1. Detecting the Inferior Thoracic Aperture using Statistical Shape Models Pahal Dalal Department of Computer Science & Engineering, University of South Carolina

2. Outline Introduction –What is the Inferior Thoracic Aperture (ITA)? –Why segment the ITA? –Why is segmenting the ITA difficult? Construction of Shape Model Detecting the ITA Conclusion

3. Inferior Thoracic Aperture 3D closed contour. Near the periphery of human diaphragm. Tissue outlining the bottom of rib cage.

4. Relation to Diaphragm Diaphragm hangs off the ITA. Diaphragm related to normal pulmonary function. Extracting ITA can help extract diaphragm.

5. Difficulty Diaphragm hangs off the ITA. Difference between ITA and boundary of diaphragm difficult to find. CT images very fuzzy in certain parts.

6. Outline Introduction –What is the Inferior Thoracic Aperture (ITA)? –Why segment the ITA? –Why is segmenting the ITA difficult? Construction of Shape Model Detecting the ITA Conclusion

7. Partitioning ITA shape Two parts A and C. A >> easy to extract. C >> difficult to extract. B >> additional anatomical points on/near ITA.

8. Additional points considered (1,2) ends of Xiphoid process. (3,4,5,6,7,8) processes from Vertebra. (9) front of 1 st lumbar. (10,11,12) front and left/right process of vertebra TX. (13,14,15,16) endpoints of curves in A.

9. Identifying Landmarks B >> Known corresponding landmarks. A, C >> Landmark sliding approach. Wang, S., Kubota, T., Richardson, T.: Shape correspondence through landmark sliding. In: CVPR. (2004) I–143–150

10. Identifying Landmarks Initial rough correspondence –Equal distance sampling of A and C. Refinement –Thin Plate Spline Bending Energy. –Landmark Sliding. –Strict partitioning enforced.

11. Constructing PDM Set of training shapes. Find corresponding landmarks on each. Mean shape >> m. Co-variance >> S. Shape model >> (m, S).

12. Outline Introduction –What is the Inferior Thoracic Aperture (ITA)? –Why segment the ITA? –Why is segmenting the ITA difficult? Construction of Shape Model Detecting the ITA Conclusion

13. Detecting the ITA v is the set of landmarks along shape to be found. m = [ m P m Q ] v = [ v P v Q ] P >> landmarks along A and B. Q >> landmarks along C.

14. Detecting landmarks along A, B B >> anatomic landmarks, easy to extract. A >> easy to extract. Landmark sliding approach. m P used as template landmarks. Gives v P.

15. Mahalanobis distance D = (v - m) T S -1 (v - m) D = (v Q m Q )S 4 (v Q - m Q ) +2(v P - m P ) T S 2 (v Q - m Q ) + k Partial derivative = 0 v Q = m Q - S 4 -1 S 2 (v P - m P ) Interpolate landmarks along A and C to obtain complete shape.

16. Experiments 14 shapes. Leave one out. e 1 = average distance between predicted shape and truth. e 2 = average distance between predicted landmark and truth landmark.

17. Results Ground Truth and Detected ITA

18. Results Better than direct interpolation.

19. Conclusion A new method to detect the Inferior Thoracic Aperture. Better performance than direct interpolation.

20. Questions?