Robust 3D–2D image registration: application to spine interventions and vertebral labeling in the presence of anatomical deformation

Probably not a substantial claim: may not pass S3 (load-bearing).

Rinnooy Kan and Timmer theoretically proved that a stochastic optimization method converges to the global optimum with probability 1.0 when the number of function evaluations is increased infinitely.

“Rinnooy Kan and Timmer (1987) theoretically proved that a stochastic optimization method converges to the global optimum with probability 1.0 when the number of function evaluations is increased infinitely.”

• cites Rinnooy Kan and Timmer (1987) sourcePartly supported

  Theorem 1 in the Pure Random Search section proves that the lowest function value found converges almost surely to the global minimum value as the uniform sample size increases. The claim omits the theorem’s conditions, including continuity of the objective function, and says the method converges to the global optimum rather than specifying convergence of its best function value. (LLM, conf=0.84)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

Comparative studies suggest that local metrics tend to demonstrate better performance than global metrics.

“Although the best performing similarity metric is application-dependent, comparative studies (Birkfellner et al 2009, Russakoff et al 2003) suggest that local metrics tend to demonstrate better performance.”

• cites Birkfellner et al 2009 sourceCould not verify

  The Introduction lists local normalized correlation among registration metrics, but does not compare local metrics with global ones. The Results compare specific methods—SRC, cross correlation, and pattern intensity—and report that SRC performed best in the tested setup. Those findings do not establish the claimed general tendency for local metrics to perform better. (LLM, conf=0.76)

  Experimental — accuracy not yet measured
• cites Russakoff et al 2003 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Other research employs 3D-2D registration incorporating a non-rigid transformation, parameterized using prior information or properties of length preservation of vessels.

“Other research reported in the literature employs 3D–2D registration incorporating a non-rigid transformation. For example, the transformation can be parameterized using prior information such as the principal components and eigen-values of motion derived from a training dataset (Wang et al 2013) or properties of length preservation of vessels (Groher et al 2009).”

• cites Wang et al 2013 sourcePartly supported

  Methods §2.1 describes a statistical mouse atlas built from training subjects, with shape-variation modes obtained by principal component analysis; Methods §2.2 uses those modes to constrain 3D deformation during 2D/3D registration. Our copy does not say that eigenvalues of motion parameterize the transformation. The vessel-length example is attributed to Groher et al., not Wang et al. (LLM, conf=0.82)

  Experimental — accuracy not yet measured
• cites Groher et al 2009 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The normalized GI (NGI) provided an absolute measure of correspondence of edges between two images.

“This normalized GI (NGI) provided an absolute measure of correspondence of edges between two images.”

May combine two claims.

The N independent CMA-ES searches performed in parallel increased the number of parallelizable function evaluations significantly (λN parallel evaluations) compared to conventional sequential CMA-ES (λ parallel evaluations), improving performance.

“This increased the number of parallelizable function evaluations significantly (λN parallel evaluations) compared to the conventional sequential CMA-ES (λ parallel evaluations), improving performance.”

May combine two claims.

Larger deformations (±3°-5° at each joint) were observed in the lumbar region, while deformations in thoracic and abdominal regions were smaller (<2° at each joint) likely due to constraint by the rib cage.

“Larger deformations (±3°–5° at each joint) were observed in the lumbar region, while deformations in thoracic and abdominal regions were smaller (<2° at each joint) likely due to constraint by the rib cage.”

May combine two claims.

Downsampling the image can suppress certain image features and make other non-corresponding features more similar, thus creating false local optima in the objective function.

“however, we also found that downsampling the image can suppress certain image features and make other non-corresponding features more similar, thus creating false local optima in the objective function.”

May combine two claims.

The implementation offers >22,000 eval s−1 and registration in <6.3 s in cases involving a constrained search space.

“For example, in the work reported below, we report an implementation offering >22 000 eval s−1 and registration in <6.3 s in cases involving a constrained search space.”

May combine two claims.

Under the conditions used for truth definition, all cases demonstrated PDE < 3 mm and were visually verified as correct alignment.

“Under such conditions, all cases demonstrated PDE < 3 mm and were visually verified as correct alignment.”

May combine two claims.

The parallelized implementation allowed orders-of-magnitude acceleration in computation time and improved the robustness of registration via multi-start global optimization.

“The parallelized implementation allowed orders-of-magnitude acceleration in computation time and improved the robustness of registration via multi-start global optimization.”

May combine two claims.

The cadaver experiments yielded a success rate of 99.993% in vertebral labeling (with success defined as PDE <5 mm) using 1,718,664 ± 96,582 function evaluations computed in 54.0 ± 3.5 s on a mid-range GPU (nVidia, GeForce GTX690).

“yielding a success rate of 99.993% in vertebral labeling (with `success' defined as PDE <5 mm) using 1,718 664 ± 96 582 function evaluations computed in 54.0 ± 3.5 s on a mid-range GPU (nVidia, GeForce GTX690).”

• AssumptionRests on an assumption: The cadaver experiments approximate the anatomical deformation in spine surgery.

May combine two claims.

The framework employs a normalized gradient information similarity metric and multi-start covariance matrix adaptation evolution strategy optimization with local-restarts, which provided improved robustness against deformation and content mismatch.

“The framework employs a normalized gradient information similarity metric and multi-start covariance matrix adaptation evolution strategy optimization with local-restarts, which provided improved robustness against deformation and content mismatch.”

May combine two claims.

At DS8, the optimization landscape exhibits numerous sharp local optima (spikes), so the optimization does not follow the exact solution in repeated trials.

“Because the optimization landscape at DS8 (first inset in figure 6) exhibits numerous sharp local optima (spikes), the optimization does not follow the exact solution in repeated trials.”

May combine two claims.

The median PDE at initialization was 129.65 mm, and that at the solution was 0.025 mm.

“The median PDE at initialization was 129.65 mm, and that at the solution was 0.025 mm, suggesting a highly consistent registration result.”

May combine two claims.

The average edge length of the local search space was 106.7 mm for N = 5, and reduced to 26.9 mm for N = 250.

“The average edge length of the local search space (i.e., leafs of the kD-tree) was 106.7 mm for N = 5, and reduced to 26.9 mm for N = 250.”

May combine two claims.

Dispersion decreased and precision improved at successively finer levels of the multiresolution pyramid.

“Moreover, the dispersion decreased and precision improved at successively finer levels of the multiresolution pyramid.”

May combine two claims.

At DS8, median PDE was 0.101 mm for downhill simplex, compared to 0.050 mm for CMA-ES.

“At DS8, median PDE was 0.101 mm for downhill simplex, compared to 0.050 mm for CMA-ES.”

May combine two claims.

For cases of minor deformation (scenarios #1 and #2), a success rate >99.99% was achieved in 0.5 s for the small search (N = 1 multi-start), and in 6.8 s for the large search (N = 20).

“For cases of minor deformation (scenarios #1 and #2), a success rate >99.99% was achieved in 0.5 s for the small search (N = 1 multi-start), and in 6.8 s for the large search (N = 20).”

May combine two claims.

Using target points defined on each pedicle, initial median PDE was 129.47 mm and solution was 0.026 mm.

“To consider a different clinical application scenario such as pedicle screw placement, the PDE was also computed using target points defined on each pedicle (Tomazevic et al 2004), showing initial median PDE of 129.47 mm and the solution of 0.026 mm.”

• cites Tomazevic et al 2004 sourceNot checked — no full text of the source

May combine two claims.

TRE significantly increased when the mask included regions with large deformation (air-filled structure in the right side of the image), whereas TRE stayed less than 5 mm for displacement to the left when the weighted structure was rigid.

“TRE significantly increased when the mask included regions with large deformation (air-filled structure in the right side of the image), whereas stayed less than 5 mm for displacement to the left when the weighted structure was rigid.”

May combine two claims.

The rigid transformation approach was still able to find the locally rigid structures (vertebrae) in both images and utilize consistent features to robustly solve the registration even in the presence of strong anatomical deformation and within a clinically realistic computation time.

“As demonstrated in the experiments, the rigid transformation approach was still able to find the locally rigid structures (vertebrae) in both images and utilize consistent features to robustly solve the registration even in the presence of strong anatomical deformation and within a clinically realistic computation time.”

• AssumptionRests on an assumption: The spine is locally rigid, so rigid registration can align vertebrae despite anatomical deformation.

May combine two claims.

NGI was highest in scenarios of smaller deformation (deformation scenario #1-#4) and lower PDE, and it was reduced in cases of larger deformation (image index #7-#8 in deformation scenario #6-#8).

“NGI was highest in scenarios of smaller deformation (deformation scenario #1–#4) and lower PDE, and it was reduced in cases of larger deformation (image index #7–#8 in deformation scenario #6–#8).”

May combine two claims.

A weighting mask centered on the fluoroscopy image reduces the contribution of the air pocket to NGI and yields correct registration of the vertebrae.

“a weighting mask centered on the fluoroscopy image (i.e., assuming the gradients of interest—namely, the spine—to be in the center of the projection) reduces the contribution of the air pocket to NGI and yields correct registration of the vertebrae.”

• AssumptionThe authors state this as an assumption: The gradients of interest (namely, the spine) are in the center of the projection image.

Classified as probably not a substantial claim.

The range of random perturbation to the initialization was chosen to emulate realistic operator variability in C-arm positioning for AP fluoroscopy similar to Otake et al (2012c).

“The range of random perturbation to the initialization was chosen to emulate realistic operator variability in C-arm positioning for AP fluoroscopy similar to Otake et al (2012c).”

• cites Otake et al 2012cNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

Geometric calibration was performed with a previously described phantom.

“Geometric calibration was performed with a previously described phantom (Navab et al 1998).”

• cites Navab et al 1998 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based).

Robustness of the optimization is still a major factor that hinders routine clinical use of intraoperative 3D-2D registration.

“However, the robustness of the optimization is still a major factor that hinders routine clinical use of intraoperative 3D–2D registration.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The step length was chosen as 2.0 voxels to achieve faster computation while not degrading accuracy, since previous work showed that registration accuracy was nearly constant up to a step length of ~3.0 voxels.

“The step length was chosen as 2.0 voxels to achieve faster computation while not degrading accuracy, since previous work (Otake et al 2012a) showed that registration accuracy was nearly constant up to a step length of ~3.0 voxels.”

• cites Otake et al 2012aNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

Consistency is a surrogate for truth and a necessary (but not sufficient) condition for truth definition appropriate to real data.

“We note that consistency is a surrogate for truth and a necessary (but not sufficient) condition for truth definition appropriate to real data (cf, image simulation).”

Classified as probably not a substantial claim. May combine two claims.

Previous work demonstrated the LevelCheck algorithm to be reasonably robust in each of the requisite DOFs by virtue of invariance against coordinate-wise scaling in CMA-ES, and robustness to image content mismatch is in part achieved in that the GI similarity metric does not weigh inconsistent gradients.

“Previous work (Otake et al 2012c) demonstrated the LevelCheck algorithm to be reasonably robust in each of the requisite DOFs by virtue of invariance against coordinate-wise scaling in CMA-ES, and robustness to image content mismatch is in part achieved in that the GI similarity metric does not weigh inconsistent gradients (i.e., disregards gradients evident in only one of the images).”

• cites Otake et al 2012cNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

Robustness generally improves by tuning optimization parameters to perform more function evaluations (e.g., increasing the population size).

“such that robustness generally improves by tuning its optimization parameters to perform more function evaluations (e.g., increasing the population size).”

Classified as probably not a substantial claim.

The GI metric was previously shown to be robust against content mismatch between two images.

“The GI metric was previously shown to be robust against content mismatch between two images (Otake et al 2012c).”

• cites Otake et al 2012cNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Local restart strategy was employed in Auger and Hansen, where application to CMA-ES demonstrated improved performance with the IEEE CEC 2005 benchmark functions.

“Analogously, the local restart strategy was employed in Auger and Hansen (2005b, 2005a), where application to CMA-ES demonstrated improved performance with the IEEE CEC 2005 benchmark functions (Suganthan et al 2005).”

• cites Auger and Hansen (2005b, 2005a)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Suganthan et al 2005Not checked — no full text of the source

Classified as probably not a substantial claim. May combine two claims.

Ground truth registration was defined by way of consistency analysis, in which multiple, independently performed registrations converged to the same result, and that result was judged sensible as assessed by a clinical expert.

“Ground truth registration was defined by way of consistency analysis (Jenkinson et al 2002), in which multiple, independently performed registrations converged to the same result, and that result was judged sensible as assessed by a clinical expert.”

• cites Jenkinson et al 2002 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

A larger value of N confines each local search to a smaller space, thus making each local search more robust, whereas it increases overall computation time in a manner proportional to N.

“A larger value of N confines each local search to a smaller space, thus making each local search more robust, whereas it increases overall computation time in a manner proportional to N.”

May combine two claims.

Initial implementation of the LevelCheck method involved a single-image 3D-2D registration applied to spine interventions and validated its performance to automatically label spine levels in fluoroscopy images using simulation and rigid physical phantom studies.

“Initial implementation of the `LevelCheck' method (Otake et al 2012c) involved a single-image 3D–2D registration applied to spine interventions and validated its performance to automatically label spine levels in fluoroscopy images using simulation and rigid physical phantom studies.”

• cites Otake et al 2012cNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Although a larger number of restarts would further improve robustness, performing only one restart limits computation time.

“Although a larger number of restarts would further improve robustness, we performed only one restart to limit computation time.”

May combine two claims.

The overlap of 26 adjacent search spaces, each initialized with a random rotation, provided increased robustness since the random rotation increased the chances that one of the 26 rotations is close to the true registration.

“This created an overlap of 26 adjacent search spaces, each of which was initialized with a random rotation, providing increased robustness since the random rotation increased the chances that one of the 26 rotations is close to the true registration (i.e., good initialization).”

May combine two claims.

In comparison to derivative-based and classic derivative-free approaches, an evolutionary strategy such as CMA-ES tends to be more robust against local optima while requiring a larger number of function evaluations.

“In comparison to the derivative-based approach and the classic derivative-free approaches, an evolutionary strategy such as CMA-ES tends to be more robust against local optima while requiring a larger number of function evaluations”

Probably not a substantial claim: may not pass S3 (load-bearing).

The multi-start strategy is traditionally used in global optimization problems to broaden the capture range.

“The multi-start strategy is traditionally used in global optimization problems to broaden the capture range.”

Classified as probably not a substantial claim. May combine two claims.

For fair comparison, the number of function evaluations was fixed in the CMA-ES search (~3,000) and multiple simplex searches were started from eight randomly selected starting points.

“For fair comparison, the number of function evaluations was fixed in the CMA-ES search (~3,000) and starting multiple simplex searches from eight randomly selected starting points.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

A stochastic optimization approach such as CMA-ES entails a non-deterministic solution and is always subject to a finite probability of failure.

“Although registration with N = 250 showed a high rate of success, it is worth noting that a stochastic optimization approach such as CMA-ES entails a non-deterministic solution and is always subject to a finite probability of failure.”

May combine two claims.

Focusing on rigid transformation including only six parameters yields a more stable optimization and reduces computational cost.

“While the registration framework proposed in the work reported here can also be applied to such parameterizations by modifying the representation of the transformation and increasing the number of optimization variables, we focused in the current study on rigid transformation including only six parameters to yield a more stable optimization and reduce computational cost.”

May combine two claims.

The main challenge in 3D-2D registration is twofold: the similarity metric and the optimization approach.

“The main challenge in 3D–2D registration is twofold: the similarity metric and the optimization approach.”

May combine two claims.

CMA-ES's better precision suggests a higher level of robustness against local optima and more consistent convergence on the optimum.

“Overall, CMA-ES achieved better precision than downhill simplex (despite its intrinsic stochasticity), suggesting a higher level of robustness against local optima and leading to more consistent convergence on the optimum.”