Generative Graphical Models for Maneuvering Object Tracking and Dynamics Analysis

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Generative Graphical Models for Maneuvering
Object Tracking and Dynamics Analysis

• Xin Fan and Guoliang Fan
• Visual Computing and Image Processing Lab
• School of Electrical and Computer Engineering
• Oklahoma State University

4th Joint IEEE International Workshop on Object
Tracking and Classification Beyond the Visible
Spectrum(OTCBVS'07) Minneapolis, MN, USA, June
22, 2007
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Problem Statement

• Motion models
• Deal with object movements
• Why important?
• complex motion patterns, e.g., maneuvering
• no good appearance model, e.g., low SNR
• provide good prediction for robust and efficient
  tracking
• Challenges
• Hardly predict maneuvering actions
• Model constraints
• A motion model that incorporates constraints

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• Our observations
• Maneuvering actions are due to forces and
  torques.
• forces and torques cause kinematic changes
• Newton equations for rigid body motion
• Rigid body motion VS point motion
• Newton equations
• Forces are dependent on kinematics
• Limited output power of engines.
• Uncertainties exist, e.g., air resistance, road
  friction, mechanical instability, etc.

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Problem Formulation

• Switching statistical models for maneuvering
  variables (forces and torques)
• Maneuvering actions are due to forces and torques.

• Newton equations to define kinematics evolution
  densities
• Newton equations of rigid body motion

• Rayleigh distribution to model velocity-force
  constraints
• Physical constraints reveal how forces are
  dependent on kinematics.

• Organize these dependencies with a probabilistic
  graphical model

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Related work

• White Gaussian noise acceleration (WGNA)
• Point target assumption
• Millers condition mean estimation
• Rigid Newton dynamics
• Jump-diffusion process, not sequentially
• Switching Linear dynamic system (SLDS) or Jump
  Markov linear system (JMLS)
• Discrete switching variables for maneuvering
  actions
• No explicit physical dynamics
• Inference algorithms
• IMM works for Gaussian densities
• BP works for tree structures
• Sampling based approximation

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Generative Model - Structure
Forces
Velocity Position
Frames
Orientation
Torques

• Generative model
• How forces and torques generate kinematics
  changes
• how kinematics generate observations

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Generative model-Cause variables

• Switching continuous probabilistic models
• Specify three switching normal distributions for
  forces.
• Ternary uniform mixture for torques (angular
  velocity)

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Generative model Temporal constraints

• Newton equations
• Investigate the dynamics of 3D rigid motion
• Define the kinematic dependence by Newton
  equations of rigid body motion.

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Generative model Temporal constraints

• Newton equations for 3D rigid motion

• p-linear momentum and f- force
• h - angular momentum and t- torque

• Simplified for ground vehicles

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Generative model Temporal constraints
Velocity
Position
Orientation

• kinematics dependency via Newton equations

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Generative model- VF constraints

• Rayleigh distribution for velocity-force
  constraints

• Driving force conditional on velocities

• Resistance force conditional on velocities

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Generative model - Likelihood

• Simple template matching to define likelihood

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Generative model - Inference

• SMC based inference algorithm

• Predict with temporal densities

• Evaluate weights with likelihood

• MCMC to generate samples of forces

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Experiments Simulated data

• Compared with a particle filter (PF) for JMLS
• Tracking with coupled linear and angular motion
• No coupling

JMPF
Ours
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Experiments Simulated data

• Compared with a particle filter (PF) for JMLS
• Tracking with coupled linear and angular motion
• Has coupling

JMPF
Ours
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Experiments Simulated data

• Compared with a particle filter (PF) for JMLS
• Tracking with velocity-force constraints

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Experiments Real world video

• Compared with constant velocity constant turn
  (CVCT) model

Ours
CVCT
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Conclusions and future work

• Conclusions
• Graphical model for maneuvering targets, which
  encode the Newtonian dynamics in a probabilistic
  framework.
• Explicitly and directly build the cause-effect
  relationship
• Feedback constraint from velocity to the forces

• Future work
• Handle multiple views.
• Multiple targets with data association