cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM
Transcript of cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM
![Page 1: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/1.jpg)
Computer Vision
Exercise Session 9 – Condensation Tracker
![Page 2: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/2.jpg)
Assignment Tasks
1. Condensation tracker with color histogram
observations
2. Experiment with the condensation tracker
![Page 3: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/3.jpg)
Task 1
§ Track an object through an image sequence
§ State space: X
§ Time t xt
![Page 4: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/4.jpg)
General Tracking Framework
1. Prediction, based on system model f = system transition function
2. Update, based on measurement model h = measurement function is the history of observations
),( 111 −−−= tttt wxfx
),( tttt vxhz =
), ... ,( 1 tt zzZ =
![Page 5: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/5.jpg)
Recursive Bayesian Filter
Object not treated as a single state but as a probability distribution:
1. Prediction
2. Update
11111 )|( )|()|( −−−−− ∫= ttttttt dxZxpxxpZxp
)|()|( )|()|(
1
1
−
−=tt
tttttt Zzp
ZxpxzpZxp
normalization factor
![Page 6: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/6.jpg)
Recursive Bayesian Filter - Bottleneck
§ Calculating numerically is very time consuming, and the probability distributions have to be known…
§ Analytic solutions are only available for the simplest of cases, e.g. when distributions are Gaussian and the system and measurement models are linear…(Kalman filter, 1960)
§ That’s where CONDENSATION comes in, acronym for CONditional DENSity propagATION
11111 )|( )|()|( −−−−− ∫= ttttttt dxZxpxxpZxp
![Page 7: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/7.jpg)
Condensation Tracker
§ The probability distribution is represented by a sample set S
§ - weights giving the sampling probability
{ }NnsS nn ... 1|),( )()( == π
π
![Page 8: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/8.jpg)
Condensation Tracker
1. Prediction Start with , the sample set of the previous step, and apply the system model to each sample, yielding predicted samples
2. Update Sample from the predicted set, where samples are drawn with replacement with probability (using measurement model)
1−tS
)(' nts
)|( )(')( ntt
n szp=π
![Page 9: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/9.jpg)
Condensation Tracker
Samples may be drawn multiple times, but noise will yield different predictions
![Page 10: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/10.jpg)
Condensation Tracker with Color Histograms
§ Track objects – bounding-boxes
§ Samples = particles = bounding-boxes
§ State =
§ Initialization: user interaction – provide bounding box
§ Use color histogram in the measurement model
![Page 11: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/11.jpg)
Task 2: Experiment with the Condensation Tracker
• Moving hand • Uniform
background
• Moving hand • Clutter • Occlusions
• Ball bouncing • Motion model
![Page 12: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/12.jpg)
Video 1: Hand, uniform background
a priori mean state
a posteriori mean state
![Page 13: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/13.jpg)
Video 2: Hand, clutter, occlusions
a priori mean state
a posteriori mean state
![Page 14: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/14.jpg)
Video 3: Ball bouncing
a priori mean state
a posteriori mean state
![Page 15: cvg.ethz.ch€¦ · Created Date: 11/28/2013 11:24:57 AM](https://reader035.fdocuments.in/reader035/viewer/2022071214/604405e902a595793d51bf7d/html5/thumbnails/15.jpg)
Report
§ MATLAB code § We provide the overall structure § Write the code to perform each step of the
CONDENSATION tracker
§ Plot the trajectories of the mean state
§ Experiment different settings § number of particles § number of bins for quantization § updating appearance model § motion model
§ Try your own video (bonus)