Landmark Based Registration Using Features Identified Through Differential Geometry

Xavier Pennec 1 Features Extraction: Extremal Points and Lines 499

Nicholas Ayache 1-1 Definition and Properties • 1.2 The Automatic Extraction of the Extremal Points •

Jean Philippe Thirion Example of Extracted Extremal Lines and Points

INRIA—Projet Epidaure 2 Rigid Registration 504

2.1 Curve Registration • 2.2 Extremal Points Registration Using Alignment • 2.3 Substructure Matching with Frame Features • 2.4 ICP on Frames • 2.5 Examples of Rigid Registrations

3 Robustness and Uncertainty Analysis 507

3.1 Robustness Analysis • 3.2 From Feature to Transformation Uncertainty • 3.3 Validation with Real Data

4 Conclusion 511

References 512

Registration of 3D medical images consists in computing the "best" transformation between two acquisitions, or equiva-lently, determines the point to point correspondence between the images. Registration algorithms are usually based either on features extracted from the image (feature-based approaches) or on the optimization of a similarity measure of the images intensities (intensity-based or iconic approaches). Another classification criterion is the type of transformation sought (e.g., rigid or nonrigid).

In this chapter, we concentrate on feature-based approaches for rigid registration, similar approaches for nonrigid registration being reported in another set of publications [35,36]. We show how to reduce the dimension of the registration problem by extracting first a surface from the 3D image, then landmark curves on this surface and possibly landmark points on these curves. This concept proved its efficiency through many applications in medical image analysis as we will see in the sequel. This work has been for a long time a central investigation topic of the Epidaure team [3], and we can only reflect here on a small part of the research done in this area.

We present in the first section the notions of crest lines and extremal points and how these differential geometry features can be extracted from 3D images. In Section 2, we focus on the different rigid registration algorithms that we used to register such features. The last section analyzes the possible errors in this registration scheme and demonstrates that a very accurate registration could be achieved.

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