Transcript Conformal Geometry Based Supine and Prone Colon Registration Wei Zeng Joseph Marino Xianfeng Gu Arie Kaufman Stony Brook University, New York, USA The MICCAI.

Conformal Geometry Based Supine
and Prone Colon Registration
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
Overview
• 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
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Algorithm
Anatomical Landmark
Extraction
Supine & Prone Colon
Surfaces (S1, S2)
Conformal Mapping
(φ1, φ2)
Holomorphic Differentials
Internal Feature
Detection & Matching
Harmonic Map
Registration
Constraints: Feature
Correspondence of (S1, S2)
Harmonic Energy
Linear System Optimization
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Anatomical Landmarks Extraction
• Idea: Extract anatomical landmarks using existing methods
– Taenia coli – Slicing the colon surface open
– Flexures – Dividing the colon to 5 segments
Taenia Coli
Flexures
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Conformal Map - Holomorphic Differentials
• Idea: Solve harmonic functions with Dirichlet boundary conditions.
– Colon segment: topological cylinder, denoted as triangular mesh
3D Surface
2D Conformal Map
Texture Map
Non-rigid Deformation
Different Conformal Modules
Angle Preserving
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Internal Feature Detection and Matching
• 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
2D Conformal Map
Segmentation
Extraction
Matching
Mean Curvature
Haustral Folds
Feature Points
Feature Correspondence
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Conformal Map - Matching Framework
3D Surface
2D Conformal Map
3D Surface
2D Conformal Map
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Conformal Map Based Surface Matching
• Idea: Compute harmonic map between two 2D maps with feature
correspondence constraints
– One-to-one mapping
– Linear computational complexity
Polyp
on Supine
Supine => Prone
Deformed Supine
Polyp
on Prone
Registration
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Experiments
•
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
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!
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