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Lecture 15-16
Pose Estimation – Gaussian
Process
Tae-Kyun Kim
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MS KINECT
http://www.youtube.com/watch?v=p2qlHoxPioM
The KINECT body pose estimation is achieved by
randomised regression forest techniques.
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We learn pose estimation as a regression
problem, and Gaussian process as a cutting edge
regression method.
We see it through the case study (slide credits to):
Semi-supervised Multi-valued Regression,
Navaratnam, Fitzgibbon, Cipolla, ICCV07,
where practical challenges addressed are
1)multi-valued regression and 2)sparsity of data.
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A mapping function is learnt from the input image I to the pose vector θ , which
is taken as a continuous variable.
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Given an image (top left) , e.g. a silhouette (top right) is obtained by background
subtraction techniques (http://en.wikipedia.org/wiki/Background_subtraction).
The estimated 3d pose is shown at two camera angels (bottom left and right).
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We attempt to map 2D image space to 3D pose space.
There is inherent ambiguity in pose estimation (as an example in the above).
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Eye tracking can be tackled as a regression problem, where
the input is an image I and the output is a eye location.
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Typical image processing steps:
Given an image, a silhouette is segmented.
A shape descriptor is applied to the silhouette to yield a finite
dimensional vector. (Belongie and Malik, Matching with Shape Contexts, 2000)
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The output is a vector of m joint angles.
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Gaussian Process
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Review of Gaussian density estimation
(lecture 1,2)
i.i.d.
(independent
identical
distributed)
We want to find the Gaussian parameters from the given data.
The problem is to find the parameters by maximising the
posterior probability
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𝑝
𝐱
𝜇,
𝜎
𝑝
𝜇,
𝜎
𝑝 𝜇, 𝜎 2 𝐱 =
𝑝(𝐱)
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Review of Gaussian density estimation
(lecture 1,2)
2
2
𝑝
𝐱
𝜇,
𝜎
𝑝
𝜇,
𝜎
𝑝 𝜇, 𝜎 2 𝐱 =
𝑝(𝐱)
We do not have priors on the parameters and data, thus we
maximise the (log) likelihood function instead.
Maximum Likelihood (ML) vs Maximum A Posterior (MAP)
solutions:
P(X|Y)P(Y)
P(X|Y)
(e.g. Gaussian Process)
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Review of polynomial curve fitting
(lecture 1,2)
We want to fit a polynomial curve to given data pairs (x,t).
= 𝐰𝑇 𝐱
where
𝑤0
𝐰= 𝑤1
⋮
1
𝑥
𝐱= 𝑥 2
⋮
The objective ftn to minimise is
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Gaussian Processes
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𝐲~𝑁(𝐲|𝟎, 𝐊)
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𝐲(𝐱)
𝐱
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Gaussian Processes for Regression
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𝑡 =𝑦 𝑥 +𝜖
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𝑁×𝑁 𝑁×1
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Gaussian Process Matlab Toolbox
http://www.lce.hut.fi/research/mm/gpstuff/i
nstall.shtml
(try demo_regression_robust.m,
demo_regression1.m)
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Learning Hyperparameters
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Automatic Relevance Determination
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Back to the pose estimation
problem
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• It’ll never work…
–
is multivalued
–
and
live in high dimensions
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GMM : Gaussian Mixture Model
GPLVM : Gaussian Process Latent Variable Model
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𝑝 𝜃𝑧 =
𝑝(𝜃, 𝑧)
𝑝(𝑧)
𝑝 𝑧
= ∫ 𝑝 𝜃, 𝑧 𝑑𝜃
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t: a continuous
latent variable
𝑝 𝑧, 𝜃 = ∫ 𝑝 𝑧, 𝜃 𝑡 𝑝 𝑡 𝑑𝑡
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Real-Time Human Pose Recognition in Parts
from Single Depth Images (J. Shotton et al, 2011)
• Key features
– Depth image as input
– Real-time by Random Forest, and Part-based
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Progressive Search Space Reduction for
Human Pose Estimation (Ferrari et al, 2008)
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