Head Pose Estimation Via Probabilistic High-Dimensional Regression - - PowerPoint PPT Presentation

Head Pose Estimation Via Probabilistic High-Dimensional Regression

Vincent Drouard 1 Sil` eye Ba 1 Georgios Evangelidis 1 Antoine Deleforge 2 Radu Horaud 1

1Team Perception - Inria Grenoble Rhˆ

• ne-Alpes, France

2Friedrich-Alexander-Universit¨

at, Erlangen, Germany

September 28, 2015, Qu´ ebec, Canada

Work supported by EU-FP7 ERC Advanced Grant VHIA (#340113) and STREP project EARS (#609645)

Introduction Head Pose Estimation Experimentations Conclusion

Motivation

Visual cue in Human-Robot and Human-Human Interaction

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Introduction Head Pose Estimation Experimentations Conclusion

Problem definition

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Introduction Head Pose Estimation Experimentations Conclusion

Problem formulation

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Introduction Head Pose Estimation Experimentations Conclusion

Method Pipeline

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Introduction Head Pose Estimation Experimentations Conclusion

High-Dimensional Regression

Problems:

• A lot of parameters to estimate
• y → x might be non linear
• y and x are obtained by measurement → might be noisy

Standard solution

• Step 1: dimension reduction, y → x′
• Step 2: regression, x′ → x
• Head-pose information may be lost when dimensionality

reduction is performed

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Introduction Head Pose Estimation Experimentations Conclusion

High-Dimensional Regression - Solution

• Inverse problem (training): easier to solve
• Forward solution (testing): closed-form

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Introduction Head Pose Estimation Experimentations Conclusion

Training: Inverse Regression (I)

y =

K

• k=1

I{Z=k} (Akx + bk + ek)

• Ak, bk: parameters of the kth affine transformation
• ek: zero-mean noise, ek ∼ N (0, Σk)
• I: indicator function
• Z: discrete latent variable selecting the affine transformation

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Introduction Head Pose Estimation Experimentations Conclusion

Training: Inverse Regression (II)

• Probabilistic model

P (y|x, Z = k) = N (y; Akx + bk, Σk) P (x|Z = k) = N (x; ck, Γk) P (Z = k) = πk

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Introduction Head Pose Estimation Experimentations Conclusion

Training: Inverse Regression (III)

• Inverse Regression

P (y|x; θ) =

K

• k=1

πkN (x; ck, Γk) K

j=1 πjN (x; cj, Γj)

• ρk→Proportion

N (y; Akx + bk, Σk)

• θ = {Ak, bk, Σk, ck, Γk, πk}K

k=1

• Estimated using EM algorithm

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Introduction Head Pose Estimation Experimentations Conclusion

Forward Testing

Bayesian inversion of the model P (x|y; θ∗) =

K

• k=1

π∗

kN (y; c∗ k, Γ∗ k)

K

j=1 π∗ jN

• y; c∗

j, Γ∗ j

• ρ∗

k→Proportion

N (A∗

ky + b∗ k, Σ∗ k)

• θ∗ = {A∗

k, b∗ k, Σ∗ k, c∗ k, Γ∗ k, π∗ k}K k=1 obtained analytically using θ

• ˆ

x = E (x|y; θ∗) =

K

• k=1

ρ∗

k (A∗ ky + b∗ k)

• Fast evaluation

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Introduction Head Pose Estimation Experimentations Conclusion

Summary of the model

• Closed-form solution for estimating inverse regression

parameters

• high dimension = 1500 and Low dimension = 3 (or 5) (K=50)
• Proposed inverse training: 375K parameters
• Standard training: 56M parameters
• Forward testing parameters obtained in closed-form from

the inverse regression parameters

• Estimation (ˆ

x) is efficient (few computations)

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Introduction Head Pose Estimation Experimentations Conclusion

Datasets

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Introduction Head Pose Estimation Experimentations Conclusion

Results with face annotations

Biwi-Kinect Head Pose Method yaw pitch roll Fanelli et al. (use 3D information) 3.5 ± 5.8 3.8 ± 6.5 5.4 ± 6.0 Wang et al. (use 2D-3D information) 8.8 ± 14.3 8.5 ± 11.1 7.4 ± 10.8 Our method (use 2D information) 4.9 ± 4.1 5.9 ± 4.8 4.7 ± 4.6

Mean Absolute Error (MAE) in degrees for head pose estimation

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Introduction Head Pose Estimation Experimentations Conclusion

Results with face detection

Prima Head Pose Method yaw pitch Gourier et al. 10.3 15.9 Ricci & Odobez 9.1 10.5 Our method 8.7 8.85 Mean Absolute Error (MAE) in degrees for head pose estimation

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Introduction Head Pose Estimation Experimentations Conclusion

Examples of head pose estimation

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Introduction Head Pose Estimation Experimentations Conclusion

Examples of head pose estimation

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Introduction Head Pose Estimation Experimentations Conclusion

Examples of head pose estimation

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Introduction Head Pose Estimation Experimentations Conclusion

Conclusion

Probabilistic piece-wise linear regression for high dimensional data:

• Efficient and accurate solution based on inverse training
• Head pose estimation in the presence of face localization

errors Next step:

• Apply to other problems: articulated motion capture,

human-body pose, etc

• Extend the model to track head pose

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Introduction Head Pose Estimation Experimentations Conclusion

Thank you for your attention

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