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PubMed1986

The accuracy of DLT extrapolation in three-dimensional film analysis.

An analysis of errors arising from the Direct Linear Transformation (DLT) approach to three-dimensional reconstructions from two-dimensional images has been undertaken, the principal factor studied being the number and distribution of control points used in the calibration procedure. Significantly increased error was found to be associated with extrapolation to unknown points outside the control point distribution space. Differences in accuracy between two camera position set-ups and 11 vs 12 DLT parameter solutions were also examined.

Analysis of Variance↗
PubMed1988

High-precision three-dimensional photogrammetric calibration and object space reconstruction using a modified DLT-approach.

Two modified DLT algorithms are presented that improve the accuracy of three-dimensional object space reconstruction by almost an order of magnitude when compared with conventional methods. The improvement in the linear modified DLT (MDLT) algorithm is achieved by satisfying certain orthogonality conditions in the form of a non-linear constraint, thereby effectively eliminating a redundant DLT parameter. In the non-linear MDLT algorithm, the improvement and computational stability results from the appropriate elimination of implicit variables from one side of the approximating relations and the corresponding reformulation of the objective function to be minimized. The highest reconstruction accuracy of 0.733 mm rms mean error was obtained with the non-linear MDLT algorithm. This corresponds to a spatial resolution of about one part in 2860 or 0.035% overall accuracy. The accuracy obtainable with the linear MDLT was found to be slightly less and about 0.041% (0.833 mm rms mean error).

Algorithms↗
PubMed1989

A stereophotogrammetric method for measurements of ligament structure.

A stereophotogrammetric method is presented to reconstruct the course of a curve in the three-dimensional space. This method is exclusively suitable as a non-destructive tool to determine the surface fiberstructure of ligaments, tendons and other organised collagenous structures. In addition, it is a convenient tool to measure the geometry of articular surfaces and other complicated surface shapes.

Hip Prosthesis↗
PubMed1990

Measurement errors in roentgen-stereophotogrammetric joint-motion analysis.

In many biomechanical motion studies, kinematic parameters are estimated from position measurements on a number of landmarks. In the present investigation, dummy motion experiments are performed in order to study the error dependence of kinematic parameters on geometric factors (number of markers, isotropic vs anisotropic landmark distributions, landmark distribution size), on kinematic factors (rotation step magnitude, the presence of translational displacements, the distance of the landmarks' mean position to the rotation axis), and on anisotropically distributed measurement errors. The experimental results are compared with theoretical predictions of a previous error analysis assuming isotropic conditions for the measurement errors and for the spatial landmark distribution. In general, the experimental findings agree with the predictions of the error model. The kinematic parameters such as translations and rotations are well-determined by the model. In the helical motion description, the same applies for the finite rotation angle about and the finite shift along the helical axis. However, the direction and position of the helical axis are ill-determined. An anisotropic landmark distribution with relatively few markers located in the direction of the rotation axis will even aggravate the ill-posed nature of the finite helical axis estimation.

Biomechanical Phenomena↗
PubMed1991

Three-dimensional tissue deformation in subcutaneous tissues overlying bony prominences may help to explain external load transfer to the interstitium.

Anesthetized, carefully positioned, female, weanling, white-haired pigs were used to test the hypothesis that (1) interface pressure, the pressure between the skin and an external load, can be used to predict the interstitial fluid pressure over the wings of ilia and the last dorsal spinous process and (2) three-dimensional tissue deformation of the interstitium under the load could partially explain how the external load is transferred at that site. When a 4 or 8 kg load was distributed over the hips of the pigs, the interface pressures over the ilia were approximately 145 and 207 cm H2O, respectively. Approximately 28% of this pressure was transferred to the tissue, resulting in an increase in interstitial fluid pressure of approximately 39 cm H2O for the 4 kg load and 60 cm H2O for the 8 kg load. However, over the spinous process, about 42-43% of the load was transferred to the interstitium. Subcutaneous tissue marker movement occurred along the gamma and theta spherical coordinate but no significant tissue marker movement along the phi coordinate. The latter indicates no significant twisting of the tissue while the former demonstrates three-dimensional shearing. There were also indications of tissue creep since the markers continued to move with constant loading.

Animals↗
PubMed1991

Biomechanical model of the human shoulder joint--II. The shoulder rhythm.

A method to investigate the rhythm of the human shoulder, i.e. the interplay between the motion of constituent parts of the shoulder, has been devised and tested. The method is based upon numerical evaluation of low dose roentgenstereophotogrammetric motion pictures of subjects equipped with radiation dense implantations in the bones. Evaluation of the method shows that it may be used in determining motion patterns and that the employed interpolation techniques can be used to simulate motions not actually performed in the laboratory. The shoulder rhythm has been previously poorly investigated and quantified results published pertain to one plane only. Our results on motion patterns correlate with previous investigations. With this method, we show that the absolute position of the bones varies significantly between individuals while the relative displacement of the bones during motion exhibit similarities. In particular the results show that, under normal conditions, the individual rhythm is very stable and insensitive to small hand-loads.

Acromion↗
PubMed1991

Quantitation of articular surface topography and cartilage thickness in knee joints using stereophotogrammetry.

An analytical stereophotogrammetry (SPG) technique has been developed based upon some of the pioneering work of Selvik [Ph.D. thesis, University of Lund, Sweden (1974)] and Huiskes and coworkers [J. Biomechanics 18, 559-570 (1985)], and represents a fundamental step in the construction of biomechanical models of diarthrodial joints. Using this technique, the precise three-dimensional topography of the cartilage surfaces of various diarthrodial joints has been obtained. The system presented in this paper delivers an accuracy of 90 microns in the least favorable conditions with 95% coverage using the same calibration method as Huiskes et al. (1985). In addition, a method has been developed, using SPG, to quantitatively map the cartilage thickness over the entire articular surface of a joint with a precision of 134 microns (95% coverage). In the present study, our SPG system has been used to quantify the topography, including surface area, of the articular surfaces of the patella, distal femur, tibial plateau, and menisci of the human knee. Furthermore, examples of cartilage thickness maps and corresponding thickness data including coefficient of variation, minimum, maximum, and mean cartilage thickness are also provided for the cartilage surfaces of the knee. These maps illustrate significant variations over the joint surfaces which are important in the determination of the stresses and strains within the cartilage during diarthrodial joint function. In addition, these cartilage surface topographies and thickness data are essential for the development of anatomically accurate finite element models of diarthrodial joints.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗
PubMed1992

Three-dimensional kinematics of the human knee during walking.

Three-dimensional kinematics of the tibiofemoral joint were studied during normal walking. Target markers were fixed to tibia and femur by means of intra-cortical traction pins. Radiographs of the lower limb were obtained to compute the position of the target markers relative to internal anatomical structures. High-speed cine cameras were used to measure three-dimensional coordinates of the target markers in five subjects walking at a speed of 1.2 m s-1. Relative motion between tibia and femur was resolved according to a joint coordinate system (JCS). The measurements have identified that substantial angular and linear motions occur about and along each of the JCS axes during walking. The results do not, however, support the traditional view that the so-called 'screw home' mechanism of the knee joint operates during gait.

Adult↗
PubMed1993

Comparative assessment of two algorithms for calibrating stereophotogrammetric systems.

In this paper, a comparison is carried out between two photogrammetric algorithms aimed at camera calibration and three-dimensional target point reconstruction by 'absolute' distributions of control points; the first is Marzan and Karara's DLT, the second is CESNO, by the author, an algorithm quite close to Hatze's modified DLT (MDLT). The comparative assessment is especially aimed at testing the capability of the two methods to produce good results when calibration data are to be extrapolated beyond the space spanned by the control distribution. The assessment was carried out not by a real stereophotogrammetric system, but by the computer simulation of a two-camera set-up. Various combinations of internal camera parameters, such as the scaled principal distances, were tried out. As for the magnitude of the simulated non-linear lens distortion, three configurations were used which produced 'low', 'medium' and 'strong' distortion. The influence of decreasing the number of control (calibration) points on the accuracy performance of the two algorithms was also investigated. The results show the superiority of CESNO, especially with medium or strong lens distortion, or when the two camera principal distances sensibly differ.

Algorithms↗
PubMed1993

Determining the movements of the skeleton using well-configured markers.

The problem of determining skeletal movements in three dimensions by using a number of landmarks is treated. We present a method that determines the motion of a rigid body by using the positions of the landmarks in least-squares sense. The method uses the singular value decomposition of a matrix derived from the positions of the landmarks. We show how one can use this method to express movement of skeleton segments relative to each other. As many others have pointed out, the movement can be very ill determined if the landmarks are badly configured. We present a condition number for the problem with good geometrical properties. The condition number depends on the configuration of the landmarks and indicates how to distribute the landmarks in a suitable way.

Algorithms↗
PubMed1995

Experimental and mathematical methods for representing relative surface elongation of the ACL.

The common approach to assess the stabilizing role of the ACL in the knee has been to measure the elongation of a few marked fibers in the ligament. A comparison of the relative elongation (RE) of these marked fibers between different specimens and studies is delicate due to the difficulty of marking the same fibers. More consistent comparisons would be achieved if the RE of the whole ligament surface was presented. Hence, we developed a mathematical method leading to a continuous description of the relative elongation of the ligament's surface based on experimental measurements of the RE of five fibers. The ligament fibers of two knee specimens were marked by radiopaque markers and a Roentgen Stereophotogrammetric Analysis system was used to reconstruct the three-dimensional positions of these artificial landmarks. The mathematical procedure used isoparametric cubic splines to interpolate the contours of the insertion sites. The results showed that the general pattern of the RE for both specimens was similar, characterized by an undulation near full flexion. In fact, close to full flexion all the RE of the fibers increased. Such a representation describes the changes in the RE for a given fiber during knee flexion and at the same time characterizes the RE distribution at a given flexion angle.

Aged↗
PubMed1994

A stereophotogrammetric method for determining in situ contact areas in diarthrodial joints, and a comparison with other methods.

Determination of contact areas in diarthrodial joints is necessary for understanding the state of stress within the articular cartilage layers and the supporting bony structures. The present study describes the use of a stereophotogrammetry (SPG) system [Huiskes et al., J. Biomechanics 18, 559-570 (1985) and Ateshian et al., J. Biomechanics 24, 761-776 (1991)] for determining contact areas in diarthrodial joints, using a surface proximity concept similar to the one used by Scherrer et al. [ASME J. biomech. Engng 101, 271-278 (1979)]. This method consists of evaluating the proximity of the articular surfaces to determine joint contact areas using precise geometric models of the joint surfaces obtained from the SPG system, and precise kinematic data, also obtained from SPG. In this study, the SPG method for determining contact areas is compared to other commonly used methods such as dye staining, silicone rubber casting and Fuji film contact measurement techniques which have been often used and reported by other investigators. The bovine glenohumeral joint and the bovine lateral tibiofemoral articulation (without the meniscus) were used to represent congruent and incongruent joints, respectively. While all the methods yielded consistent contact patterns for the incongruent tibiofemoral articulations, the results for the congruent bovine glenohumeral joints showed that the SPG and Fuji film methods were in better agreement than those obtained from the dye staining and silicone rubber casting methods. The advantages of the new SPG method are that it can be used for intact joints, and used repeatedly and quickly thus making contact-area movement analyses possible [Soslowsky et al., J. orthop. Res. 10, 524-534 (1992)]. The results of this comparison study show that the SPG technique is a reliable and versatile method for determining contact areas in diarthrodial joints.

Animals↗
PubMed1994

A note on some identification problems arising in roentgen stereo photogrammetric analysis.

When studying skeleton movements by using implanted landmarks and Roentgen stereo photogrammetric analysis (RSA), some identification problems arise. One is to put the same label on a landmark at different examinations, another is to use the correct pairs of landmark images in order to compute a correct three-dimensional position of each landmark. We will present some methods that can be used as a support for solving these problems. We will also show how it is possible to detect and exclude landmarks that are loose and landmarks that have large measurement errors in their positions.

Algorithms↗
PubMed1995

NLT and extrapolated DLT:3-D cinematography alternatives for enlarging the volume of calibration.

This study investigated the accuracy of the direct linear transformation (DLT) and non-linear transformation (NLT) methods of 3-D cinematography/videography. A comparison of standard DLT, extrapolated DLT, and NLT calibrations showed the standard (non-extrapolated) DLT to be the most accurate, especially when a large number of control points (40-60) were used. The NLT was more accurate than the extrapolated DLT when the level of extrapolation exceeded 100%. The results indicated that when possible one should use the DLT with a control object, sufficiently large as to encompass the entire activity being studied. However, in situations where the activity volume exceeds the size of one's DLT control object, the NLT method should be considered.

Calibration↗
PubMed1988

In vivo wear. Part I: The Michigan computer-graphic measuring system.

Three-dimensional coordinate measuring machines for examining the quality of industrial castings were reviewed. The concept was modified and successfully converted to examine the minute geometric configurations of the surfaces of dental materials. The wear of composites has undoubtedly precipitated this perceptive, thorough study.

Computer Systems↗