Detecting the Inferior Thoracic Aperture using Statistical Shape

Models

Pahal DalalDepartment of Computer Science &

Engineering,University of South Carolina

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

Inferior Thoracic Aperture

• 3D closed contour.• Near the periphery of

human diaphragm.• Tissue outlining the

bottom of rib cage.

Relation to Diaphragm

• Diaphragm hangs off the ITA.

• Diaphragm related to normal pulmonary function.

• Extracting ITA can help extract diaphragm.

Difficulty

• Diaphragm hangs off the ITA.

• Difference between ITA and boundary of diaphragm difficult to find.

• CT images very fuzzy in certain parts.

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

Partitioning ITA shape

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

Additional points considered

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

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

Identifying Landmarks

• Initial rough correspondence– Equal distance sampling of A and C.

• Refinement– Thin Plate Spline Bending Energy.– Landmark Sliding.– Strict partitioning enforced.

Constructing PDM

• Set of training shapes.

• Find corresponding landmarks on each.

• Mean shape >> m.

• Co-variance >> S.

• Shape model >> (m, S).

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

Detecting the ITA

• v is the set of landmarks along shape to be found.

• m = [ mP mQ ]

• v = [ vP vQ ]

• P >> landmarks along A and B.

• Q >> landmarks along C.

Detecting landmarks along A, B

• B >> anatomic landmarks, easy to extract.

• A >> easy to extract.• Landmark sliding approach.

• mP used as template landmarks.

• Gives vP.

Mahalanobis distance

• D = (v - m)TS-1(v - m)

• D = (vQ mQ)S4(vQ- mQ)

+2(vP - mP)TS2(vQ- mQ) + k

• Partial derivative = 0

• vQ = mQ - S4-1 S2(vP - mP)

• Interpolate landmarks along A and C to obtain complete shape.

Experiments

• 14 shapes.

• Leave one out.

• e1 = average distance between predicted shape and truth.

• e2 = average distance between predicted landmark and truth landmark.

Results

Ground Truth and Detected ITA

Results

• Better than direct interpolation.

Conclusion

• A new method to detect the Inferior Thoracic Aperture.

• Better performance than direct interpolation.

Questions?