A variational framework for integrating segmentation and registration through active contours

Abstract

Traditionally, segmentation and registration have been solved as two independent problems, even though it is often the case that the solution to one impacts the solution to the other. In this paper, we introduce a geometric, variational framework that uses active contours to simultaneously segment and register features from multiple images. The key observation is that multiple images may be segmented by evolving a single contour as well as the mappings of that contour into each image.

Introduction

Segmentation and registration have been established as important problems in the field of medical image analysis Ayache, 1995, Cline et al., 1990, Grimson et al., 1994, Vannier et al., 1985. Traditionally, solutions have been developed for each of these two problems in relative isolation from the other, but with increasing dependence on the existence of a solution for the other. In the rest of this section, we discuss the interdependence of segmentation and registration solutions and introduce our motivation for a method that simultaneously estimates the two.

A large class of registration solutions, referred to as ‘feature-based’ methods, require that some features be identified or segmented in the images prior to their registration. These features may be identified using low-level methods such as edge-detection, or segmented using higher level methods that are customized for specific anatomical structures. Contour- and point-based techniques Tang et al., 2000, Weese et al., 1997a, Weese et al., 1997b, Yaniv, 1998 are examples of this strategy, as well as registration methods that compare medialness properties of segmented anatomies (Yushkevich et al., 1999). In contrast to feature-based registration methods, a second class of methods, referred to as ‘intensity-based’ segmentation methods, require no a priori segmentation, which makes them an attractive proposition. Some of the most frequently used objective functions in such registration frameworks are: normalized cross-correlation (Lemieux et al., 1994), entropy of the difference image (Buzug et al., 1997), pattern intensity (Weese et al., 1997b), gradient correlation (Brown, 1996) and gradient difference (Penney et al., 1998). Mutual-Information was introduced as a particularly effective intensity-based metric for registration of medical imagery Collignon et al., 1995, Wells et al., 1995, and its applicability has been repeatedly demonstrated for solving rigid-body (6 degrees of freedom) registration problems. No such consensus, feature-based or intensity-based, seems to have been reached for the domain of non-rigid registration.

The dependence of segmentation on registration is somewhat more subtle. A large class of segmentation methods do not depend on explicit registration between multiple data sets. We will refer to these as ‘low-level’ segmentation methods. In these low-level segmentation methods, the algorithm designers typically use information synthesized from their knowledge of several example data sets to set the parameters of their segmentation algorithms, but no explicit process of registering those data sets to a common reference frame is carried out prior to segmentation. These methods may process a single channel input image using image-processing techniques such as thresholding, connectivity analysis, region-growing, morphology, snakes, and Bayesian MAP estimation. Or, they may process multi-channel data in which the channels are naturally registered because they are acquired simultaneously.

While it is easier to get started in segmentation using these methods because there is no need to solve the cumbersome registration problem a priori, efforts in low-level segmentation of medical imagery often conclude that ‘model-based’, higher level information such as the shape, appearance, and relative geometry of anatomy needs to be incorporated into the solution in order to complete the segmentation task Baillard et al., 2000, Cootes et al., 1994, Kapur et al., 1998, Staib and Duncan, 1992, Szekely et al., 1996. And it is in the building of these models of anatomy that registration plays a key role. Individual data sets need to be registered to a common frame of reference, so that statistics about their shape, appearance, or relative geometry can be gathered.

The work presented in this paper is motivated by the desire to interleave the process of segmentation and registration so that both solutions may be built simultaneously and hence to eliminate the need to completely deliver one solution before being able to start on the other. This challenge has been approached with a min–max entropy-based framework to segment and register portal images to CT (Bansal et al., 1999), and with the ATM SVC algorithm which applies an iterative sequence of elastic warping of the input to an already segmented model in order to automate the classification of normal and abnormal anatomy from medical images (Warfield et al., 2000). A novel extension to level set representations and active contour models by incorporating shape priors Chen et al., 2001, Paragios and Rousson, 2002, Paragios et al., 2002 have also been recently introduced, which frameworks could potentially be used to address our proposed task.

The focus of this paper is to introduce a geometric, variational, active contour framework that allows us to interleave powerful level-set-based formulations of segmentation with a feature-based registration method.