Digital homeomorphisms in deformable registration.
A common goal in deformable registration applications is to produce a spatial transformation that is diffeomorphic, thereby preserving the topology of structures being transformed. Because this constraint is typically enforced only on the continuum, however, topological changes can still occur within discretely sampled images. This work discusses the notion of homeomorphisms in digital images, and how it differs from the diffeomorphic/homeomorphic concepts in continuous spaces commonly used in medical imaging. We review the differences and problems brought by considering functions defined on a discrete grid, and propose a practical criterion for enforcing digital homeomorphisms in the context of atlas-based segmentation.
Bazin
Pierre-Louis
PL
Johns Hopkins University, Baltimore, USA.
Ellingsen
Lotta Maria
LM
Pham
Dzung L
DL
D000465:Algorithms; D001185:Artificial Intelligence; D001921:Brain / Q000033:anatomy & histology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique