Raport - System wraz z bibliotekÄ modułów dla zaawansowanej ...

Raport
Raport
„System wraz z biblioteką modułów dla zaawansowanej analizy i
interaktywnej syntezy ruchu postaci ludzkiej.”
Projekt współfinansowany przez Unię Europejską ze środków Europejskiego Funduszu Rozwoju
Regionalnego w ramach Programu Operacyjnego Innowacyjna Gospodarka 2007-2013.

Działanie nr 4.6 Raport nr: 4.6
Tytuł: Segmentacja ruchu postaci
Tytuł Projektu:
„System wraz z biblioteką modułów dla zaawansowanej analizy i
interaktywnej syntezy ruchu postaci ludzkiej”
Data rozpoczęcia Projektu: 01/04/2009
Czas trwania Projektu
Koordynator Projektu:
36 miesięcy
Polsko Japooska Wyższa Szkoła Technik Komputerowych
Termin przedłożenia Raportu 31/05/2011
Autorzy:
Akceptujący
Dostępne na:
Poziom rozpowszechniania
Kamil Lebek, Jakub Stępieo
prof. dr hab. inż. Konrad Wojciechowski
ftp://83.230.112.38/opi/raporty
PP
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Summary
Our aim was to provide flexible method of joint's limits estimation, employing PCA-based
methods (essentially QuTEM model, which is a statistical model, containing probability densities of a
joint's possible configurations). We believe that QuTEM addresses some of the problems of analyzing
and interpreting joint motion data acquired using numerous available devices. The theoretical
introduction is followed by a measurement noise robustness test and two usage scenarios describing
actual, practical applications of this procedure.
For testing purposes we implemented these procedures as MatLab scripts (with C3D files
parsing handled through MatLab-compatible plugin written in C++/MEX) and ran offline on C3D files.
Each of the aforementioned files contained motion data (inverse kinematics/dynamics) of a walking
individual; every trial was recorded in our laboratory using Vicon Nexus with Plug-In-Gait postprocessing
step. Final implementation was made in native C++, using the Eigen library - it allows user
to access estimated joint limits, check an arbitrary joint configuration for a limit violation and
generate random, valid joint configurations.
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Document revision history
Date Revision Author Change description
20.06.20
11
1.0 Kamil Lebek Initial revision.
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Table of contents
Summary ............................................................................................................................................3
Document revision history ..................................................................................................................4
Table of contents ................................................................................................................................5
Index of figures ...................................................................................................................................6
1. Introduction ................................................................................................................................7
1.1 Abstract ............................................................................. Błąd! Nie zdefiniowano zakładki.
2. QuTEM ........................................................................................................................................9
3. Use cases .................................................................................................................................. 10
3.1 Knee angular data dimensionality reduction ...................................................................... 12
3.1.1 Preprocessing the data .............................................................................................. 12
3.1.2 Mean flexion axis ....................................................................................................... 12
3.1.3 Projection .................................................................................................................. 12
3.1.4 Results ....................................................................................................................... 13
4. Conclusions and future work ..................................................................................................... 15
5. Bibliography .............................................................................................................................. 17
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Index of figures
Fig 1 Calibration of knee joint frame of reference: (a) lateral axis roughly coincides with knee fexion
axis so angle changes will mostly occur in a single channel; (b) knee flexion axis is between lateral and
anterior axes and thus Euler angle decomposition will have significant changes in two channels ...... 11
Fig 2 Euler angle data series of a knee joint (subject X). ..................................................................... 13
Fig 3 Rotation around the mean flexion axis calculated in the dimensionality reduction .................... 14
Fig 4 Euler angle data series of a knee before (dashed) and after (solid) aligning - normal data (subject
W). ................................................................................................................................................... 15
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1. Introduction
Nowadays, it is hard to imagine a state of the art orthopedic or biomechanical facility devoid
of computer-aided diagnostic systems. However crucial the great variety of specialized devices, tools
and software may be, one must not forget that precision and repeatability of performed
measurements is paramount since they have an obvious direct impact on the quality of ensuing
analysis and research. Therefore, continuous leveraging of tools and techniques applied to verify and
correct the measured data is crucial for reliability of the clinical motion analysis based on it.
In this work we are focused on the errors and interpretation difficulties caused by imprecise
estimation of joint parameters (i.e. centers and axes [20]). The most common way of defining joint
parameters is by positioning joint markers over anatomical landmarks and then following a number
of ad hoc rules which introduce numerous sources of error. This common procedure, referred to as
the standard protocol [20] or the anatomical method [26], is best represented by the well known
works [4, 5]. An alternative trend is to extract joint parameters from the actual relative motion of the
limbs/segments [16, 10, 18, 12, 20] which releases the anatomical landmarks constraints. These
methods utilize a wide variety of techniques (combinations of kinematic constraints, optimization
and non-parametric statistical methods) but often lack generality and robustness in the presence of
factors such as noise in the data or small ranges of captured motion. What is also noteworthy is that
not all of the cited procedures provide both joint centers and axes of rotation as their results. In this
context the procedure presented in [20] stands out, since, as reported in [26], it copes best with the
aforementioned di-culties, while providing both joint centers and axes of rotation.
The precise estimation of joint parameters is vital not only to the analysis of motion
kinematics but also in the course of determining its causative factors [7] using the procedure of
Inverse Dynamics (ID), which is very sensitive to a number of factors, including poorly estimated joint
parameters [21].
The aim of this paper is to describe an alternative procedure for estimating actual joint axes.
We propose to utilize QuTEM [17] (Quaternion Tangent Ellipsoid at the Mean) distribution of the
given joint's quaternion series, which is essentially Principal Component Analysis performed on
logarithmically mapped quaternion series in a tangent space at mean. To the best of our knowledge,
so far QuTEM has not been used in the context of clinical gait/motion analysis.
The natural applications of the proposed technique include:
• estimating bases/coordinate frames in which the relative limb rotation introduced by a joint
is expressed in anatomically justied and intuitive terms
• reducing the dimensionality of joint angular data if the relative motion of a limb in certain
dimensions/degrees of freedom can be neglected for specific experimental scenarios
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Having described the theoretical foundations behind QuTEM, we shall prove its usefulness by
providing two sample usage scenarios as well as proposing prospective development of this method
to make it more reliable in the context of clinical motion measurement and analysis.
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2. QuTEM
QuTEM, as introduced by Johnson [17] in his thesis, is an abbreviation of Quaternion Tangent
Ellipsoid at the Mean. Basically, it is a statistical model of an individual joint learnable from example
motion data (e.g. motion capture). While QuTEM distribution might be mathematically similar to
Bingham distribution [2], it employs wrapping approach [13] (tangential space) instead of being
estimated directly in R4. The main idea of this particular approach can be summarized as wrapping
zero-mean Gaussian distribution in R3 onto a hemisphere of S3 using the exponential map at the one
of the modes (unit quaternion manifold (S3) embedded in R4). Full model consists of the mean joint
coordinate frame, principal axes of joint variation (plus variances associated with them) and joint
limits defined as isoprobability contour beyond which probability density is equal to zero (impossible
joint configurations). It allows us to learn the probability density from motion data, sample new
points from that density and test if arbitrary joint orientations violate estimated joint limits.
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3. Use cases
We will now present two scenarios in which we have found QuTEM particularly useful in the
context of practical human gait analysis. These applications were inspired/provoked by the
imperfections of the measurements performed using well known Vicon Motion Capture System and
certain level of indetermination in anatomical measures of joint motion [8, 15].
First scenario concerns the dimensionality reduction of knee angular data, which - although
in fact acting as a 3DoF rotational joint (not to mention the translational movement [14]) - is
commonly and intuitively simplied to a single-DoF joint because the fact that the knee exion axis is
almost constant [14, 19, 9, 24]. The simplest way of extracting a single-axis of rotation is to observe
only the sagittal plane motion of a limb [22, 14]. We claim, however, that important motion
information may be lost by blindly defining the simplified joint with the mediolateral axis and thus
propose to employ QuTEM to extract the actual dominant axis of rotation.
The second scenario is focused on correcting the orientation of the joint/segment coordinate
frames output from the Vicon software. The problem is that the exact orientations of these frames
are random to some extent since the procedure of their estimation heavily depends on a number of
factors which are hard to control in practice [25]. Obviously, the orientation of the reference frames
directly inuences the Euler angles (rotation convention chosen by Vicon) describing the joint motion
(Figure 1). The more flaws and imprecision occur in the measurement process, the further measured
Euler angles float away from the actual anatomical angles making the nal output highly
counterintuitive and extremely hard for clinicians to assess (visually). However, one should notice
that it is possible to dramatically improve the quality of motion data stored as Euler angle series only
by rotating local reference frames of adjacent segments (Figure 1). Therefore, we propose to use
QuTEM to determine the dominant, orthogonal axes of rotation and use them as basis vectors for
the segment reference frames in order to correct the joint angle data and thus enhance its
readability.
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Fig 1 Calibration of knee joint frame of reference: (a) lateral axis roughly coincides with knee fexion axis
so angle changes will mostly occur in a single channel; (b) knee flexion axis is between lateral and anterior
axes and thus Euler angle decomposition will have significant changes in two channels
Additionally, the noise robustness of the method is tested by conducting the second scenario
using noisy data.
The proposed (or equivalent) post-processing procedures are not the only way of obtaining
the goals of measured data correction or dimensionality reduction but the alternative is quite
cumbersome. It boils down to employing the so called static trial step (mocap equipment calibration
before performing data acquisition of each patient) - one can manipulate knee markers until knee
exion axis "matches" (roughly) the real one. Despite giving acceptable results, the above-mentioned
procedure is obviously very time consuming. Interestingly, Vicon seems to favor this approach by
promoting a third party device called KAD (knee alignment device) making "knee calibration" faster.
The detailed description of the proposed application scenarios is provided in the forthcoming
sections. For testing purposes we implemented these procedures as MatLab scripts (with C3D files
parsing handled through MatLab-compatible plugin written in C++/MEX) and ran offline on C3D files.
Each of the aforementioned files contained motion data (inverse kinematics/dynamics) of a walking
individual; every trial was recorded in our laboratory using Vicon Nexus with Plug-In-Gait postprocessing
step. To avoid biased conclusions, the experiments were conducted using motion data of
subjects with normal and impaired physical mobility. For convenience, the subjects chosen for this
article are encoded (X - W) and rigidly assigned to specific experiments:
• subject X (male, 66, left/right knee osteoarthritis) - scenario 1
• subject Y (male, 26, healthy) - scenario 2
• subject Z (female, 64, lumbar and cervical spine osteoarthritis) - scenario 2
• subject W (female, 22, healthy) - noise robustness
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3.1 Knee angular data dimensionality reduction
3.1.1 Preprocessing the data
The first step extracts quaternion time-series representing relative rotation at the knee joint.
Vicon's C3D les, aside from the standard marker data, contain trajectories of artificial markers (virtual
markers estimated by Plug-In-Gait). Their names are suffixed withO, A, L and P denoting origin,
anterior, lateral and vertical axes of the given segment, respectively. In case of the knee joint the
considered segments are RFE/LFE (right/left femur) and RTI/LTI (right/left tibia) which dene the two
coordinate frames in the global coordinate system. Therefore, the virtual markers of interest are:
RFEO/LFEO, RFEA/LFEA, RFEL/LFEL and so on, accordingly with the above-described naming
convention.
Knee orientation (or more precisely tibia segment orientation relative to femur segment) can
be easily found by normalizing given basis vectors and treating them as rotation matrices. Having
determined the rotation matrix expressing orientation of tibia segment relative to femur segment,
we can compare our results with Vicon's Euler angles (proof of concept [11]) to ensure the
correctness of the conversion or go straight to quaternion representation treating the matrix in
question as a direction-cosine matrix [3].
As a result of this initial processing we obtain inverse kinematics data of the given joint
expressed as quaternion series, defining tibia segment orientation relative to femur segment.
3.1.2 Mean flexion axis
Intuitively, one may think of this step as finding the most common flexion axis by extracting
an average rotation direction from a given quaternion sequence.
In this processing stage we apply QuTEM to analyze the quaternion series in order to extract
principal axes in the warped tangent space. These axes represent greatest variances ordered
decreasingly. Properly processed data for a knee joint should exhibit a close correlation between
joint exion axis and the extracted highest variance axis (later referred to as a mean exion axis).
Therefore, this stage of the procedure requires taking an arbitrary non-zero point lying on the
highest variance axis in the scaled tangent space (R3 space tangent to R4) with respect to QuTEM by
employing SMT mapping.
There resulting quaternion contains an arbitrary rotation (irrelevant in this stage) around the
most common rotation axis. By extracting and re-normalizing the vector part of that quaternion, we
can express the mean flexion axis as a R3-vector.
3.1.3 Projection
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Finally, thanks to the SMT, we can reduce the joint dimensionality by projecting (in the scaled
tangent space) each quaternion in the sequence onto the previously determined mean flexion axis.
Projection can be calculated directly in that space by extracting the rest component of the resulting
3-component vectors (s) (SMT mapping with respect to the QuTEM aligns trial data to the principal
axes).
3.1.4 Results
Figure 2 depicts the Euler angle data series of a knee joint. Calculating QuTEM model
parameters for that particular motion data enabled us to estimate the mean flexion axis and describe
the whole sequence of the orientations as a rotation around a single axis. As one can see in Figure 3,
the aforementioned rotation can be expressed as one channel series (one-dimensional case) - yet it
shares the specific features and shape of 3-dimensional Euler angle decomposition. We believe that
presented dimensionality reduction method offers high quality results with a minimal amount of
data loss, which is thanks to variance-based approach (low-variance direction components were
projected on the highest variance direction).
Fig 2 Euler angle data series of a knee joint (subject X).
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Fig 3 Rotation around the mean flexion axis calculated in the dimensionality reduction
process (subject X).
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4. Conclusions and future work
The presented usage scenarios have proven that QuTEM can be a very useful tool for motion
analysis but along the process of implementation and testing we have come to the conclusion that it
has a few limitations. Firstly, if the angle between femur and tibia segment in the coronal plane is
large (more than 20-30 degrees) we might still have the impression of more than 1 DoF (basis vectors
of femur and tibia reference frames will not be even roughly parallel in a neutral position). Another
erroneous case involves misplaced markers causing twisting motion of a joint (along vertical axes) -
statistically correct mean flexion axis placement might be quite unnatural from the anatomical point
Fig 4 Euler angle data series of a knee before (dashed) and after (solid) aligning - normal data (subject
W).
of view.
Currently, we plan on developing a similar solution for spherical joints (e.g. 3 DoF ankle or hip
joints) enabling us to create a unified and robust algorithm to be used in medical diagnostics.
Another step could involve creating a joint model incorporating translational element, thus providing
a full joint model for the state of the art diagnostic environments.
An interesting secondary conclusion drawn in the course of the research is that nonzero
variances in QuTEM distribution of knee inverse kinematics data (expressed as a quaternion series)
may confirm that knee flexion axis varies over time [14, 19]. However, additional research is required
in order to clearly distinguish between the genuine movement of the knee flexion axis and
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potentially misleading artifacts due to imperfect data acquisition method (markers placed on soft
tissue) and intrinsic limitations of the model itself (constant CoR position assumed).
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5. Bibliography
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