1. Learning Based Hierarchical Vessel Segmentation
Presenter:
Richard Socher
Authors:
Richard Socher
Adrian Barbu
Dorin Comaniciu
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2. Overview Background Hierarchical Vessel Segmentation
Machine Learning
Marginal Space Learning
Probabilistic Boosting Trees
Visual Features
Haar and Steerable Features
Hierarchical Vessel Segmentation
Results and Future Work

3. Marginal Space Learning
General Framework which tackles problem of high dimensional parameter spaces
Posterior distribution of the parameters lies in a small region of the n-dimensional parameter space
Idea: Start in small marginal spaces and increase dimensionality of the search space
Fewer parameters have to be examined
Large speed-ups

4. Marginal Spaces of Vessels
Marginal Space 1: Gradient Candidates
Marginal Space 2: Cross Segments
Marginal Space 3: Quadrilaterals

5. Machine Learning: Probabilistic Boosting Trees
Each node is a strong boosting classifier:
Transform into probability:
During training, samples are divided into subnodes
During testing, the top recursively collects the probabilities:

6. Visual Features Sample features and use them as input to classifier
Haar Features
Thousands of cheap features through integral image:
Steerable Features
Useful for finding the orientation and scale of an object, given its location
Intensity, gradient,…

7. Hierarchical Vessel Segmentation
1. Learning Based Edge Detection
2. Cross-Segment Detection: Width
3. Quadrilateral Detection: Length
4. Dynamic Programming

8. Level 1 – Learning Based Edge Detection
Goal: Rough estimation of vessel borders
Candidates are pixels with large gradient
Annotation used to create positive and negative samples for the PBT learning
Fast and little limitation for higher levels
Samples with gradient direction (gy,-gx)
Original Frame Large Gradients

9. Level 2: Cross Segment Detection
Goal: cross segments, loosely corresponding to width of vessel
Candidates are created by going in opposite gradient direction from all locations of Level 1, until another point from Level 1 is hit
Segments and their Haar Features are given to a PBT

10. Level 3: Quadrilateral Detection
Goal: find pairs of cross segments that, if connected as a quadrilateral, capture an area of the vessel.
The probability of such a quadrilateral shows how likely two cross segments are connected in the complete vessel.
Steerable Features are sampled and used for training a PBT:
Gradient, grey value; probability map of Level 1, differences in grey value
Coordinate System for steerable Features Positive and Negative Training Samples

11. Level 4: Dynamic Programming
Goal: Final vessel segmentation, the most likely connection of cross segments
Formulation as lowest cost path in weighted graph G = (V,E) V = cross-segments, E = edges between segments, if they form a quadrilateral Weight(e(v1,v2)) = log((1-p)/p) p = P(Quadrialateral(v1,v2))
Solved by dynamic programming

12. Results

13. Results on unseen data of very low quality

14. Results on Testing Set Training on 134 frames Testing on 64 frames
Detection Rate: 90.1% False Alarm 29%
Example of distracting side vessel

15. Future Work
Extension to full vessel tree through a junction point detector

16. Conclusion Hierarchical learning based vessel segmentation method
highly driven by data: applicable to any tube like structure
generalizes well to lower quality X-ray images.
New representation of a vessel consisting of three marginal spaces: border points, vessel width and vessel pieces (quadrilaterals)
Novel use of MSL and steerable features in segmentation of objects without a mean shape.
Results for single vessel segmentation are preliminary but promising
Work in progress: time consistency, full tree, …
More details in my thesis:

17. Thank you! Questions? 1. Learning Based Edge Detection
2. Cross-Segment Detection: Width
3. Quadrilateral Detection: Length
4. Dynamic Programming

18. References
Friedman, J. H., Hastie, T. and Tibshirani, R., "Additive Logistic Regression: a Statistical View of Boosting." (Aug. 1998)
A. Torralba, K. P. Murphy and W. T. Freeman. (2004). "Sharing features: efficient boosting procedures for multiclass object detection". Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). Pp
T. Zhang, "Convex Risk Minimization", Annals of Statistics, 2004.
Zhuowen Tu, “Probabilistic boosting-tree: Learning discriminative models for classification, recognition, and clustering.,” in ICCV, 2005, pp. 1589–1596.
Y. Zheng, A. Barbu, B. Georgescu, M. Scheuering, and D. Comaniciu, “Fast automatic heart chamber segmentation from 3d ct data using marginal space learning and steerable features,” in IEEE Int’l Conf. Computer Vision (ICCV’07), Rio de Janeiro, Brazil, 2007.
P. Viola and M. Jones, “Rapid object detection using a boosted cascade of simple features,” 2001.