Report assignment (1):
2me‐course modeling
Build a tracking system that captures loca2on of an object in the noisy movie data of
30 [pixel] x 40 [pixel] x 1[bit] x 400[frames]
: e e e ey
Report assignment (1): hint
A possible observa2on model
x: loca2on of the object
y: num. of white pixels around x
P( y | x ) : likelihood of x is a probability that the num. is y
You will need parameters a=0.5 and b=0.2 that stands for propor2ons
of white pixels around the object and on
background.
• Are a=0.5 and b=0.2 the best?
• Is b changing along 2me‐frame?
Report assignment (1): hint (contd.)
System model p( x(t+1) | x(t) )
[A] 2‐dimensional coordinate x(t) =( X(t), Y(t) )
• x( t+1 ) = x( t ) + epsilon( t ), epsilon(t) ~ N( 0, sigma^2 * I2 )
[B] 2‐dim. loca2on + 2‐dim. Velocity x(t) =( X(t), Y(t), Vx(t), Vy(t) )
• x( t+1 ) = x( t ) + [Vx(t), Vy(t), 0, 0] + epsilon(t) epsilon(t) ~ N(0, sigma^2 * I4 )
[C] are there any be[er models?
Report assignment (1): hint (contd.)
Must we use par2cle filter? No!
A simple HMM may work well, where Alpha_t at 2me t is a vector of dimensionality 30x40.
Forward and backward algorithm of HMM may be be[er than the ordinary PF,
Gamma_t( x, y ) = Alpha_t( x, y ) * Beta_t( x, y )
Es2ma2on variance should be changing? Probably
Yes!
When the true background noise level is changing, the es2ma2on variance should change accordingly.
