Verification of the blobby quaternion model of human joint limits
Introduction
With the popularization of motion acquisition methods, motion analysis is a active area of research. Proposed advanced solutions for motion capture, analysis and synthesis have a wide range of different applications [1], [2], [3], [4], [5], [6], [7].
This work concerns a joint limit model built on the basis of reference data acquired through the mocap system without need more complicated medical procedures like CT, MRI [8], [9]. The model can be the base for subsequent tools like tracking, classification or comparison of joint limit ranges. It can be essential in automated methods, such as physical simulation, forward and inverse kinematics. Joint limits are used, for example, in defining the pose of a character for animation. Application of joint limits can overcome errors in pose estimation during motion tracking. For example, in inertial motion capture systems estimated orientations are based on signals from IMU (inertial measurement unit) sensors. The errors can be large (about 10 degrees), so introduction of joint angles constraints can improve the pose calculation [10], [11].
Joint motion articulating surface is an important concept for the assessment of joint wear, stability and degeneration as well as to determine the proper diagnosis and treatment of joint diseases [12]. The method described in this paper uses the concepts of joint motion articulating surface.
Current tools, especially animation editors, express joint limits in the range of three Euler rotation angles (box model) without taking into account dependencies between the angles. In opposition, this paper presents a quaternion based model to represent the range of valid joint orientations. This representation allows characterizing intra- and inter-joint dependencies.
The purpose of this study is to present the general and flexible blobby quaternion model of joint orientations. The model can represent the individual person's joint, or be a general model built on a broad set of data. The blobby model is parameterised be two parameters and can be based on different metrics. In paper two metrics are used: Euclidean and geodesic quaternion distance function. The model is based on captured motion data. Motion acquisitions methods, like optical or inertial motion capture systems, are becoming more and more popular so such model can be easily obtained.
The paper also describes the model verification performed based on the motion captured shoulder joint data. The analyzed joint is a three degree of freedom (3-DOF) ball-and-socket joint which normally allows a wide range of movements.
The most models are verified by visual verification of simulation or tracking results with using the model. Quantitative assessments are not included. In the following the quantitative results as a number of incorrect orientation in test set are presented. The results shown, that quaternion blobby model can be better fitted to real joint limits that more general models.
Section snippets
Human joints
A system of rigid bodies interconnected by joints is called a kinematic chain. Joints are movable connections between skeleton elements (rigid bodies) and allow relative motion between them with imposed constrains.
In humans, motion is dictated by the shape of the bones in the joint and by supporting soft tissue, e.g. muscle attachments and joint capsules (ligaments). To model human movement it is necessary to consider synovial joints which contain a fluid-filled cavity between two or more
Representation of joints limits
In this subsection some reviews of methods to model joint limits are presented. Summary information is collected in Table 1.
Most current tools which use joint limits allow definition of limits on individual rotation angles that do not account for dependencies between those angles. Each DOF of a joint is treated individually and limits are described by minimal and maximal values of three Euler angles. This is the box limit model which is the prevalent model for joint limits, used in file formats
Implicit modeling
Isosurface generation is a standard method for volume data exploration, where a surface is defined according to a chosen isovalue of some trivariate function, . An isosurface is defined implicitly as the solution of Eq. (1).
Implicit surface is surface defined by all points P = (xi, yi, zi), iϵ[0, n − 1] fulfilling the equation . Such a surface is an isosurface for value of scalar field F.
Implicit functions have been very popular as a modeling tool for creating
Quaternion volume
Rotations can be represented by unit quaternions signal in time q1, q2, … qn forming a unit sphere in 4-dimensional space . The signal has been processed by the selective negation (hemispherization), i.e. every quaternion qi (i > 1) is converted to −qi if 〈qi, qi−1〉<0, where 〈, 〉 is inner product of two quaternions. It means that arcs on the hypersphere between adjacent quaternions are the shortest. The first quaternion q1 is checked with identity quaternion [1, 0, 0, 0], to avoid distortion
Metric
In the literature [36] we can find several functions for measuring the distance between two rotations. In experiments the following quaternion distance metrics were used:
- •
The distance between two rotations as the Euclidean distance between two vectors in tangent space:
- •
The geodesic distance between related quaternions, which is reflected by the angle between vectors formed by their components:
Enforcing constraints
The quaternion volume map of an experimentally determined range of motion for a joint have an arbitrarily complex boundary surface described as an implicit isosurface. This surface defines the allowed domain for plausible orientations of the given joint and more interestingly the domain to which any proposed positions of the joint can be clamped. To determine the optimal allowed reinterpretation of the joint orientation, one should locate the nearest point in appropriate quaternion metric on
Data measuring and preparation
Data was recorded with use of the Vicon Nexsus mocap system. The skeleton model of 22 segments is applied and positions are traced based on 39 markers in standard full body Plug-In Gait marker placement. We plan verify also models of next human joints so the recordings were with full body marker setup.
The Plug-In Gait tool was used for calculation of joint centers and definition of the rigid body segments based on markers placements. The result are joint Euler angles between these segments in
Summary
The main aim of the study was to propose general model of joint limits which allows adaptation to individual characteristics of different persons. As a solution developed the new quaternion blobby model. A new method has been defined by connecting implicit surface modeling, quaternion volume as a representation of all possible joint orientations and a fast and an efficient algorithm for finding the intersection of rays with surface (as in ray tracing algorithms). The results can be used in
Acknowledgements
This work was supported by statute project of the Silesian University of Technology, Institute of Informatics (BK/RAU-2/2016-2017). This work was also partly conducted using the infrastructure supported by the POIG.02.03.01-24-099/13 grant: GCONiI – Upper-Silesian Center for Scientific Computation.
Data was captured in the Human Motion Laboratory in Research and Development Center of Polish-Japanese Academy of Information Technology in Bytom, Poland (http://bytom.pja.edu.pl/).
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