Learning Based Hierarchical Vessel Segmentation Presenter: Richard Socher www.socher.org Authors: Richard Socher Adrian Barbu Dorin Comaniciu TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAA

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

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

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

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:

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,…

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

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

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

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

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

Results

Results on unseen data of very low quality

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

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

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: www.socher.org

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

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