Wei Zeng Joseph Marino Xianfeng Gu Arie Kaufman Stony Brook University, New York, USA The MICCAI 2010 Workshop on Virtual Colonoscopy and Abdominal Imaging 2010-09-20 Conformal Geometry Based Supine and Prone Colon Registration
Jan 11, 2016
Wei Zeng Joseph Marino Xianfeng Gu Arie Kaufman
Stony Brook University, New York, USA
The MICCAI 2010 Workshop on Virtual Colonoscopy and Abdominal Imaging
2010-09-20
Conformal Geometry Based Supine and Prone Colon Registration
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• Problem - Supine and Prone Colon Registration– Challenge: Non-rigid deformation and substantial distortion,
due to position shifting
• Solution - Conformal Mapping Based Registration– Formulation: Matching between 3D topological cylinders– Key: 3D => 2D matching problem– Goal: One-to-one map
• Contribution - Diffeomorphism between Surfaces– Advantage: Guarantee one-to-one map of whole surface– Efficiency: Linear time complexity
Overview
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Algorithm
Anatomical Landmark Extraction
Constraints: FeatureCorrespondence of (S1, S2)
Harmonic Energy
Linear System Optimization
Conformal Mapping(φ1, φ2)
Supine & Prone ColonSurfaces (S1, S2)
Internal Feature Detection & Matching
Harmonic Map Registration
Holomorphic Differentials
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• Idea: Extract anatomical landmarks using existing methods– Taenia coli – Slicing the colon surface open– Flexures – Dividing the colon to 5 segments
Anatomical Landmarks Extraction
Taenia Coli Flexures
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• Idea: Solve harmonic functions with Dirichlet boundary conditions.– Colon segment: topological cylinder, denoted as triangular mesh
Conformal Map - Holomorphic Differentials
3D SurfaceNon-rigid Deformation
2D Conformal MapDifferent Conformal Modules
Texture MapAngle Preserving
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• Idea: Perform detection and matching on conformal mapping images color encoded by mean curvature of 3D surface.– Method: 1) Graph Cut Segmentation and 2) Graph Matching methods
Internal Feature Detection and Matching
2D Conformal MapMean Curvature
Segmentation Haustral Folds
ExtractionFeature Points
MatchingFeature Correspondence
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Conformal Map - Matching Framework
3D Surface
2D Conformal Map
3D Surface
2D Conformal Map
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• Idea: Compute harmonic map between two 2D maps with feature correspondence constraints– One-to-one mapping– Linear computational complexity
Conformal Map Based Surface Matching
Supine =>Prone Deformed Supine Registration
Polyp on Prone
Polyp on Supine
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• Data– National Institute of Biomedical Imaging and Bioengineering (NIBIB) Image and
Clinical Data Repository, provided by the National Institute of Health (NIH) • Registration Accuracy
– Averaged distance error in R3 (mm)– Better than existing centerline-based methods, similar to [4]
• Advantage: One-to-one surface registration
Experiments
Table 1. Comparison of average millimeter distance error between existing methods.
Methods Distance Error
Our Conformal Geometry Based Method 7.85mm
Haustral fold registration [4] 5.03 mm
Centerline registration + statistical analysis [12] 12.66mm
Linear stretching / shrinking of centerline [1] 13.20mm
Centerline feature matching + lumen deformation [14] 13.77mm
Centerline point correlation [3] 20.00mm
Taenia coli correlation [10] 23.33mm
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Conclusion
• Conformal Geometry for Supine-Prone Registration– 3D problem => 2D matching problem– Internal feature correspondence based on 2D conformal
mapping images color encoded by mean curvature. – Surface registration by harmonic map with feature
correspondences, not only the feature points.
• Advantage– One-to-one and onto surface registration (diffeomorphism)– Efficiency: linear time complexity– Accuracy: low averaged distance error
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Questions?
Thanks!