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

Motivation

Even more difficult?

Outline Shape Related Shape Prior Work Segmentation Alignment Applications and Results Conclusion and Outlook

Outline Shape Related Shape Prior Work Segmentation Alignment Applications and Results Conclusion and Outlook

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]

Mumford-Shah Segmentation 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 and Shah 1988]

Active Contours without Edges • Special case of the Mumford-Shah model for Segmentation proposed by Chan and Vese: f … input image c 1 , c 2 … mean values of the fore- and background intensities • Segmentation not bound to image gradients. [Chan and Vese 2001]

Diffusion Snakes • Mumford-Shah segmentation • Incorporate statistical shape knowledge [Cremers et al. 2002]

Outline Shape Related Shape Prior Work Segmentation Alignment Applications and Results Conclusion and Outlook

Variational Segmentation & Shape Information • Reconsider Chan-Vese Segmentation Model: • Restated as TV functional: [Chan et al. 2006]

Shape Prior Segmentation • Data-Fidelity Term: Shape Force • Regularization: Weighted TV-norm s … Shape representation g … Edges of input image u … Segmentation result. u … Segmentation result. • Signed distance map as shape representation.

Shape Prior Transformation • Transformation parameters Á = {t,R,S} t … Translation R … Rotation S … Scale • Parameter ¸ controls influence of the shape force.

Influence of ¸ ¸ = 0.20 ¸ = 0.15 ¸ = 0.10 ¸ = 0.05 ¸ = 0.01

Solving the Shape Prior Segmentation Model Updating Update transformation segmentation u parameters Á (t,R,S) Iterate

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]

Primal-Dual update scheme 1. Primal update: Gradient descend Iterate 2. Dual update: Gradient ascend + reprojection 3. Iterate until convergence.

Primal-Dual Gap

Outline Shape Related Shape Prior Work Segmentation Alignment Applications and Results Conclusion and Outlook

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]

Which position to take? • Depending on the Primal energy. E Primal = -530 E Primal = -430 E Primal = -338

Outline Related Shape Prior Shape Work Segmentation Alignment Applications and Results Conclusion and Outlook

Evaluation on hand-labeled data Thresholding pure GAC Shape Prior

User Interaction + Shape Position Optimization

Low contrast image Thresholding pure GAC Shape Prior

Occlusion

Tracking

Performance • Use benefit of parallelization with CUDA. (Nvidia GTX 280) • Shape Prior segmentation (using 200 iterations): Image Size Shape Prior Size Performance 416x800 160x160 115 fps 2267x1558 600x600 20 fps • Shape Alignment (optimizing Á (t,R,S)): Image Size Shape Prior Size Performance 416x800 160x160 25 fps 2267x1558 600x600 5 fps

Outline Related Shape Prior Shape Work Segmentation Alignment Applications and Results Conclusion and Outlook

Conclusion Shape Alignment Segmentation Tracking

Outlook • Shape space instead of single prior. • Use multiple shapes simultaneously. • Optimizing elastic instead of rigid shape transformation. • Use anisotropic regularization. • Extend to 3D.

Thank you very much for your attention! Manuel Werlberger, Thomas Pock, Markus Unger, and Horst Bischof