Kalman Filter: for tracking

Final Project

CSE 378 : Robotics

Background Subtraction: Subtract Background Image from Foreground Image, then threshold.
Computer Vision: Extracting information from images.
Causal Probabilty: P(E|H)
Diagnostic Probability: P(H|E)
Kinematics: Solve for points in space given system parameters.
Inverse Kinematics: Solve for System Parameters given points in space.
Markov Process: A Stochastic Process that has the Markov Property.
Markov Property: Given a system's current state, the system's future state is conditionally independent of the past.
Robotics: The study of robots.
Robot: A mechanical agent.

Rx = 100 0cosθ-sinθ 0sinθcosθ Ry = cosθ0sinθ 010 -sinθ0cosθ Rz = cosθ-sinθ0 sinθcosθ0 001 RV = eV⨯θ

Jacobian = dF1/dX1dF1/dX2dF1/dX3 dF2/dX1dF2/dX2dF2/dX3 dF3/dX1dF3/dX2dF3/dX3

dF = Jacobian * dX
dX = Jacobian-1 * dF

Convolution Theorem: ℱ{f * g} = ℱ{f} · ℱ{g} and ℱ{f · g} = ℱ{f} * ℱ{g}
Example: N(1,V₁)·N(1,V₂) = ℱ{ℱN(1,V₁)*ℱN(1,V₂)} = ℱ{N(1,1/V₁)*N(1,1/V₂)} = ℱ{N(1,1/V₁+1/V₂)} = N(1,1/(1/V₁+1/V₂))