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
2
• 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
3
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
4
• 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
5
• 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
6
• 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
7
Conformal Map - Matching Framework
3D Surface
2D Conformal Map
3D Surface
2D Conformal Map
8
• 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
9
• 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
10
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
11
Questions?
Thanks!
Top Related