Distribution of fiducial registration error in rigid-body point-based registration

Research on Manufacturing Equipment Operation State Evaluation Technology Based on Fractional Calculus

The operational status of manufacturing equipment is directly related to the reliability of the operation of manufacturing equipment and the continuity of operation of the production system. Based on the analysis of the operation status of manufacturing equipment and its characteristics, it is proposed that the concept of assessing the operation status of manufacturing equipment can be realized by applying the real-time acquisition of accurate inspection data of important parts of weak-motion units and comparing them with their motion status evaluation criteria. A differential data fusion model based on the fractional-order differential operator is established through the study of the application characteristics of fractional-order calculus theory. The advantages of Internet of Things (IoT) technology and a fractional order differential fusion algorithm are integrated to obtain real-time high-precision data of the operating parameters of manufacturing equipment, and the research objective of the operating condition assessment of manufacturing equipment is realized. The feasibility and effectiveness of the method are verified by applying the method to the machining center operation status assessment.

Stereotactic navigation using registration based on intra-abdominal landmarks in robotic-assisted lateral pelvic lymph node dissection

BACKGROUND

We carried out robot-assisted lateral pelvic lymph node dissection (LPLND) for rectal cancer with a stereotactic navigation system. The purpose of this study was to evaluate the accuracy and feasibility of the system.

METHODS

We constructed a navigation system based on the Polaris Spectra optical tracking device (Northern Digital Inc., Canada) and the open-source software 3D Slicer (version 3.8.1; http://www.slicer.org ). We used the landmark-based registration method for patient-to-image registration. Body surface landmarks and intra-abdominal landmarks were used. We evaluated the time required for registration and target registration error (TRE; the distance between corresponding points after registration) for the root of the superior gluteal artery the root of the obturator or superior vesical artery, and the obturator foramen during minimally invasive LPLND for rectal cancer. Five patients who had LPLND for rectal cancer at the University of Tokyo Hospital between September 2020 and May 2021 were enrolled.

RESULTS

The mean time required for registration was 49 s with the body surface landmarks and 88 s with the intra-abdominal landmarks. The mean TRE improved markedly when the registration was performed using intra-abdominal landmarks. The mean TRE of the root of the superior gluteal artery, the root of the obturator or superior vesical artery, and the obturator foramen were 55.8 mm, 53.4 mm, and 55.2 mm with the body surface landmarks and 11.8 mm, 10.0 mm, and 12.6 mm with the intra-abdominal landmarks, respectively. There were no adverse events related to the registration process.

CONCLUSIONS

When stereotactic navigation systems are used for minimally invasive LPLND, the use of intra-abdominal landmarks for registration is feasible and may allow simpler and more accurate navigation than the use of body surface landmarks.

Estimating Maximum Target Registration Error Under Uniform Restriction of Fiducial Localization Error in Image Guided System

In this paper, we investigate the estimation of the maximum target registration error (TRE) magnitude of the target location while using point-based rigid registration in the image guided system. Under the uniform restriction of fiducial localization error (FLE) magnitude, we explicitly formulate the estimation as an optimization problem. Through analyzing the approximated problem which assumes the rigidity of the fiducial set holds with the perturbation of FLE, we present a strict lower bound for the maximum TRE magnitude. The simulations show that the lower bound is close to the actual maximum TRE magnitude for the target locations lying far away from the fiducial points. Unlike the expected TRE magnitude in which all fiducial points contribute, the lower bound is only related to the fiducial points serving as the vertices of the convex hull of the fiducial set. Our analysis provides a new perspective of investigating the problem of TRE estimation and is helpful for the surgeons to learn about the worst situation during using the image guided system.

Quantitative error analysis for computer assisted navigation: a feasibility study

PURPOSE

The benefit of computer-assisted navigation depends on the registration process, at which patient features are correlated to some preoperative imagery. The operator-induced uncertainty in localizing patient features-the user localization error (ULE)-is unknown and most likely dominating the application accuracy. This initial feasibility study aims at providing first data for ULE with a research navigation system.

METHODS

Active optical navigation was done in CT-images of a plastic skull, an anatomic specimen (both with implanted fiducials), and a volunteer with anatomical landmarks exclusively. Each object was registered ten times with 3, 5, 7, and 9 registration points. Measurements were taken at 10 (anatomic specimen and volunteer) and 11 targets (plastic skull). The active NDI Polaris system was used under ideal working conditions (tracking accuracy 0.23 mm root-mean-square, RMS; probe tip calibration was 0.18 mm RMS). Variances of tracking along the principal directions were measured as 0.18 mm(2), 0.32 mm(2), and 0.42 mm(2). ULE was calculated from predicted application accuracy with isotropic and anisotropic models and from experimental variances, respectively.

RESULTS

The ULE was determined from the variances as 0.45 mm (plastic skull), 0.60 mm (anatomic specimen), and 4.96 mm (volunteer). The predicted application accuracy did not yield consistent values for the ULE.

CONCLUSIONS

Quantitative data of application accuracy could be tested against prediction models with iso- and anisotropic noise models and revealed some discrepancies. This could potentially be due to the facts that navigation and one prediction model wrongly assume isotropic noise (tracking is anisotropic), while the anisotropic noise prediction model assumes an anisotropic registration strategy (registration is isotropic in typical navigation systems). The ULE data are presumably the first quantitative values for the precision of localizing anatomical landmarks and implanted fiducials. Submillimetric localization is possible for implanted screws; anatomic landmarks are not suitable for high-precision clinical navigation.

Deformable medical image registration: a survey

Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: 1) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; 2) longitudinal studies, where temporal structural or anatomical changes are investigated; and 3) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.

Medical image registration: a review

This paper presents a review of automated image registration methodologies that have been used in the medical field. The aim of this paper is to be an introduction to the field, provide knowledge on the work that has been developed and to be a suitable reference for those who are looking for registration methods for a specific application. The registration methodologies under review are classified into intensity or feature based. The main steps of these methodologies, the common geometric transformations, the similarity measures and accuracy assessment techniques are introduced and described.

General approach to first-order error prediction in rigid point registration

A general approach to the first-order analysis of error in rigid point registration is presented that accommodates fiducial localization error (FLE) that may be inhomogeneous (varying from point to point) and anisotropic (varying with direction) and also accommodates arbitrary weighting that may also be inhomogeneous and anisotropic. Covariances are derived for target registration error (TRE) and for weighted fiducial registration error (FRE) in terms of covariances of FLE, culminating in a simple implementation that encompasses all combinations of weightings and anisotropy. Furthermore, it is shown that for ideal weighting, in which the weighting matrix for each fiducial equals the inverse of the square root of the cross covariance of its two-space FLE, fluctuations of FRE and TRE are mutually independent. These results are validated by comparison with previously published expressions and by simulation. Furthermore, simulations for randomly generated fiducial positions and FLEs are presented that show that correlation is negligible (correlation coefficient < 0.1) in the exact case for both ideal and uniform weighting (i.e., no weighting), the latter of which is employed in commercial surgical guidance systems. From these results we conclude that for these weighting schemes, while valid expressions exist relating the covariance of FRE to the covariance of TRE, there are no measures of the goodness of fit of the fiducials for a given registration that give to first order any information about the fluctuation of TRE from its expected value and none that give useful information in the exact case. Therefore, as estimators of registration accuracy, such measures should be approached with extreme caution both by the purveyors of guidance systems and by the practitioners who use them.

Understanding the effect of bias in fiducial localization error on point-based rigid-body registration

Image registration is a single point of failure in the image-guided computer-assisted surgery. Registration is primarily used to align and fuse the data sets taken from patient's anatomy before and during surgeries. Point-based rigid-body registration is usually performed by identifying corresponding fiducials (either natural landmarks or implanted ones) in the data sets. Since the localization of fiducials is imprecise and is generally perturbed by random noise, the performed registration is imperfect and has some error. Previous work has extensively analyzed the behavior of this error when the fiducial localization error has zero-mean over the entire set of fiducials. However, if noise has a nonzero-mean or a bias, no formulation yet exists to determine the effect of noise on the overall registration accuracy. In this work, we derive novel formulations that relate the bias in the localized fiducials to the accuracy of the performed registration. We analytically and numerically demonstrate that by eliminating the estimated bias from the measured fiducial locations, one can effectively increase the accuracy of the performed registration.