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Transcript of CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from...
![Page 1: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/1.jpg)
CSCE643: Computer VisionBayesian Tracking & Particle Filtering
Jinxiang Chai
Some slides from Stephen Roth
![Page 2: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/2.jpg)
Appearance-based Tracking
![Page 3: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/3.jpg)
Review: Mean-Shift Tracking
• Key idea #1: Formulate the tracking problem as nonlinear optimization by maximizing color histogram consistency between target and template.
]),([maxarg qypfy
q p y
![Page 4: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/4.jpg)
• Key idea #2: Solving the optimization problem with mean-shift techniques
Review: Mean-Shift Tracking
![Page 5: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/5.jpg)
Review: Mean-Shift Tracking
![Page 6: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/6.jpg)
Lucas-Kanade Registration & Mean-Shift Tracking
• Key Idea #1: Formulate the tracking/registration as a function optimization problem
x
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]),([maxarg qypfy
Lucas-Kanade registration Mean Shift Tracking
![Page 7: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/7.jpg)
• Key Idea #2: Iteratively solve the optimization problem with gradient-based optimization techniques
xp
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Gauss-Newton Mean Shift
Lucas-Kanade Registration & Mean-Shift Tracking
![Page 8: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/8.jpg)
Optimization-based Tracking
Pros:
+ computationally efficient
+ sub-pixel accuracy
+ flexible for tracking a wide variety of objects (optical flow, parametric motion models, 2D color histograms, 3D objects)
![Page 9: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/9.jpg)
Optimization-based Tracking
Cons: - prone to local minima due to local optimization
techniques. This could be improved by global optimization techniques such as Particle swamp and Interacting Simulated Annealing
- fail to model multi-modal tracking results due to tracking ambiguities (e.g., occlusion, illumination changes)
![Page 10: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/10.jpg)
Optimization-based Tracking
Cons: - prone to local minima due to local optimization
techniques. This could be improved by global optimization techniques such as Particle swamp and Interacting Simulated Annealing
- fail to model multi-modal tracking results due to tracking ambiguities (e.g., occlusion, illumination changes)
Solution: Bayesian Tracking & Particle Filter
![Page 11: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/11.jpg)
Particle Filtering
• Many different names- Sequential Monte Carlo filters- Bootstrap filters- Condensation Algorithm
![Page 12: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/12.jpg)
Bayesian Rules
)(
)()|()|(
ZP
XPXZPZXP
Observed measurementsHidden states
• Many computer vision problems can be formulated a posterior estimation problem
![Page 13: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/13.jpg)
Bayesian Rules
)(
)()|()|(
ZP
XPXZPZXP
Posterior: This is what you want. Knowingp(X|Z) will tell us what is themost likely state X.
• Many computer vision problems can be formulated a posterior estimation problem
![Page 14: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/14.jpg)
Bayesian Rules
)(
)()|()|(
ZP
XPXZPZXP
Posterior: This is what you want. Knowingp(X|Z) will tell us what is themost likely state X.
Likelihood term: This is what you canevaluate
![Page 15: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/15.jpg)
Bayesian Rules
)(
)()|()|(
ZP
XPXZPZXP
Posterior: This is what you want. Knowingp(X|Z) will tell us what is themost likely state X.
Likelihood term: This is what you canevaluate
Prior: This is what you mayknow a priori, or whatyou can predict
![Page 16: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/16.jpg)
Bayesian Rules
)(
)()|()|(
ZP
XPXZPZXP
Posterior: This is what you want. Knowingp(X|Z) will tell us what is themost likely state X.
Likelihood term: This is what you canevaluate
Prior: This is what you mayknow a priori, or whatyou can predict
Evidence: This is a constant for observed measurements such as images
![Page 17: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/17.jpg)
Bayesian Tracking
• Problem statement: estimate the most likely state xk given the observations thus far Zk={z1,z2,…,zk}
……
……
x1 xk-2 xk-1 xk
z1 zk-2 zk-1 zkObserved measurements
Hidden state
![Page 18: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/18.jpg)
Notations
![Page 19: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/19.jpg)
Examples
• 2D region tracking
xk:2D location and scale of interesting regionszk: color histograms of the region
![Page 20: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/20.jpg)
Examples
• 2D Contour tracking
xk: control points of spline-based contour representation
zk: edge strength perpendicular to contour
![Page 21: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/21.jpg)
Examples
• 3D head tracking
xk:3D head position and orientationzk: color images of head region
[Jing et al , 2003]
![Page 22: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/22.jpg)
Examples
• 3D skeletal pose tracking
xk: 3D skeletal poses
zk: image measurements including silhouettes, edges, colors, etc.
![Page 23: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/23.jpg)
Bayesian Tracking• Construct the posterior probability
density function of the state based on all available information
• By knowing the posterior many kinds of estimates for can be derived– mean (expectation), mode, median, …– Can also give estimation of the accuracy (e.g.
covariance)
)|( :1 kk zxpThomas Bayes
kx
Sample space
Posterior
![Page 24: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/24.jpg)
Bayesian Tracking
State posterior Mean state
![Page 25: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/25.jpg)
Bayesian Tracking
• Goal: estimate the most likely state given the observed measurements up to the current frame
![Page 26: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/26.jpg)
Recursive Bayesian Estimation
![Page 27: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/27.jpg)
Bayesian Formulation
![Page 28: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/28.jpg)
Bayesian Tracking
![Page 29: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/29.jpg)
Bayesian Tracking
……
……
x1 xk-2 xk-1 xk
z1 zk-2 zk-1 zkObserved measurements
Hidden state
![Page 30: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/30.jpg)
Bayesian Tracking
……
……
x1 xk-2 xk-1 xk
z1 zk-2 zk-1 zkObserved measurements
Hidden state
![Page 31: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/31.jpg)
Bayesian Tracking
![Page 32: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/32.jpg)
Bayesian Tracking
……
……
x1 xk-2 xk-1 xk
z1 zk-2 zk-1 zkObserved measurements
Hidden state
![Page 33: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/33.jpg)
Bayesian Tracking:Temporal Priors
• The PDF models the prior knowledge that predicts the current hidden state using previous states
- simple smoothness prior, e.g.,
- linear models, e.g.,
- more complicated prior models can be constructed via data-driven modeling techniques or physics-based modeling techniques
)2
exp()|(2
2
11
kk
kk
xxxxp
)2
exp()|(2
2
11
BAxxxxp kkkk
1-kxkx
![Page 34: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/34.jpg)
Bayesian Tracking: Likelihood
……
……
x1 xk-2 xk-1 xk
z1 zk-2 zk-1 zkObserved measurements
Hidden state
![Page 35: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/35.jpg)
Bayesian Tracking: Likelihood
• The likelihood term measures how well the hidden state matches the observed measurements
)|( kk xzp
kx
kz
![Page 36: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/36.jpg)
Bayesian Tracking: Likelihood
• The likelihood term measures how well the hidden state matches the observed measurements
- In general, we can define the likelihood using analysis-by-synthesis strategy.
- We often assume residuals are normal distributed.
)|( kk xzp
kx
kz
![Page 37: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/37.jpg)
Bayesian Tracking: Likelihood
• The likelihood term measures how well the hidden state matches the observed measurements
)|( kk xzp
xk:2D location and scalezk: color histograms
kx
kz
How to define the likelihood term for 2D region tracking?
![Page 38: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/38.jpg)
Bayesian Tracking: Likelihood
• The likelihood term measures how well the hidden state matches the observed measurements
)|( kk xzp
xk:2D location and scalezk: color histograms
kx
kz
)2
)]),([1(exp()|(
2
2
qxpf
xzp kkk
Matching residuals
![Page 39: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/39.jpg)
Bayesian Tracking: Likelihood
• The likelihood term measures how well the hidden state matches the observed measurements
)|( kk xzp
xk:2D location and scalezk: color histograms
kx
kz
)2
)]),([1(exp()|(
2
2
qxpf
xzp kkk
Matching residuals
2)]),([1(minarg qxpf kxk
Equivalent to
![Page 40: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/40.jpg)
Bayesian Tracking: Likelihood
• The likelihood term measures how well the hidden state matches the observed measurements
)|( kk xzp
kx
kz
)2
)(exp()|(
2
2
kk
kk
zxIxzp
xk:3D head position and orientationzk: color images of head region
Synthesized image
![Page 41: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/41.jpg)
Bayesian Tracking: Likelihood
• The likelihood term measures how well the hidden state matches the observed measurements
)|( kk xzp
kx
kz
)2
)(exp()|(
2
2
kk
kk
zxIxzp
xk:3D head position and orientationzk: color images of head region
observed image
![Page 42: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/42.jpg)
Bayesian Tracking: Likelihood
• The likelihood term measures how well the hidden state matches the observed measurements
)|( kk xzp
kx
kz
)2
)(exp()|(
2
2
kk
kk
zxIxzp
xk:3D head position and orientationzk: color images of head region
Matching residuals
![Page 43: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/43.jpg)
Bayesian Tracking
• How to estimate the following posterior?
![Page 44: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/44.jpg)
Bayesian Tracking
• How to estimate the following posterior?
• The posterior distribution p(x|z) may be difficult or impossible to compute in closed form.
![Page 45: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/45.jpg)
Bayesian Tracking
• How to estimate the following posterior?
• The posterior distribution p(x|z) may be difficult or impossible to compute in closed form.
• An alternative is to represent p(x|z) using Monte Carlo samples (particles):– Each particle has a value and a weight
x
x
![Page 46: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/46.jpg)
Multiple Modal Posteriors
![Page 47: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/47.jpg)
Non-Parametric Approximation
![Page 48: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/48.jpg)
Non-Parametric Approximation
- This is similar kernel-based density estimation!- However, this is normally not necessary
![Page 49: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/49.jpg)
Non-Parametric Approximation
![Page 50: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/50.jpg)
Non-Parametric Approximation
![Page 51: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/51.jpg)
How Does This Help Us?
![Page 52: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/52.jpg)
Monte Carlo Approximation
![Page 53: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/53.jpg)
Filtering: Step-by-Step
![Page 54: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/54.jpg)
Filtering: Step-by-Step
![Page 55: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/55.jpg)
Filtering: Step-by-Step
![Page 56: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/56.jpg)
Filtering: Step-by-Step
![Page 57: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/57.jpg)
Filtering: Step-by-Step
![Page 58: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/58.jpg)
Filtering: Step-by-Step
![Page 59: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/59.jpg)
Temporal Propagation
![Page 60: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/60.jpg)
Temporal Propagation
after a few iterations, most particles have negligible weight (the weight is concentrated on a few particles only)!
![Page 61: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/61.jpg)
Resampling
![Page 62: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/62.jpg)
Particle Filtering
Isard & Blake IJCV 98
![Page 63: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/63.jpg)
Particle Filtering
Isard & Blake IJCV 98
![Page 64: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/64.jpg)
Particle Filtering
Isard & Blake IJCV 98
![Page 65: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/65.jpg)
Particle Filtering
Isard & Blake IJCV 98
![Page 66: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/66.jpg)
Particle Filtering
Isard & Blake IJCV 98
![Page 67: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/67.jpg)
Particle Filtering in Action
• Video (click here)
![Page 68: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/68.jpg)
State Posterior
Isard & Blake IJCV 98
![Page 72: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/72.jpg)
Some Properties
• It can be shown that in the infinite particle limit this converges to the correct solution [Isard & Blake].
• In practice, we of course want to use a finite number.
- In low-dimensional spaces we might only need 100s of particles for the procedure to work well.
- In high-dimensional spaces sometimes 1000s, 10000s or even more particles are needed.
• There are many variants of this basic procedure, some of which are more efficient (e.g. need fewer particles)
- See e.g.: Arnaud Doucet, Simon Godsill, Christophe Andrieu: On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, vol. 10, pp. 197-- 208, 2000.
![Page 73: CSCE643: Computer Vision Bayesian Tracking & Particle Filtering Jinxiang Chai Some slides from Stephen Roth.](https://reader030.fdocuments.net/reader030/viewer/2022032516/56649c765503460f9492a275/html5/thumbnails/73.jpg)
Summary: Particle Filtering
• Advantages + can deal with nonlinearities and non-Gaussian noise
+ use temporal priors for tracking
+ Multi-modal posterior okay
+ Multiple samples provides multiple hypotheses
+ Easy to implement
• Disadvantages
- might become computationally inefficient, particularly when tracking in a high-dimensional state space (e.g., 3D human bodies)
- but parallelizable and thus can be accelerated via GPU implementations.