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A Variational Model for Interactive Shape Prior Segmentation and - - PowerPoint PPT Presentation
A Variational Model for Interactive Shape Prior Segmentation and - - PowerPoint PPT Presentation
A Variational Model for Interactive Shape Prior Segmentation and Real-Time Tracking Manuel Werlberger, Thomas Pock, Markus Unger, and Horst Bischof 05/26/2009 Institute for Computer Graphics and Vision Graz University of Technology Motivation
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Motivation
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Even more difficult?
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Outline
Shape Alignment Related Work Shape Prior Segmentation Conclusion and Outlook Applications and Results
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Outline
Shape Alignment Related Work Shape Prior Segmentation Conclusion and Outlook Applications and Results
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Geodesic Active Contour Model
- Based on Snake Model (Kass et al.)
- Minimizing weighted length:
|C| … Euclidean length of curve C g … Edge image: g 2 (0,1]
- Variational formulation – weighted TV:
[Caselles 1997; Bresson 2005; Leung 2005]
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f … observed image u … piecewise smooth approximation ¡ … edges in u
- Does not pick up textured objects.
- Only objects featuring a homogeneous region inside the
boundary ¡.
Mumford-Shah Segmentation
[Mumford and Shah 1988]
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Active Contours without Edges
- Special case of the Mumford-Shah model for Segmentation
proposed by Chan and Vese: f … input image c1, c2 … mean values of the fore- and background intensities
- Segmentation not bound to image gradients.
[Chan and Vese 2001]
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Diffusion Snakes
- Mumford-Shah segmentation
- Incorporate statistical shape knowledge
[Cremers et al. 2002]
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Outline
Shape Alignment Related Work Shape Prior Segmentation Conclusion and Outlook Applications and Results
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Variational Segmentation & Shape Information
- Reconsider Chan-Vese Segmentation Model:
- Restated as TV functional:
[Chan et al. 2006]
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- Data-Fidelity Term: Shape Force
s … Shape representation u … Segmentation result.
Shape Prior Segmentation
- Signed distance map as shape representation.
- Regularization: Weighted TV-norm
g … Edges of input image u … Segmentation result.
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Shape Prior Transformation
- Transformation parameters Á = {t,R,S}
t … Translation R … Rotation S … Scale
- Parameter ¸ controls influence of the shape force.
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Influence of ¸
¸ = 0.15 ¸ = 0.10 ¸ = 0.05 ¸ = 0.01 ¸ = 0.20
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Solving the Shape Prior Segmentation Model
Updating segmentation u Update transformation parameters Á(t,R,S) Iterate
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Solving the Shape Prior Segmentation Model
- Dual formulation of weighted TV-norm:
- Represents a typical saddle-point problem.
[Arrow, Hurwicz 1958; Zhu and Chan 2008]
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Primal-Dual update scheme
- 1. Primal update:
- 2. Dual update:
- 3. Iterate until convergence.
Gradient descend Gradient ascend + reprojection Iterate
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Primal-Dual Gap
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Outline
Shape Alignment Related Work Shape Prior Segmentation Conclusion and Outlook Applications and Results
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Optimizing Shape Transformation
- Transformation parameters Á = {t,R,S}
t … Translation R … Rotation S … Scale
- Brute force search:
– simple, but computationally costly. – Performance ok for local optimization. – Not reasonable for a global optimization: The complete subspace Ω has to be sampled.
[Cremers 2008]
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Which position to take?
- Depending on the Primal energy.
EPrimal = -530 EPrimal = -430 EPrimal = -338
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Outline
Shape Alignment Related Work Shape Prior Segmentation Conclusion and Outlook Applications and Results
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Evaluation on hand-labeled data
Thresholding pure GAC Shape Prior
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User Interaction + Shape Position Optimization
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Low contrast image
Thresholding pure GAC Shape Prior
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Occlusion
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Tracking
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Performance
- Use benefit of parallelization with CUDA. (Nvidia GTX 280)
- Shape Prior segmentation (using 200 iterations):
- Shape Alignment (optimizing Á(t,R,S)):
Image Size Shape Prior Size Performance 416x800 160x160 115 fps 2267x1558 600x600 20 fps Image Size Shape Prior Size Performance 416x800 160x160 25 fps 2267x1558 600x600 5 fps
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Outline
Shape Alignment Related Work Shape Prior Segmentation Conclusion and Outlook Applications and Results
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Conclusion
Segmentation Shape Alignment Tracking
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Outlook
- Shape space instead of single prior.
- Use multiple shapes simultaneously.
- Optimizing elastic instead of rigid shape transformation.
- Use anisotropic regularization.
- Extend to 3D.
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