Landmark-Based Registration Using Features Identified Through Differential Geometry

Abstract

Registration of 3D medical images consists in computing the "best" transformation between two acquisitions, or equivalently, 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 (intensitybased or iconic approaches). Another classification criterion is the type of transformation sought (e.g. rigid or non-rigid).In this chapter, we concentrate on feature-based approaches for rigid registration, similar approaches for non-rigid registration being reported in another set of publication [35,36]. We show how to reduce the dimension of the registration problem by first extracting 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 [2] 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.

Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

“…It turns out that they also optimize the length functional but they are moreover parameterized proportionally to arc-length. 3 …”

“…Examples of manifolds we routinely use in medical imaging applications are 3D rotations, 3D rigid transformations, frames (a 3D point and an orthonormal trihedron), semi-or non-oriented frames (where 2 (resp. 3) of the trihedron unit vectors are given up to their sign) [3,4], oriented or directed points [5,6], positive definite symmetric matrices coming from diffusion tensor imaging [7,8,9,10,11] or from variability measurements [12]. We have already shown in [13,2] that this is not an easy problem and that some paradoxes can arise.…”

Ridges and Umbilics of Polynomial Parametric Surfaces

“…Whenever the datasets processed model piecewise smooth surfaces, a precise description of the models naturally calls for differential properties. In particular, applications such as shape matching [HGY + 99], surface analysis [HGY + 99], or registration [PAT00] require the characterization of high order properties and in particular the characterization of curves of extremal curvatures, which are precisely the so-called ridges. Interestingly, (selected) ridges are also central in the analysis of Delaunay based surface meshing algorithms [ABL03].…”

A Multistage Registration Method Using Texture Features

“…8 Numerous examples in the literature show promising results for registration based on geometrical features. 1,[9][10][11] However, geometrical features are obtained through a segmentation step before the actual registration is performed. Segmentation is, by itself, already a complex and tedious task; therefore, the success of geometricalfeature-based registration is mainly dependent on the success of the segmentation step.…”