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Detecting the Inferior Thoracic Aperture using Statistical Shape Models Pahal Dalal Department of Computer Science & Engineering, University of South Carolina
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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
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Inferior Thoracic Aperture 3D closed contour. Near the periphery of human diaphragm. Tissue outlining the bottom of rib cage.
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Relation to Diaphragm Diaphragm hangs off the ITA. Diaphragm related to normal pulmonary function. Extracting ITA can help extract diaphragm.
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Difficulty Diaphragm hangs off the ITA. Difference between ITA and boundary of diaphragm difficult to find. CT images very fuzzy in certain parts.
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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
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Partitioning ITA shape Two parts A and C. A >> easy to extract. C >> difficult to extract. B >> additional anatomical points on/near ITA.
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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.
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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
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Identifying Landmarks Initial rough correspondence –Equal distance sampling of A and C. Refinement –Thin Plate Spline Bending Energy. –Landmark Sliding. –Strict partitioning enforced.
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Constructing PDM Set of training shapes. Find corresponding landmarks on each. Mean shape >> m. Co-variance >> S. Shape model >> (m, S).
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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
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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.
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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.
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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.
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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.
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Results Ground Truth and Detected ITA
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Results Better than direct interpolation.
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Conclusion A new method to detect the Inferior Thoracic Aperture. Better performance than direct interpolation.
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Questions?
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