10.3 Data filtering and smoothing techniques

Data filtering and smoothing are crucial in motion capture analysis. They help clean up raw data, removing noise and artifacts that can skew results. Understanding these techniques is key to extracting accurate information from movement recordings.

Filtering methods range from simple moving averages to complex wavelet transforms. Choosing the right approach depends on the type of motion, research goals, and noise characteristics. Proper filtering ensures reliable biomechanical measurements and meaningful interpretations of human movement.

Noise in Motion Capture Data

Sources and Characteristics of Noise

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• Noise in motion capture data manifests as unwanted variations or distortions in recorded signals
• Common sources include
  • Electronic interference
  • Marker occlusion
  • Skin movement artifacts
  • Quantization errors in analog-to-digital conversion
• Noise appears as
  • High-frequency oscillations
  • Sudden spikes
  • Low-frequency drift
• Signal-to-noise ratio (SNR) quantifies noise relative to desired signal
• Noise patterns vary
  • Random (white noise)
  • Systematic (colored noise)
• Frequency content of true motion signal and noise guides filtering technique selection

Noise Variation by System Type

• Optical systems (infrared cameras tracking reflective markers)
  • Prone to marker occlusion and misidentification
  • Affected by ambient light interference
• Inertial systems (accelerometers and gyroscopes)
  • Susceptible to drift over time
  • Influenced by electromagnetic fields
• Electromagnetic systems (sensors in magnetic field)
  • Sensitive to metal objects in capture volume
  • May experience distortion from nearby electronic devices

Filtering Techniques for Motion Capture

Common Filtering Methods

• Low-pass filters attenuate high-frequency noise while retaining lower frequency human movement components
• High-pass filters remove low-frequency drift or baseline wander
• Moving average filters smooth data by averaging fixed number of adjacent data points
• Savitzky-Golay filters combine smoothing and differentiation
  • Preserve higher order moments in data
  • Useful for calculating velocities and accelerations
• Butterworth filters widely used in biomechanics
  • Flat frequency response in passband
  • Good roll-off characteristics
• Kalman filters apply to real-time noise reduction and state estimation in dynamic systems

Advanced Filtering Approaches

• Wavelet transforms decompose signal into different frequency bands
  • Allow for localized filtering in both time and frequency domains
• Adaptive filters automatically adjust parameters based on input signal characteristics
  • Useful for non-stationary noise or varying movement patterns
• Ensemble empirical mode decomposition (EEMD)
  • Decomposes signal into intrinsic mode functions
  • Separates noise from meaningful motion components

Filtering Methods Comparison

Selection Criteria

• Type of motion analyzed influences filter choice (cyclic vs. discrete movements)
• Frequency content of signal guides cut-off frequency selection
• Research objectives determine acceptable trade-offs between noise reduction and signal preservation
• Fourier analysis examines frequency spectrum of motion capture data
  • Informs selection of appropriate cut-off frequencies
• For impact or high-acceleration movements, zero-phase filters preserve timing information
• Multi-segment movements require consistent filter parameters across all segments
• Filter order affects roll-off steepness and passband ripple amount
  • Higher order filters provide sharper cut-offs but may introduce more artifacts
• Cyclic movements (gait) benefit from frequency domain analysis techniques (harmonic analysis)
• Computational efficiency consideration for real-time applications or large datasets

Specialized Filtering Approaches

• Spline smoothing fits smooth curves to data points
  • Balances smoothness with closeness of fit
  • Useful for continuous motion data
• Singular spectrum analysis (SSA) decomposes time series into trend, oscillatory components, and noise
  • Effective for separating signal from complex noise structures
• Particle filters handle non-linear and non-Gaussian systems
  • Useful for tracking complex movements or multiple markers simultaneously

Effects of Filtering Parameters

Cut-off Frequency Impact

• Cut-off frequency determines boundary between attenuated and passed frequencies
• Lower cut-off frequencies result in smoother data
  • May remove important high-frequency signal components
  • Can lead to underestimation of peak values
• Higher cut-off frequencies preserve more original signal
  • May insufficiently remove noise
  • Can lead to overestimation of derivatives (velocity and acceleration)

Filter Order and Window Size Effects

• Filter order influences transition band width and stop-band attenuation degree
  • Higher orders provide steeper roll-offs
  • May introduce ringing artifacts
• Phase shift from causal filters alters timing relationships
  • Critical for rapid movement analysis
  • Important when comparing events across different signals
• Window size in moving average or Savitzky-Golay filters affects smoothing degree
  • Larger windows provide more smoothing
  • May obscure short-duration events

Optimization Techniques

• Residual analysis objectively determines optimal cut-off frequencies
  • Examines relationship between residual noise and cut-off frequency
• Cross-validation techniques assess filter performance on unseen data
  • Help prevent overfitting or underfitting
• Spectral analysis guides filter design by revealing dominant frequencies in motion
  • Assists in separating signal from noise components