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Tracking

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Generate some conclusions about the motion of the scene, objects, or the camera, ... The 'big numbers' low. The distribution of many 'natural' things. ... – PowerPoint PPT presentation

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Title: Tracking


1
Tracking
  • using the
  • Kalman Filter

2
Point Tracking
  • Estimate the location of a given point along a
    sequence of images.

(x0,y0)
(xn,yn)
3
Object Tracking
  • Generate some conclusions about the motion of
    the scene, objects, or the camera, given a
    sequence of images.
  • Knowing this motion, predict where things are
    going to project in the next image, so that we
    dont have so much work looking for them.
  • For example- unstable camera Walking man
  • a. Stabilize the camera using the dominant
    motion ( find motion parameters ! )
  • b. Assume that the man translates
    horizontally.

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Modeling noise or uncertainty
rotation
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11
The General Model
Dynamics
Process noise N(0,Q)
Measurement noise N(0,R)
Projection
12
Prediction
Estimated state
Estimated uncertainty / noise
13
Update
Updated state
Updated uncertainty / noise
The weighting factor
14
Summery
Prediction
Update
15
Gaussian Normal distribution
  • 1D Gaussian
  • General Gaussian

16
Adding two information sources
  • We are given to information sources Z1 and Z2
  • Both are normally distributed (v1 gt v2)
  • We would like to believe more to Z2, but still
    use the information from Z1 !
  • Mathematically

17
The solution
18
The solution (cont)
19
The merging of two Gaussians
A more reliable measure
A noisy measure, be dont believe it very much
20
The merging of two Gaussians (cont)
The result is a new Gaussian with a smaller
variance than the original ones !
21
Why to use the normal distribution?
  • Simple to manipulate
  • Minimize the squared error.
  • The big numbers low.
  • The distribution of many natural things.

22
What happens when we have a wrong estimation of
the measurements variance ?
The variance is too small The estimation doesnt
converge
The correct variance (The same variance that was
used to simulate the points)
The variance is too large The convergence is
very slow
23
Tracking using the Kalman Filter Two more
examples.
24
The General Model
Dynamics
Process noise
Measurement noise
Projection
25
Example 1 Estimating a constant
Measurement noise
26
Prediction
Update
27
We can combine the prediction and update
28
Claim1
Claim2
ConclusionThe Kalman filter gives a weighted
mean !
29
Example 2 Shihab4
In X constant velocity In Y constant
acceleration
30
Example2 -dynamics
31
Example2 -measurements
Given an image of the missile (or other source of
information)
  • For each possible location, give a score
  • Normalize the sum of the scores to 1.
  • The result is a matrix of probabilities for
    each location.
  • Fit a 2D Gaussian to this matrix, whose center is
    given by
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