Real Time Visual Tracking
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Transcript of Real Time Visual Tracking
![Page 1: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/1.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Robust Visual Tracking Using CompressedSensing
Jainisha Sankhavara (201311002)Falak Shah (201311024)
MTech, DA-IICT
April 16, 2014
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VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Outline
1 Introduction
2 Particle FilterDefinitionParticle Filter VisualisationParticle Filter Equations
3 Template DictionaryEquationUnderdetermined systemTemplate Update
4 Real-Time Compressive Sensing Tracking (RTCST)Dimensionality ReductionOMPConclusion
5 References
![Page 3: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/3.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Introduction
• Just an attempt to explain the implementation of visualtracking as explained in[1] Hanxi Li; Chunhua Shen; Qinfeng Shi, ”Real-timevisual tracking using compressive sensing,” ComputerVision and Pattern Recognition (CVPR), 2011 IEEEConference on , vol., no., pp.1305,1312, 20-25 June 2011[2] Xue Mei; Haibin Ling, ”Robust visual tracking using l1minimization,” Computer Vision, 2009 IEEE 12thInternational Conference on , vol., no., pp.1436,1443,Sept. 29 2009-Oct. 2 2009
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VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Introduction
• Tracking object through frames video in real time.
• Assume initial position of object available in the first frame
• Challenges: Occlusion,illumination changes, shadows,varying viewpoints, etc
![Page 5: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/5.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Definition
• Posterirori density estimation algorithm
• There is some unknown we are interested in called statevariable (eg. location of object)
• We can measure something (measurement variable),related to the unknown variable
• Relation between state variable and measurement variableknown.
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VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Visualisation
Figure 1: Plane moving- Position unknown 1
1Andreas Svensson, Ph.D Student, Uppsala University
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VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Visualisation
Figure 2: Available data
![Page 8: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/8.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Visualisation
Figure 3: Initial distribution of particles
![Page 9: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/9.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Visualisation
Figure 4: Observation Likelihood
![Page 10: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/10.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Visualisation
Figure 5: Resampling Step
![Page 11: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/11.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Visualisation
Figure 6: Posteriori estimate
![Page 12: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/12.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Visualisation
Figure 7: Observation likelihood: step 2
![Page 13: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/13.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Visualisation
Figure 8: Resample: step 2
![Page 14: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/14.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Visualisation
Figure 9: Particles converge very close to object
![Page 15: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/15.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter visulisation
Figure 10: Issues
![Page 16: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/16.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Visualisation
Figure 11: Back to tracking
![Page 17: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/17.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Equations
• xt - state variable
• zt - observation at time t
• xt is modeled by six parameters of affine transformations.xt = (α1, α2, α3, α4, tx , ty )
• All six parameters are independent.
• State transition model p(xt |xt−1) is gaussian.
• p(zt |xt) is also gaussian.
![Page 18: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/18.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Particle Filter Equations
• state vector prediction
p(xt |z1:t−1) =
∫p(xt |xt−1)p(xt−1|z1:t−1)dxt−1
• state vector update
p(xt |z1:t) =p(zt |xt)p(xt |z1:t−1)
p(zt |z1:t−1)
• weight update
w it = w i
t−1
p(zt |x it)p(x it |x it−1)
q(xt |x1:t−1, z1:t)
![Page 19: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/19.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Template Dictionary
Figure 12: Target and Trivial Templates [2]
• Represent each of the particles as a linear combination oftarget templates and trivial templates.
![Page 20: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/20.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Equation
y =[T I −I
] ae+
e−
where,
• T = (t1; t2 ... ; tn) ∈ Rdxn (d � n) is the target templateset, containing n target templates such that each templateti ∈ Rd .
• a = (a1; a2 ... ; an)T ∈ Rn is called a target coefficientvector and
• e+ ∈ Rd and e− ∈ Rd are called a positive and negativetrivial template coefficient vectors.
• A tracking result y ∈ Rd approximately lies in the linearspan of T.
![Page 21: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/21.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Underdetermined system
• No unique solution
• For a good target candidate, there are only a limitednumber of nonzero coefficients in e+ and e−
min ‖ Ax − y ‖22 +λ ‖ c ‖1
where,
• A = [T, I,-I] ∈ Rd×(n+2d)
• x = [a; e+ ; e−] ∈ R(n+2d) is a non-negative coefficientvector.
![Page 22: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/22.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Template Update
• Template replacement : If the tracking result y is notsimilar to the current template set T, it will replace theleast important template in T.
• Template updating: It is initialized to have the medianweight of the current templates.
• Weight update: The weight of each template increaseswhen the appearance of the tracking result and template isclose enough and decreases otherwise.
![Page 23: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/23.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Dimensionality Reduction
• l1 tracker
min ‖ x ‖21 s.t. ‖ Ax − y ‖2
2≤ ε
• Dimensionality reduction if the measurement matrix φfollows the Restricted Isometry Property (RIP) 1, then asparse signal x can be recovered from
min ‖ x ‖21 .s.t. ‖ φAx − φy ‖2≤ ε, x ≥ 0.
where, φ ∈ Rd0xd d0 � d and φj ∼ N(0, 1)
1E. Cand‘es, J. Romberg, and T. Tao, “Stable signal recovery fromincomplete and inaccurate measurements,” Communications on Pure andApplied Mathematics, vol. 59, pp. 1207–1223, 2006.
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VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
OMP
Figure 13: l1 norm minimization
![Page 25: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/25.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
OMP
Figure 14: Customize OMP algorithm [1]
![Page 26: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/26.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
Conclusion
• The RTCST tracker achieves higher accuracy than existingtracking algorithms, i.e., the PF tracker.
• Dimension reduction methods and a customized OMPalgorithm enable the CS-based trackers to run real-time.
![Page 27: Real Time Visual Tracking](https://reader033.fdocuments.net/reader033/viewer/2022050919/54812056b37959c22b8b469f/html5/thumbnails/27.jpg)
VisualTracking
JainishaSankhavara
(201311002)Falak Shah
(201311024)
Introduction
Particle Filter
Definition
Particle FilterVisualisation
Particle FilterEquations
TemplateDictionary
Equation
Underdeterminedsystem
TemplateUpdate
Real-TimeCompressiveSensingTracking(RTCST)
DimensionalityReduction
OMP
Conclusion
References
References
• Hanxi Li; Chunhua Shen; Qinfeng Shi, ”Real-time visual tracking using compressive sensing,”Computer Vision and Pattern Recognition (CVPR), 2011 IEEE Conference on , vol., no.,pp.1305,1312, 20-25 June 2011
• Xue Mei; Haibin Ling, ”Robust visual tracking using l1 minimization,” Computer Vision, 2009 IEEE12th International Conference on , vol., no., pp.1436,1443, Sept. 29 2009-Oct. 2 2009
• D. Donoho, “For Most Large Underdetermined Systems of Linear Equations the Minimal l1-NormSolution Is Also the Sparsest Solution,” Comm. Pure and Applied Math., vol. 59, no. 6, pp. 797-829, 2006.
• E. Cande‘s and T. Tao, “Near-Optimal Signal Recovery from Random Projections: UniversalEncoding Strategies?” IEEE Trans. Information Theory, vol. 52, no. 12, pp. 5406-5425, 2006.
• Wright, J.; Yang, A.Y.; Ganesh, A.; Sastry, S.S.; Yi Ma, ”Robust Face Recognition via SparseRepresentation,” Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.31, no.2,pp.210,227, Feb. 2009
• E. Cand‘es, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccuratemeasurements,” Communications on Pure and Applied Mathematics, vol. 59, pp. 1207–1223, 2006.
• A. Yilmaz, O. Javed, and M. Shah. ‘Object tracking: A survey”. ACM Comput. Surv. 38(4), 2006.