Centre Of Rotation Estimation Research Articles

Real-time marker prediction and CoR estimation in optical motion capture

Optical motion capture systems suffer from marker occlusions resulting in loss of useful information. This paper addresses the problem of real-time joint localisation of legged skeletons in the presence of such missing data. The data is assumed to be labelled 3d marker positions from a motion capture system. An integrated framework is presented which predicts the occluded marker positions using a Variable Turn Model within an Unscented Kalman filter. Inferred information from neighbouring markers is used as observation states; these constraints are efficient, simple, and real-time implementable. This work also takes advantage of the common case that missing markers are still visible to a single camera, by combining predictions with under-determined positions, resulting in more accurate predictions. An Inverse Kinematics technique is then applied ensuring that the bone lengths remain constant over time; the system can thereby maintain a continuous data-flow. The marker and Centre of Rotation (CoR) positions can be calculated with high accuracy even in cases where markers are occluded for a long period of time. Our methodology is tested against some of the most popular methods for marker prediction and the results confirm that our approach outperforms these methods in estimating both marker and CoR positions.

Repeatability assessment of functional methods to estimate the glenohumeral joint centre

Functional methods can be used to determine the centre of rotation (CoR) of a ball-and-socket joint. The algorithms are used to locate rather the hip joint centre than the glenohumeral joint centre. The choice of the most suitable method depends especially on the intra- and inter-session repeatability of these methods. This paper aims at evaluating the intra- and inter-session repeatability of functional methods with which the glenohumeral joint rotation centre (GHRC) can be estimated in vivo. It also estimates the most suitable amplitude of functional movements. Five functional methods were tested: the algorithms of Gamage and Lasenby, bias compensation, symmetrical CoR estimation, normalisation method and helical axis. Ten subjects performed three cycles of three different movements (flexion–extension, abduction–adduction and circumduction). These movements were repeated three times with three different ranges of motion. Six subjects came back in order to evaluate the inter-session repeatability. For each test, the location of the GHRC was estimated by the five methods. The method to solve the functional problem and the range of functional movement affected the GHRC location. The results showed a good to excellent intra-session repeatability. The lowest repeatability error was found for the high amplitude whatever the methods used. The inter-session reliability was moderate. Finally, we suggest the use of functional methods with high amplitude movement in order to locate the GHRC with the best reliability.

A SVD-Based Method to Assess the Uniqueness and Accuracy of SPECT Geometrical Calibration

Geometrical calibration is critical to obtaining high resolution and artifact-free reconstructed image for SPECT and CT systems. Most published calibration methods use analytical approach to determine the uniqueness condition for a specific calibration problem, and the calibration accuracy is often evaluated through empirical studies. In this work, we present a general method to assess the characteristics of both the uniqueness and the quantitative accuracy of the calibration. The method uses a singular value decomposition (SVD) based approach to analyze the Jacobian matrix from a least-square cost function for the calibration. With this method, the uniqueness of the calibration can be identified by assessing the nonsingularity of the Jacobian matrix, and the estimation accuracy of the calibration parameters can be quantified by analyzing the SVD components. A direct application of this method is that the efficacy of a calibration configuration can be quantitatively evaluated by choosing a figure-of-merit, e.g., the minimum required number of projection samplings to achieve desired calibration accuracy. The proposed method was validated with a slit-slat SPECT system through numerical simulation studies and experimental measurements with point sources and an ultra-micro hot-rod phantom. The predicted calibration accuracy from the numerical studies was confirmed by the experimental point source calibrations at approximately 0.1 mm for both the center of rotation (COR) estimation of a rotation stage and the slit aperture position (SAP) estimation of a slit-slat collimator by an optimized system calibration protocol. The reconstructed images of a hot rod phantom showed satisfactory spatial resolution with a proper calibration and showed visible resolution degradation with artificially introduced 0.3 mm COR estimation error. The proposed method can be applied to other SPECT and CT imaging systems to analyze calibration method assessment and calibration protocol optimization.

P041 A comparison of two functional methods for calculating joint centers and axes in a clinical setting

The determination of an accurate centre of rotation (CoR) from segment marker positions is of interest across a wide range of applications, but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee, for limb alignment purposes. For the first time in this survey of formal methods, we classify, analyse and compare different methods (geometric, algebraic, bias compensated algebraic, and Pratt sphere fit methods, as well as the centre transformation technique, the Holzreiter approach, the helical pivot technique, the Schwartz transformation techniques, the minimal amplitude point method and the Stoddart approach) for the determination of spherical joint centres from marker position data. In addition, we propose a new method, the symmetrical CoR estimation or SCoRE, in which the coordinates of the joint centre must only remain constant relative to each segment, thus not requiring the assumption that one segment should remain at rest.For each method, 1000 CoR estimations were analysed with the application of isotropic, independent and identically distributed Gaussian noise (standard deviation 0.1 cm) to each of the marker positions, to all markers on the segment simultaneously and the two in combination. For the test conditions used here, most techniques were capable of determining the CoR to within 0.3 cm, as long as the spherical range of motion (RoM) of the joint was 45° or more. Under the most stringent conditions tested, however, the SCoRE was capable of best determining the CoR, to within approximately 1.2 mm with a RoM of 20°. The correct selection and application of these methodologies should help improve the accuracy of surgical navigation and clinical kinematic measurement.

Constrained least-squares optimization for robust estimation of center of rotation

This paper presents a new direct method for estimating the average center of rotation (CoR). An existing least-squares (LS) solution has been shown by previous works to have reduced accuracy for data with small range of motion (RoM). Alternative methods proposed to improve the CoR estimation use iterative algorithms. However, in this paper we show that with a carefully chosen normalization scheme, constrained least-squares solutions can perform as well as iterative approaches, even for challenging problems with significant noise and small RoM. In particular, enforcing the normalization constraint avoids poor fits near plane singularities that can affect the existing LS method. Our formulation has an exact solution, accounts for multiple markers simultaneously, and does not depend on manually-adjusted parameters. Simulation tests compare the method to four published CoR estimation techniques. The results show that the new approach has the accuracy of the iterative methods as well as the short computation time and repeatability of a least-squares solution. In addition, application of the new method to experimental motion capture data of the thumb carpometacarpal (CMC) joint yielded a more plausible CoR location compared to the previously reported LS solution and required less time than all four alternative techniques.

A survey of formal methods for determining the centre of rotation of ball joints

The determination of an accurate centre of rotation (CoR) from segment marker positions is of interest across a wide range of applications, but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee, for limb alignment purposes. For the first time in this survey of formal methods, we classify, analyse and compare different methods (geometric, algebraic, bias compensated algebraic, and Pratt sphere fit methods, as well as the centre transformation technique, the Holzreiter approach, the helical pivot technique, the Schwartz transformation techniques, the minimal amplitude point method and the Stoddart approach) for the determination of spherical joint centres from marker position data. In addition, we propose a new method, the symmetrical CoR estimation or SCoRE, in which the coordinates of the joint centre must only remain constant relative to each segment, thus not requiring the assumption that one segment should remain at rest. For each method, 1000 CoR estimations were analysed with the application of isotropic, independent and identically distributed Gaussian noise (standard deviation 0.1 cm) to each of the marker positions, to all markers on the segment simultaneously and the two in combination. For the test conditions used here, most techniques were capable of determining the CoR to within 0.3 cm, as long as the spherical range of motion (RoM) of the joint was 45° or more. Under the most stringent conditions tested, however, the SCoRE was capable of best determining the CoR, to within approximately 1.2 mm with a RoM of 20°. The correct selection and application of these methodologies should help improve the accuracy of surgical navigation and clinical kinematic measurement.