Orthop. Relat. Res., vol. 469, no. 2, pp. 319–329, 2011.
-  Y. Otake et al., “Comparison of optimization strategy and similarity metric in atlas-to-subject registration using statistical deformation model,” in Proc. SPIE. International Society for Optics and Photonics, 2015, pp. 94 150Q–94 150Q.
-  O. Sadowsky, G. Chintalapani, and R. Taylor, “Deformable 2D-3D registration of the pelvis with a limited field of view, using shape statistics,” in Proc. Med. Image Comput. Comput.-Assist. Interv, 2007, pp. 519–526.
-  R. Grupp et al., “Pelvis surface estimation from partial CT for computer-aided pelvic osteotomies,” in Orthop. Proc., vol. 98, no. SUPP_5. The British Editorial Society of Bone & Joint Surgery, 2016, pp. 55–55.
-  G. Chintalapani et al., “Statistical atlas based extrapolation of CT data,” Proc. SPIE, pp. 762 539–762 539, 2010.
-  A. Fedorov et al., “3D Slicer as an image computing platform for the Quantitative Imaging Network,” Magnetic resonance imaging, vol. 30, no. 9, pp. 1323–1341, 2012.
-  C. Chu et al., “FACTS: fully automatic CT segmentation of a hip joint,” Ann. Biomed. Eng., vol. 43, no. 5, pp. 1247–1259, 2015.
-  C. Chu et al., “MASCG: multi-atlas segmentation constrained graph method for accurate segmentation of hip CT images,” Med Image Anal, vol. 26, no. 1, pp. 173–184, 2015.
-  F. Yokota et al., “Automated CT segmentation of diseased hip using hierarchical and conditional statistical shape models,” in Proc. Med. Image Comput. Comput.-Assist. Interv. Springer, 2013, pp. 190–197.
-  D. F. Dementhon and L. S. Davis, “Model-based object pose in 25 lines of code,” Int J Comput Vis, vol. 15, no. 1, pp. 123–141, 1995.
-  N. Navab et al., “3D reconstruction from projection matrices in a C-arm based 3D-angiography system,” in Proc. Med. Image Comput. Comput.-Assist. Interv, 1998, pp. 119–129.
-  M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM, vol. 24, no. 6, pp. 381–395, 1981.
-  P. J. Besl and N. D. McKay, “A method for registration of 3-D shapes,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 14, no. 2, pp. 239–256, Feb 1992.