Biomedical Engineering Reference
In-Depth Information
3
Registration Methodology: Concepts
and Algorit
hms
Derek L.G. Hill and Philipe Batchelor
CONTENTS
3.1 Introduction .................................................................................................. 40
3.2 Notation and Terminology ......................................................................... 40
3.2.1 Image Field of View ......................................................................... 42
3.2.2 The Discrete Nature of the Images ................................................ 43
3.3 Types of Transformation ............................................................................. 44
3.4 Registration Algorithms.............................................................................. 47
3.4.1 Points and the Procrustes Problem................................................ 47
3.4.1.1 The Orthogonal Procrustes Problem .............................. 47
3.4.1.2 Errors in Rigid-Body Point Registration........................ 49
3.4.2 Surface Matching ............................................................................. 49
3.4.2.1 The Head and Hat Algorithm ......................................... 50
3.4.2.2 Distance Transforms ......................................................... 50
3.4.2.3 Iterative Closest Point (ICP) ............................................ 51
3.4.3 Voxel Similarity Measure ................................................................ 52
3.4.4 Minimizing Intensity Difference.................................................... 53
3.4.5 Correlation Techniques ................................................................... 54
3.4.6 Ratio Image Uniformity (RIU) ....................................................... 55
3.4.7 Partitioned Intensity Uniformity (PIU)......................................... 55
3.4.8 Information Theoretic Techniques................................................. 56
3.4.8.1 Joint Entropy...................................................................... 57
3.4.8.2 Mutual Information .......................................................... 60
3.4.8.3 Normalized Mutual Information.................................... 61
3.4.9 Optimization and Capture Ranges................................................ 62
3.5 Image Transformation ................................................................................. 63
3.5.1 A Consideration of Sampling and Interpolation Theory ........... 64
3.5.2 Interpolation during Registration.................................................. 65
3.5.3 Transformation for Intermodality Image Registration ............... 66
3.6 Conclusions................................................................................................... 66
References ............................................................................................... 67
