Homeomorphic brain image segmentation with topological and statistical atlases

Abstract

Atlas-based segmentation techniques are often employed to encode anatomical information for the delineation of multiple structures in magnetic resonance images of the brain. One of the primary challenges of these approaches is to efficiently model qualitative and quantitative anatomical knowledge without introducing a strong bias toward certain anatomical preferences when segmenting new images. This paper explores the use of topological information as a prior and proposes a segmentation framework based on both topological and statistical atlases of brain anatomy. Topology can be used to describe continuity of structures, as well as the relationships between structures, and is often a critical component in cortical surface reconstruction and deformation-based morphometry. Our method guarantees strict topological equivalence between the segmented image and the atlas, and relies only weakly on a statistical atlas of shape. Tissue classification and fast marching methods are used to provide a powerful and flexible framework to handle multiple image contrasts, high levels of noise, gain field inhomogeneities, and variable anatomies. The segmentation algorithm has been validated on simulated and real brain image data and made freely available to researchers. Our experiments demonstrate the accuracy and robustness of the method and the limited influence of the statistical atlas.

Fig. 1

Importance of the topology of groups: the individual structures in above images have the same topology, but the relationships between them are different, corresponding to changes in the topology of groups (unions) of structures.

Fig. 2

Simple points for multiple objects: a) the central point can be exchanged between 2 and 4, but not 1 and 2 or 2 and 3 since these latter two cases would allow 1 and 3 to touch, b) the central point can swap from 1 to 3, but not 2 or 4, c) the central point is non-simple for any change if the objects are 6-connected, but can move from 3 to 2 if the objects are 26-connected (note that the groups 2–3 and 1–4 intersect each other in the latter case).

Fig. 3

The statistical atlas derived from the IBSR V2 delineations.

Fig. 4

The topological atlas in axial, coronal and sagittal views.

Fig. 5

The segmentation software: original image, user interface (image and parameter panels) and result.

Fig. 6

Influence of the atlas coefficient over the overlap for the IBSR dataset.

Fig. 7

Influence of the atlas coefficient over the average surface distance for the IBSR dataset.

Fig. 8

Dice overlap coefficients for the IBSR experiments.

Fig. 9

Average surface distances for the IBSR experiments.

Fig. 10

Example of segmentation from the IBSR dataset. From left to right, top to bottom: original image, computed segmentation, membership functions for CRW, CRG, CSF, VEN CAU, THA, PUT, BS, CBW, CBG, and 3D rendering.

Fig. 11

Examples of segmentation from research studies: a) subjects from a MDMA study, b) patients with Sturge-Weber Syndrome, c) subjects from the BLSA.