Evidence for surface-based processing of binocular disparity

It is convenient to think of an object's location as a point within a Cartesian framework; the x axis corresponds to right and left, the y axis to up and down, and the z axis to forward or backward. When an observer is looking straight ahead, binocular disparities provide information about distance along the z axis from the fixation plane. In this coordinate system, changes in disparity are treated as independent of changes in location along the orthogonal x and y axes. Does the human visual system use this three-dimensional coordinate system, or does it specify feature location in a coordinate frame determined by other nearby visible features? Here we show that the sensitivity of the human stereo system is determined by the distance of points with respect to a local reference plane, rather than by the distance along the z axis with respect to the fixation plane. There is a distinct advantage to using a local frame of reference for specifying location. It obviates the need to construct a complex three-dimensional space in either eye-centered or head-centered coordinates that must be updated with every shift of the eyes and head.     

Determining rigid body transformation parameters from ill-conditioned spatial marker co-ordinates

The three-dimensional location of a body-fixed axis system is described by position and orientation parameters that can be calculated knowing local and global coordinates of three or more body-fixed markers. However, marker distribution can become ill-conditioned when marker placement is symmetrical with respect to the mean of the markers. As symmetry and ill-conditioning increases, random errors in marker locations can affect the stability of orientation parameters as a result of the mathematical approach adopted. The present study investigates the methods of Veldpaus et al. [1988; Journal of Biomechanics 21, 45], Challis [1995; Biomechanics 28, 733] and Andriacchi et al. [1998; Journal of Biomedical Engineering 120, 743] for obtaining segment orientation parameters when segment markers ranged from well-defined to highly ill-conditioned depending on the symmetry of segment markers. A novel fourth approach is also presented that enabled comparisons of the root mean square error of reconstructed marker coordinates to verify that an optimal solution was obtained. No single method produced optimal results for all axis orientation parameters when reconstructing movement trials. The best performed was the method of Veldpaus et al. [1988; Journal of Biomechanics 21, 45] based on consistent results and ease of implementation. The fourth approach presented provided a reliable method in all but the highly ill-conditioned markers, however implementation was computationally difficult. The method of Challis [1995; Biomechanics 28, 733] was only suited to well-conditioned marker sets which avoided markers lying in a single plane with symmetries in marker distribution relative to the mean. The method of Andriacchi et al. [1998; Journal of Biomedical Engineering 120, 743] produced, at best, orientation parameters that approximated the results obtained by least squares methods.     

Sagittal kinematics of the cervical spine--how constant are the motor axes?

The aim of this study was to establish whether or not the axes of cervical spine movement in the sagittal plane are constant (an impression conveyed by the literature). Based on 60 functional radiographs (of which 24 showed degenerative discopathy or atlas subluxations), the axes of seven motor segments (C1-D1) were determined geometrically. The axes of the segments C5/C6 proved to scatter least; the further the distance of a segment is to the latter, the larger the tendency of scattering appears. Hence, the axes are neither constant in time nor in location and thus only convey the momentary kinematic situation of the cervical spine. Clearly pathologic axis positions could not be found, except in the case of an extreme atlas subluxation.     

Algorithm and validation of a computer method for quantifying attachment locus of glenohumeral ligament in vivo

The aim of this work is to validate an algorithm that quantifies the locus of glenohumeral ligament (GHL) attachments on glenohumeral joint (GHJ) bones. A computed tomography scan of a GHJ was segmented to reconstruct the humerus, scapula, anatomical neck (AN) and glenoid rim (GR) into 3D meshes of interconnecting nodal vectors. These were applied to construct a 'clock face' coordinate system in which 3 o'clock points anteriorly. Based on the assigned clock face coordinate frame and the fitted plane, the error between the fitted plane and the actual bony node was quantified through manual data extraction. This was tested on 50 specimens. Mean algorithm quantification errors for GHL attachments were 4.8 (SD 2.2?mm) and 4.5?mm (1.7?mm) for the humerus and glenoid, respectively. Further studies would apply this to investigate GHL length changes during function and may suggest how these structures should be handled during surgical repairs.     

Can axes conventions of the trunk reference frame influence breast displacement calculation during running?

To obtain breast motion relative to the trunk, skin markers are used to define a local coordinate system (trunk), with respect to the global reference frame. This study aimed to quantify any differences in multiplanar breast displacement relative to the trunk using the first axis of rotation as either the mediolateral or longitudinal axis. Ten female participants ran on a treadmill (10 kph) in three different breast supports (no bra, everyday bra, sports bra). Four reflective markers placed on the trunk and right nipple were tracked using eight infrared cameras (200 Hz) during five running gait cycles in each breast support condition. Following marker identification, right breast multiplanar displacements were calculated relative to the trunk using either the mediolateral axis or the longitudinal axis as the first rotational axis to define the orthogonal local coordinate system. Results showed that there was a significant difference (8.2%) in superioinferior breast displacement in the sports bra condition when calculated using different axes conventions for the trunk segment. Furthermore, the greatest magnitude of breast displacement occurred in a different direction depending upon the selection of the first rotational axis. The definition of the primary reference axis of the trunk significantly alters the magnitude of superioinferior breast displacement and therefore it is recommended that the previously reported ‘stable’ longitudinal axis should be defined as the first rotational axis during running. Caution should also be used as the axes convention influences the magnitude and direction of breast support requirements, which has important implications for bra design.     

A motion-decomposition approach to address gimbal lock in the 3-cylinder open chain mechanism description of a joint coordinate system at the glenohumeral joint

In this study, the standard-sequence properties of a joint coordinate system were implemented for the glenohumeral joint by the use of a set of instantaneous geometrical planes. These are: a plane that is bound by the humeral long axis and an orthogonal axis that is the cross product of the scapular anterior axis and this long axis, and a plane that is bounded by the long axis of the humerus and the cross product of the scapular lateral axis and this long axis. The relevant axes are updated after every decomposition of a motion component of a humeral position. Flexion, abduction and rotation are then implemented upon three of these axes and are applied in a step-wise uncoupling of an acquired humeral motion to extract the joint coordinate system angles. This technique was numerically applied to physiological kinematics data from the literature to convert them to the joint coordinate system and to visually reconstruct the motion on a set of glenohumeral bones for validation.     

Algorithm and validation of a computer method for quantifying attachment locus of glenohumeral ligament in vivo

The aim of this work is to validate an algorithm that quantifies the locus of glenohumeral ligament (GHL) attachments on glenohumeral joint (GHJ) bones.

A computed tomography scan of a GHJ was segmented to reconstruct the humerus, scapula, anatomical neck (AN) and glenoid rim (GR) into 3D meshes of interconnecting nodal vectors. These were applied to construct a ‘clock face’ coordinate system in which 3 o'clock points anteriorly.

Based on the assigned clock face coordinate frame and the fitted plane, the error between the fitted plane and the actual bony node was quantified through manual data extraction. This was tested on 50 specimens.

Mean algorithm quantification errors for GHL attachments were 4.8 (SD 2.2 mm) and 4.5 mm (1.7 mm) for the humerus and glenoid, respectively. Further studies would apply this to investigate GHL length changes during function and may suggest how these structures should be handled during surgical repairs.     

Proposal of a thorax segment coordinate system for the 3D kinematical analysis of the cervical spine

The International Society of Biomechanics detailed the recommendations for 3D kinematics of intervertebral movements (Wu, et al. 2002. J Biomech. 35:543-548), but does not specify how to adapt this proposal to describe the kinematics of the cervical spine, between the head and the thorax. The analysis of the literature shows that no consensus exists at the present time on this subject. The objective of our study was to identify the reference points that formed the most rigid triplet allowing building an optimal thorax segment coordinate system (SCS). We thus measured the variations of distances between markers placed on various anatomical landmarks, and then the deformations of the combinations of three markers on different cervical movements of a sample of 10 asymptomatic subjects. The results show that the triplet formed by the sternum and both acromions undergoes less deformation on the flexion-extension movement. For all the other movements (lateral bending, axial rotation and complex movements), the triplet formed by sternum, T3 and TH (positioned on the thoracic spinal column, in a horizontal plane containing the sternal marker), undergoes less deformation. As a conclusion, the optimal triplet to define the thorax SCS for 3D kinematical analysis of the cervical spine is that formed by the markers: sternum, T3 and TH. This triplet makes it possible to define an orthonormal SCS, the axes of which coincide with anatomical directions, i.e. with the functional axes of the movement.     

Proposal of a thorax segment coordinate system for the 3D kinematical analysis of the cervical spine

The International Society of Biomechanics detailed the recommendations for 3D kinematics of intervertebral movements (Wu, et al. 2002. J Biomech. 35:543–548), but does not specify how to adapt this proposal to describe the kinematics of the cervical spine, between the head and the thorax. The analysis of the literature shows that no consensus exists at the present time on this subject. The objective of our study was to identify the reference points that formed the most rigid triplet allowing building an optimal thorax segment coordinate system (SCS). We thus measured the variations of distances between markers placed on various anatomical landmarks, and then the deformations of the combinations of three markers on different cervical movements of a sample of 10 asymptomatic subjects. The results show that the triplet formed by the sternum and both acromions undergoes less deformation on the flexion–extension movement. For all the other movements (lateral bending, axial rotation and complex movements), the triplet formed by sternum, T3 and TH (positioned on the thoracic spinal column, in a horizontal plane containing the sternal marker), undergoes less deformation. As a conclusion, the optimal triplet to define the thorax SCS for 3D kinematical analysis of the cervical spine is that formed by the markers: sternum, T3 and TH. This triplet makes it possible to define an orthonormal SCS, the axes of which coincide with anatomical directions, i.e. with the functional axes of the movement.     

Comparison of the hindfoot axes of a multi-segment foot model to the underlying bony anatomy

Musculoskeletal models used in gait analysis require coordinate systems to be identified for the body segments of interest. It is not obvious how hindfoot (or rearfoot) axes defined by skin-mounted markers relate to the anatomy of the underlying bones. The aim of this study was to compare the marker-based axes of the hindfoot in a multi-segment foot model to the orientations of the talus and calcaneus as characterized by their principal axes of inertia. Twenty adult females with no known foot deformities had radio-opaque markers placed on their feet and ankles at the foot model marker locations. CT images of the feet were acquired as the participants lay supine with their feet in a semi-weight bearing posture. The spatial coordinates of the markers were obtained from the images and used to define the foot model axes. Segmented masks of the tali and calcanei were used to create 3D bone models, from which the principal axes of the bones were obtained. The orientations of the principal axes were either within the range of typical values reported in the imaging literature or differed in ways that could be explained by variations in how the angles were defined. The model hindfoot axis orientations relative to the principal axes of the bones had little bias but were highly variable. Consideration of coronal plane hindfoot alignment as measured clinically and radiographically suggested that the model hindfoot coordinate system represents the posterior calcaneal tuberosity, rather than the calcaneus as a whole.     

An alternative definition of the scapular coordinate system for use with RSA

When performing radiostereometric analysis (RSA), computed tomography scans are often taken to obtain the landmarks used to create anatomical coordinate systems (CSs) for quantifying joint kinematics. Different conventions for defining CSs lead to an inability to compare results among studies. The International Society of Biomechanics (ISB) has proposed a set of CSs; however, the landmarks needed to create the recommended scapular CS require the entire scapula to be scanned, thereby also exposing breast and other tissues to radiation. The main purpose of this work was to investigate an alternate definition of the CS that has repeatably attainable landmarks and axes as close as possible to those recommended by the ISB, while limiting the portion of the scapula requiring scanning. Intra- and inter-investigator variabilities of landmark digitization were quantified in one model of a scapula and one cadaveric specimen. Based on the variability of the digitizations, an alternative CS was defined. The differences between the ISB and alternative CSs were evaluated on 11 cadaveric specimens. Beaded biplanar RSA was performed on the glenohumeral joint model in 15 different configurations and the resulting kinematics were calculated for each set of landmark digitizations using both sets of coordinate systems. While the kinematic angles obtained using the alternative CS were statistically different from those obtained using the ISB standard, these differences were small (on the order of 5°) and therefore considered to be of little clinical significance. In all likelihood, the benefits of decreasing radiation exposure outweigh these differences in angles.     

A comparison and update of direct kinematic-kinetic models of leg stiffness in human running

Direct kinematic-kinetic modelling currently represents the “Gold-standard” in leg stiffness quantification during three-dimensional (3D) motion capture experiments. However, the medial-lateral components of ground reaction force and leg length have been neglected in current leg stiffness formulations. It is unknown if accounting for all 3D would alter healthy biologic estimates of leg stiffness, compared to present direct modelling methods. This study compared running leg stiffness derived from a new method (multiplanar method) which includes all three Cartesian axes, against current methods which either only include the vertical axis (line method) or only the plane of progression (uniplanar method). Twenty healthy female runners performed shod overground running at 5.0 m/s. Three-dimensional motion capture and synchronised in-ground force plates were used to track the change in length of the leg vector (hip joint centre to centre of pressure) and resultant projected ground reaction force. Leg stiffness was expressed as dimensionless units, as a percentage of an individual’s bodyweight divided by standing leg length (BW/LL). Leg stiffness using the line method was larger than the uniplanar method by 15.6%BW/LL (P < .001), and multiplanar method by 24.2%BW/LL (P < .001). Leg stiffness from the uniplanar method was larger than the multiplanar method by 8.5%BW/LL (6.5 kN/m) (P < .001). The inclusion of medial-lateral components significantly increased leg deformation magnitude, accounting for the reduction in leg stiffness estimate with the multiplanar method. Given that limb movements typically occur in 3D, the new multiplanar method provides the most complete accounting of all force and length components in leg stiffness calculation.     

Mandibular kinematics represented by a non-orthogonal floating axis joint coordinate system

There are many methods used to represent joint kinematics (e.g., roll, pitch, and yaw angles; instantaneous center of rotation; kinematic center; helical axis). Often in biomechanics internal landmarks are inferred from external landmarks. This study represents mandibular kinematics using a non-orthogonal floating axis joint coordinate system based on 3-D geometric models with parameters that are "clinician friendly" and mathematically rigorous. Kinematics data for two controls were acquired from passive fiducial markers attached to a custom dental clutch. The geometric models were constructed from MRI data. The superior point along the arc of the long axis of the condyle was used to define the coordinate axes. The kinematic data and geometric models were registered through fiducial markers visible during both protocols. The mean absolute maxima across the subjects for sagittal rotation, coronal rotation, axial rotation, medial-lateral translation, anterior-posterior translation, and inferior-superior translation were 34.10 degrees, 1.82 degrees, 1.14 degrees, 2.31, 21.07, and 6.95 mm, respectively. All the parameters, except for one subject's axial rotation, were reproducible across two motion recording sessions. There was a linear correlation between sagittal rotation and translation, the dominant motion plane, with approximately 1.5 degrees of rotation per millimeter of translation. The novel approach of combining the floating axis system with geometric models succinctly described mandibular kinematics with reproducible and clinician friendly parameters.     

Effect of axis alignment on in vivo shoulder kinematics

BACKGROUND. To describe 3D shoulder joint movements, the International Society of Biomechanics (ISB) recommends using segment coordinate systems (SCSs) on the humerus, scapula and thorax, and joint coordinate systems (JCSs) on the shoulder. However, one of the remaining problems is how to define the zero angles when the arm is in an initial reference position. The aim of this paper is to compare various methods of determining the JCSs of the shoulder that make it possible to define the zero angles of the arm in the resting position. METHODS. Able-bodied subjects performed elevation movements in the scapular plane, specifically neutral, internal and external rotations of the humerus. The initial humerus position (at the beginning of the arm movement) and range of motion were analysed for the purpose of clinical interpretation of arm attitude and movement. The following four different JCSs were explored: (1) the standard JCS, defined as recommended by the ISB, (2) a first aligned JCS, where the humerus SCS is initially aligned with the scapula SCS, (3) a second aligned JCS, where the opposite operation is performed and 4) a third aligned JCS, where both the humerus and the scapular SCS are initially aligned with the thorax SCS. FINDINGS. The second aligned JCS was the only method that did not produce any exaggerated range of movement in either anatomical plane. INTERPRETATION. Mathematical JCS alignment allows clearer clinical interpretation of arm attitude and movement.     

An anatomy-based coordinate system for the description of the kinematic displacements in the human knee

The effects and interaction of the anatomical displacements in the human knee are a prerequisite to an accurate assessment and communication of the kinematic data. For the kinematic information to be used to improve diagnosis and treatment, and for better prosthetic design and installation, there must be clear, concise, and universal definitions of the displacements. In general, the displacements are defined as three translations and three rotations. In this paper, anatomic landmarks on the femur and on the tibia are used to define the locations and orientations of the six displacement axes; i.e. three translational and three rotational displacement axes. The most commonly accepted kinematic representation of the knee joint, in the literature, is a special geometry three-cylindric open chain in which the axes of the cylindric joints are defined according to the rotational displacement axes. The sequentially adjacent joint axes are assumed to not only intersect but to intersect at right-angles. The open chain permits a total of six degrees of freedom between a Cartesian reference frame attached to the femur and a Cartesian reference frame attached to the tibia. In this paper, the three rotational axes are shown to be skewed and off-set from each other, therefore, a three-cylindric open chain with skewed joint axes is proposed to measure the six displacements between the two reference frames. The authors believe that the proposed open chain is the most general to date and provides a more realistic representation of the displacements in the knee. To illustrate the significance of the reference frames on the interpretation of measured data, the anterior/posterior drawer is plotted against per cent gait cycle for three existing open chains and the proposed open chain.     

A Flexible Calibration Method Using the Planar Target with a Square Pattern for Line Structured Light Vision System

A flexible calibration approach for line structured light vision system is proposed in this paper. Firstly a camera model is established by transforming the points from the 2D image plane to the world coordinate frame, and the intrinsic parameters of camera can be obtained accurately. Then a novel calibration method for structured light projector is presented by moving a planar target with a square pattern randomly, and the method mainly involves three steps: first, a simple linear model is proposed, by which the plane equation of the target at any orientations can be determined based on the square’s geometry information; second, the pixel coordinates of the light stripe center on the target images are extracted as the control points; finally, the points are projected into the camera coordinate frame with the help of the intrinsic parameters and the plane equations of the target, and the structured light plane can be determined by fitting these three-dimensional points. The experimental data show that the method has good repeatability and accuracy.     

Functional knee axis based on isokinetic dynamometry data: Comparison of two methods, MRI validation, and effect on knee joint kinematics

This paper compares geometry-based knee axes of rotation (transepicondylar axis and geometric center axis) and motion-based functional knee axes of rotation (fAoR). Two algorithms are evaluated to calculate fAoRs: Gamage and Lasenby's sphere fitting algorithm (GL) and Ehrig et al.'s axis transformation algorithm (SARA). Calculations are based on 3D motion data acquired during isokinetic dynamometry. AoRs are validated with the equivalent axis based on static MR-images. We quantified the difference in orientation between two knee axes of rotation as the angle between the projection of the axes in the transversal and frontal planes, and the difference in location as the distance between the intersection points of the axes with the sagittal plane. Maximum differences between fAoRs resulting from GL and SARA were 5.7° and 15.4mm, respectively. Maximum differences between fAoRs resulting from GL or SARA and the equivalent axis were 5.4°/11.5mm and 8.6°/12.8mm, respectively. Differences between geometry-based axes and EA are larger than differences between fAoR and EA both in orientation (maximum 10.6°).and location (maximum 20.8mm). Knee joint angle trajectories and the corresponding accelerations for the different knee axes of rotation were estimated using Kalman smoothing. For the joint angles, the maximum RMS difference with the MRI-based equivalent axis, which was used as a reference, was 3°. For the knee joint accelerations, the maximum RMS difference with the equivalent axis was 20°/s(2). Functional knee axes of rotation describe knee motion better than geometry-based axes. GL performs better than SARA for calculations based on experimental dynamometry.     

Double calibration: an accurate, reliable and easy-to-use method for 3D scapular motion analysis

The most recent non-invasive methods for the recording of scapular motion are based on an acromion marker (AM) set and a single calibration (SC) of the scapula in a resting position. However, this method fails to accurately measure scapular kinematics above 90° of arm elevation, due to soft tissue artifacts of the skin and muscles covering the acromion. The aim of this study was to evaluate the accuracy, and inter-trial and inter-session repeatability of a double calibration method (DC) in comparison with SC. The SC and DC data were measured with an optoelectronic system during arm flexion and abduction at different angles of elevation (0-180°). They were compared with palpation of the scapula using a scapula locator. DC data was not significantly different from palpation for 5/6 axes of rotation tested (Y, X, and Z in abduction and flexion), where as SC showed significant differences for 5/6 axes. The root mean square errors ranged from 2.96° to 4.48° for DC and from 6° to 9.19° for SC. The inter-trial repeatability was good to excellent for SC and DC. The inter-session repeatability was moderate to excellent for SC and moderate to good for DC. Coupling AM and DC is an easy-to-use method, which yields accurate and reliable measurements of scapular kinematics for the complete range of arm motion. It can be applied to the measurement of shoulder motion in many fields (sports, orthopaedics, and rehabilitation), especially when large ranges of arm motion are required.     

Contextual Effects of Scene on the Visual Perception of Object Orientation in Depth

We investigated the effect of background scene on the human visual perception of depth orientation (i.e., azimuth angle) of three-dimensional common objects. Participants evaluated the depth orientation of objects. The objects were surrounded by scenes with an apparent axis of the global reference frame, such as a sidewalk scene. When a scene axis was slightly misaligned with the gaze line, object orientation perception was biased, as if the gaze line had been assimilated into the scene axis (Experiment 1). When the scene axis was slightly misaligned with the object, evaluated object orientation was biased, as if it had been assimilated into the scene axis (Experiment 2). This assimilation may be due to confusion between the orientation of the scene and object axes (Experiment 3). Thus, the global reference frame may influence object orientation perception when its orientation is similar to that of the gaze-line or object.