Topology Constraints in Segmentation

Topology Constraints on Segmentation

Pierre-Louis Bazin and Dzung L. Pham

Overview

The topological properties of objects are often very simple, regardless of their geometric complexity. Human anatomy follows this rule, even for extremely convoluted shapes like the cerebral cortex or the vasculature. An algorithm is described for segmenting structures in medical images while respecting the topological properties and anatomical relationships of the structures as given by a template. The algorithm, called TOpology-preserving Anatomy-Driven Segmentation (TOADS) combines advantages of tissue classification, digital topology, and image registration to handle any given topology and enforces object-level relationships with little constraint over the geometry.

Introduction

The topological properties of 2D and 3D objects are often very simple, regardless of the complexity of the geometric object. The cortex of the human brain is a striking example; despite its intricate folds, it is considered to have the topology of a sphere, without any hole or handle-like junction. Most organs and sub-structures found in the human body also have a simple topology.

Ideally, segmentation algorithms that extract objects from images should respect the object topology. A major problem is that topology is a global property of the object, whereas most extraction techniques operate locally on the pixels of an image. Two approaches to addressing this issue are to correct the extracted object to obtain the desired topology, or to start from a template object, with the correct topology, and deform it with topology-preserving deformations.

Bazin and Pham introduced an efficient topology-preserving fast marching technique to be used in both approaches, for topology correction [2] and topology-preserving segmentation [3]. The topology correction method enforces topology constraints a posteriori with little alteration of the original data and is the method of choice to correct a well segmented object. The method has been released as a Mipav plug-in in the Download section of this site.

The main challenge, however, is to enforce topology constraints prior to the segmentation and to consider multiple objects simultaneously. In [3], the methodology for TOADS was presented: an iterative procedure comprised of joint object thinning and growing steps with a topology-preserving fast marching method and tissue classification steps using methods from FANTASM. The topology properties of the set of objects to segment are encoded in a topology template, registered to the image and then transformed in the iterative procedure. The complete algorithm, fully described in [1,4], first registers a topology template to the brain image, then estimates the segmentation with iterated thinning and growing steps, while correcting for gain field inhomogeneity. The resulting segmentation has been utilized to simplify the processing pipeline of CRUISE [5].

Applications

Topology correction for cortical unfolding

To unfold the cortical surface onto a spherical or hemispherical map, a perfectly spherical topology is needed. However, due to the cortical folds, both the gray / white matter interface and the gray matter / pial interface recovered from tissue classification have many handles, holes and separate parts. (a) shows themembership function for the gray / white matter interface initially recovered, (b) shows the result of the proposed topology correction. The images are almost the same, so the geometry of the extracted surface will be very similar, but the topology of any isosurface extracted from (b) will be spherical, allowing its unfolding.

Cortical segmentation

TOADS directly enforces the topology constraints desired for cortical unfolding in the segmentation: (a) classification results with TOADS (from left to right: original image, topology template, hard classification, membership functions for cerebro-spinal fluid, gray matter, white matter), (b) 3D renderings of the cortical gray matter, white matter, sub-cortinal gray matter, ventricles all with correct topology, (c) the boundaries of the classification superimposed on two orthogonal slices of the original image.

Publications

P.-L. Bazin and D.L. Pham, ``Topology-Preserving Tissue Classification of Magnetic Resonance Brain Images", IEEE Transactions on Medical Imaging, special issue on Computational Neuroanatomy, 2007.
P.-L. Bazin and D.L. Pham, ``Topology correction using fast marching methods and its application to brain segmentation,'' Proceedings of MICCAI 2005.
P.-L. Bazin and D.L. Pham, ``Topology preserving tissue classification with fast marching and topology templates,'' Proceedings of IPMI 2005.
P.-L. Bazin and D.L. Pham, ``TOADS: Topology-preserving, anatomy-driven segmentation,'' Proceedings of ISBI 2006.
P.-L. Bazin, X. Han, D. Tosun, J.L. Prince, D.L. Pham, "Cortical Reconstruction using Topology Preserving Tissue Classification," Human Brain Mapping 2006.