Multiple cortical surface correspondence using pairwise shape similarity

Abstract

Accurately corresponding a population of human cortical surfaces provides important shape information for the diagnosis of many brain diseases. This problem is very challenging due to the highly convoluted nature of cortical surfaces. Pairwise methods using a fixed template may not handle well the case when a target cortical surface is substantially different from the template. In this paper, we develop a new method to organize the population of cortical surfaces into pairs with high shape similarity and only correspond such similar pairs to achieve a higher accuracy. In particular, we use the geometric information to identify co-located gyri and sulci for defining a new measure of shape similarity. We conduct experiments on 40 instances of the cortical surface, resulting in an improved performance over several existing shape-correspondence methods.

Fig. 1

An illustration of the left hemisphere of cortical surfaces and their co-registration. (a) The pial surface of a subject. (b) The inflated version of the pial surface (a). (c) The spherical mapping, S̃, of (a). (d) Spherical mapping of a second subject. (e) Deformed version of (d) after co-registration with (c).

Fig. 2

The shape-organization trees constructed from LONI LPBA40 dataset using (a) the MST-based method in [10], (b) the pairwise method with a fixed template, and (c) the proposed method. In (b) and (c), the ellipsis represents all the unlisted subjects, which are directly linked to the root as its children.

Fig. 3

Average of the error $e_i^j$ in terms of (a) each subject and (b) each set of corresponded landmarks, for the correspondence obtained by the proposed method.

Fig. 4

A visualization of the error $e_i^j$ on the spherical mapping of one subject (subject 18): red area indicates $e_i^j>0$ and green area indicates $e_i^j=0$. The top and bottom rows show the views that are the same as and diametrically opposite to the one used in Fig. 1(c), respectively. (a–d) the results from M1, M2, M3, and the proposed method, with green area accounting for 75.4%, 75.5%, 75.7% and 77.2% of the sphere, respectively.