real time visual tracking

VisualTracking

JainishaSankhavara

(201311002)Falak Shah

(201311024)

Introduction

Particle Filter

Definition

Particle FilterVisualisation

Particle FilterEquations

TemplateDictionary

Equation

Underdeterminedsystem

TemplateUpdate

Real-TimeCompressiveSensingTracking(RTCST)

DimensionalityReduction

Conclusion

References

Robust Visual Tracking Using CompressedSensing

Jainisha Sankhavara (201311002)Falak Shah (201311024)

MTech, DA-IICT

April 16, 2014

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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.

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Particle Filter Visualisation

Figure 1: Plane moving- Position unknown 1

1Andreas Svensson, Ph.D Student, Uppsala University

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 2: Available data

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 3: Initial distribution of particles

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 4: Observation Likelihood

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 5: Resampling Step

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 6: Posteriori estimate

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 7: Observation likelihood: step 2

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 8: Resample: step 2

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 9: Particles converge very close to object

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Particle Filter visulisation

Figure 10: Issues

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 11: Back to tracking

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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.

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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

p(zt |x it)p(x it |x it−1)

q(xt |x1:t−1, z1:t)

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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.

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Equation

y =[T I −I

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.

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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.

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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.

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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.

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 13: l1 norm minimization

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

References

Figure 14: Customize OMP algorithm [1]

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

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.

VisualTracking

JainishaSankhavara

(201311024)

Introduction

Particle Filter

Definition

TemplateDictionary

Equation

TemplateUpdate

Conclusion

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.

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