Title: Tracking
1Tracking
2Point Tracking
- Estimate the location of a given point along a
sequence of images.
(x0,y0)
(xn,yn)
3Object 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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9Modeling noise or uncertainty
rotation
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11The General Model
Dynamics
Process noise N(0,Q)
Measurement noise N(0,R)
Projection
12Prediction
Estimated state
Estimated uncertainty / noise
13Update
Updated state
Updated uncertainty / noise
The weighting factor
14Summery
Prediction
Update
15Gaussian Normal distribution
- 1D Gaussian
- General Gaussian
16Adding 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
17The solution
18The solution (cont)
19The merging of two Gaussians
A more reliable measure
A noisy measure, be dont believe it very much
20The merging of two Gaussians (cont)
The result is a new Gaussian with a smaller
variance than the original ones !
21Why to use the normal distribution?
- Simple to manipulate
- Minimize the squared error.
- The big numbers low.
- The distribution of many natural things.
22What 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
23Tracking using the Kalman Filter Two more
examples.
24The General Model
Dynamics
Process noise
Measurement noise
Projection
25Example 1 Estimating a constant
Measurement noise
26Prediction
Update
27We can combine the prediction and update
28Claim1
Claim2
ConclusionThe Kalman filter gives a weighted
mean !
29Example 2 Shihab4
In X constant velocity In Y constant
acceleration
30Example2 -dynamics
31Example2 -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