evidential modeling for pose estimation fabio cuzzolin, ruggero frezza computer science department...
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Evidential modeling for Evidential modeling for pose estimationpose estimation
Fabio Cuzzolin, Ruggero Frezza
Computer Science Department
UCLA
Myself
Master’s thesis on gesturegesture recognitionrecognition
at the University of Padova Ph.D. thesis on the theory of theory of
evidenceevidence Post-doc in Milan with the Image and
Sound Processing group Post-doc at UCLA in the Vision Lab
Px
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F (s)x
F (s)y
y
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My past work…
geometric approachgeometric approach to the theory of belief functions space of belief functions geometry of Dempster’s rule
.. again ..
algebra of compatible frames linear independence on lattices action recognition and object
tracking metrics on the space of dynamical
models
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… and today’s talk
the pose estimation problemthe pose estimation problem
model-free pose estimationmodel-free pose estimation
evidential modelevidential model
experimental resultsexperimental results
Pose estimation estimating the “posepose” (internal configuration)
of a moving body from the available images
salient image measurements: featuresfeatures
Qtq k ˆt=0
t=T
Model-based estimation if you have an a-priori modela-priori model of the object .. .. you can exploit it to help (or drive) the
estimation
example: kinematic model
Model-free estimation
if you do not have any information about the body..
the only way to do inference is to learn a maplearn a map between features and
poses directly from the data
this can be done in a training stagetraining stage
Collecting training data motion capture system
3D locations of markers = pose
Training data when the object performs some “significant”
movements in front of the camera … … a finite collection of configuration values
are provided by the motion capture system
… while a sequence of features is computed from the image(s)
q q
y y
Q~
1
1
T
T
Learning feature-pose maps
Hidden Markov modelsHidden Markov models provide a way to build feature-pose maps from the training data
a Gaussian density for each state is set up on the feature space -> approximate feature spaceapproximate feature space
mapmap between each region and the set of training poses qk with feature value yk inside it
Evidential model
approximate feature spaces ..
.. and approximate parameter space ..
.. form a family of compatible family of compatible frames: the evidential modelframes: the evidential model
Estimation
these belief functions are projected onto the approximate parameter space ..
.. and combined through Dempster’s rule
a point-wise estimate of the pose is obtained by probabilistic approximation
new features are represented as belief functions ..
Human body tracking
two experiments, two views
four markers on the right arm
six markers on both legs
Feature extraction
three steps: original image, color segmentation, bounding box
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Performances comparison of three models: left view
only, right view only, both views
pose estimation yielded by the overall model
estimate associated with the “right” model
“left” model
ground truth
Estimation errors Euclidean distance between real and
predicted marker position
marker 4
3cm
marker 2
8cm
Visual estimate
Tk
kIkpI..1
)()(ˆˆ compares the actual image
with the weighted sum of the training images
Conclusions pose estimation of unknown objects is a
difficult task a bottom-up model has to be built from the
data in a training session the DS framework allows to formalize the
idea of feature-pose maps in a natural way through the notion of compatible frames
Dempster’s combination provides a method to integrate features to increase robustness