Error Analysis

Direct error reasons:

1.      Lose frames

Reason:

1)      Miss synchronization between real-time server and Lithtech engine while recording the data.

2)      It cost the real-time server extra time to calculate one frame (position, rotation), thus delay the delivering time.

Result:

1)      No frame information available->all variables (position, rotation) keep stable  -> the action freezes.

2.      Markers invisible (all/any)

Reason:

1.      The Vicon system cannot see the markers

o       Position out of range

o       Hidden markers

2.      The Vicon system cannot label the markers

o       Fast actions

o       See more than actual markers

Result:

1)      Uncertain data generated from remaining visible markers

2)      Uncertain data generated from springs attached on the skeleton

3.      Markers mislabeled

Reason:

1.      The Vicon system gets confused

o       Fast actions

o       Sudden actions

2.      Some markers are invisible

Result:

1)      Error data of specific body

2)      Impact on the whole object

Typical error & Kalman filter performance

1.      Data flipping

o       Position & Rotation (fig. ErrorJump.gif)

o       Rotation (fig. ErrorFlip.gif)

Solution: Kalman Filter does a great job on such kind of error

2.      Data jump after a long frame-losing period

o       Position  (fig. ErrorLong_pos.gif)

o       Rotation  (fig. ErrorLong_angle.gif))

Solution: Delete/correct wrong data by adding some latency (Wait to make sure)

3.      Data change when no/seldom markers visible

o       Position (fig. ErrorNoMarkerVisible_pos.gif)

o       Rotation (fig. ErrorNoMarkerVisible_angle.gif)

Solution: Combine the previous two solutions

4.      Chaos Data (fig. ErrorChaos.gif)

Solution: Combine the previous two solutions

Mocap Data Analysis &Filter Research Program

1.      Interface Outlook (fig. ChooseFile.gif, UIBox1.gif, UIBox2.gif)

2.      Read in Mocap data stored in delimited text format

3.      Automatically categorize data

o       Marker: position (P-X, P-Y, P-Z)

o       Body:  Position (T-X, T-Y, T-Z)

Rotation (A-X, A-Y, A-Z)

Marker set

4.      Transform rotation data:

o       Angle-Axis -> Quaternion

o       Choose right Quaternion vector (Q or ¨CQ) to make the curve continuous

5.      Do filter process

Current method: Kalman Filter

6.      Plot original and filtered data (fig. PlotVariables.gif)

o       Position: T-X, T-Y, T-Z

o       Rotation in Quaternion: e0, e1, e2, e3

o       Marker set (marker names, visible marker number)

o       Lost frame number

7.      Show different properties of the data

o       Original

o       Velocity

o       Acceleration

o       Impulse

8.      Zoom Ability

o       Plots zoom in and out freely (fig. UIPlot.gif)

o       Two plots zoom in/out the same position and scale

9.      Output filtered data in delimited text format

Filter Research

Rotation Representation

1.      Common rotation representation in Computer Graphics

o       Angle-Axis

o       Matrices

o       Euler Angle

o       (Unit) Quaternion/Euler Parameters

2.      Q & A

Q: Why is that important for us?

A: We need to find a good representation for rotation that can present meaningful, exact, continuous data curve for analysis and interpolation

Q: Why use Quaternion?

A:  Advantage

o       The Quaternion space has the same topology and geometry as the set of rotations

o       Simple extrinsic equation (Angle-Axis <-> Quaternion)

o       Easy interpolation by using SLERP (Spherical Linear Interpolation)

Disadvantage

o       Its 2-1 nature (Two Quaternion (Q, -Q) represent the same rotation) necessitates a preprocessing step

Kalman Filter

1.      What is Kalman filter?

o       The Kalman filter is an optimal recursive data processing algorithm

o       Best possible estimator for a large class of problems and a very effective and useful estimator for an even larger class.

2.      Target System

o       General Kalman filter ¨C Stochastic Linear system with Gaussian noise

o       Extended Kalman filter (EKF), Unscented Kalman filter (UKF) ¨C Stochastic non-linear system with Gaussian noise

3.      It WORKS!!!

Future Plan

1.      Delete/correct wrong data by adding some latency (Wait to make sure)

2.      Use EKF or UKF instead of general Kalman filter

3.      Filter Parameters and tuning

o       System noise covariance

o       Measurement noise covariance

o       Mathematical model

o       Initial state and covariance

4.      Dual Quaternions representation

Reference

¡¤        Kalman Filter

[1]         An Introduction to the Kalman Filter

Gary Bishop; Greg Welch

ACM SIGGRAPH 2001 course

[2]         Chapter 1, Stochastic Models, Estimation, and Control, Peter Maybeck

Peter Maybeck

Volume 1, Academic Press, Inc

[3]         The square-root unscented Kalman filter for state and parameter-estimation
van der Merwe, R.; Wan, E.A.
Acoustics, Speech, and Signal Processing, 2001. Proceedings. 2001 IEEE International Conference on, Volume: 6, 2001
Page(s): 3461 -3464

[4]         The unscented Kalman filter for nonlinear estimation
Wan, E.A.; Van Der Merwe, R.
Adaptive Systems for Signal Processing, Communications, and Control Symposium 2000. AS-SPCC. The IEEE 2000, 2000
Page(s): 153 ¨C158

[5]         Pose and Motion Estimation Using Dual Quaternion-Based Extended Kalman Filtering

J.S. Goddarda and M.A. Abidib

[6]         Kalman Filter Toolbox

Kevin Murphy, 1999

[7]         Sequential Monte Carlo Methods Homepage

Nando de Freitas

¡¤        Quaternion

[8]         Smooth interpolation of rotational motions

Roberts, K.S.; Bishop, G.; Ganapathy, S.K.
Computer Vision and Pattern Recognition, 1988. Proceedings CVPR '88.,   Computer Society Conference on , 1988
Page(s): 724 -729

[9]         Smooth Interpolation of Orientations With Angular Velocity Constraints Using Quaternions

Alan H.B.; Bena C.; Steven, G.; John F.H

[10]    Recursive Methods for the Estimation of Rotation Quaternions

August W.Rihaczek

[11]    Using Quaternions to Represent Rotation

[12]    A Proof of the Quaternion Rotation Representation

[13]    The Matrix and Quaternions FAQ

¡¤        Motion Capture

[14]    A Real-Time Anatomical Converter for Human Motion Capture

T. Molet, R. Boulic, D. Thalmann

[15]    Kwon3D Motion Analysis Web

Young-Hoo Kwon, 1998-

[16]    Motion -- Feature-Based, Long Range, Motion and Structure Estimates, Surveillance

[17]    A Real Time Anatomical Converter For Human Motion Capture

Tom Molet, Ronan Boulic, Daniel Thalmann

[18]    Motion Balance Filtering

Seyoon Tak, Oh-young Song, and Hyeong-Seok Ko

[19]    Real-time human motion analysis and IK-based human figure control
Yonemoto, S.; Arita, D.; Taniguchi, R.
Human Motion, 2000. Proceedings. Workshop on , 2000
Page(s): 149 ¨C154