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.

Tracing ridges on B-Spline surfaces

“…Since then, ridges have proven valuable in a variety of applications spanning diverse domains. They are view independent curves and more stable with surface deformation compared to other feature curves such as curvature lines, which makes them very useful for shape matching [13,21,35,39]. They are useful in visualization applications since they capture perceptually salient features of an object [9,18,27].…”

Ridge Extraction from Isosurfaces of Volumetric Data Using Implicit B-Splines

“…Ridges have been used as landmarks for shape matching and registration [12], [13], [14], [15], as indicators of the quality of product designs [16], [17], as visual cues for effective visualization [18], [19], [20] and several other shape analysis tasks [21], [22]. Most of the previous applications use crests mainly because there are few methods for robust extraction of all types of ridges.…”

Demarcating curves for shape illustration

“…They can therefore be utilized in a large spectrum of applications, including non-photorealistic rendering [Strothotte and Schlechtweg 2002], segmentation [Stylianou and Farin 2004], robot navigation [Page et al 2006], simplification [Pauly et al 2003], brain analysis [ Bartesaghi and Sapiro 2001], registration of anatomical structures [Pennec et al 2000], and the recovery of archaeological and architectural information [Maaten et al 2006]. Recent user studies [Cole et al 2008] do not conclusively choose one of the current types of curves as the best for all cases.…”