We have described a general procedure for selecting subsets of sulcal landmarks for use in constrained cortical registration. The procedure can be used to reduce the time required for manual labeling of sulci in group studies of cortical anatomy and function.
The optimal subsets of curves, shown in , provide an idea of the criteria used by the method to select curves. First notice that the central sulcus is not selected for protocols with a small number of curves (less than 16). This is probably because sulci that are most stable and consistent among brains, such as the central sulcus, may tend to align well even without explicitly tracing them. Therefore, they may not improve the registration error sufficiently to justify their inclusion in the tracing protocol. Furthermore, short sulci neighboring other candidate curves are not preferred by the algorithm, because they do not sufficiently add constraints to the registration. For example, the paracentral sulcus which is close to the cingulate sulcus, and the subparietal sulcus which is close to the cingulate and the parieto-occipital sulcus are not preferred by the method.
On the other hand, one of the most important sulci for surface based registration seems to be the superior temporal sulcus with its upper branch. This is possibly for two reasons: (1) it is one of the longest sulci and hence aligning it will help register a large region of the brain; (2) in cortical flat maps where the corpus callosum is mapped on the edges of a unit square, such as in our method in , the temporal lobe is far from the edge of the unit square, which always maps to the corpus callosum by construction. Therefore when no sulcal constraint are placed in the temporal lobe, we tend to see large registration error. Consequentially, it is important to align at least one sulcus in temporal lobe accurately, and hence it is selected by our method. The other important sulcus is the Calcarine, which is not as long as the superior temporal sulcus, but is highly variable among subjects.
Our mapping method biases sulcal selection to the extent that corpus callosum is already aligned when performing the flattening. Since we align the corpus callosum for the mapping, the registration errors tend to be smaller in this region, which biases our optimal curve set. This is not necessarily a disadvantage. Every surface registration method requires some initial mapping. For example, surface registration in FreeSurfer and BrainVoyager is properly initialized by 1) volumetric alignment of brain scans to the Talairach space, and then 2) inflation of surfaces to the unit sphere. Our goal is to define optimal sets of curves for registration; in this paper we provide the optimal sets of curves when the registration method in (Joshi et al., 2007b
) is used. If another registration method is chosen, it is straightforward to extend our method to find corresponding optimal sets of curves.
Registration error always remains when only a subset of sulci is used for registration. Whether this is acceptable or not depends on the particular study being contemplated. For example, anatomical studies (Thompson et al., 2001b
; Sowell et al., 2002
; Changeux, 1998
; Gogtay et al., 2004
) require high accuracy and might need more sulci, whereas some functional studies, such as those using low resolution magnetoencephalography data (Pantazis et al., 2005
), can tolerate higher registration error. can be used as a guideline: based on the registration accuracy required, a different number of curves may be used.
Our method determines the subset of sulci to be delineated in a registration study based solely on the registration error. However, some changes in the selected subset can be made based on other practical considerations, such as convenience in tracing. For instance, identification and tracing of the central sulcus is always easy and it could be helpful in identifying the surrounding sulci. Therefore we expect that it would be typically included in a tracing protocol. Furthermore, for neuroscience studies focusing on particular cortical regions, the registration error metric defined in Sec. 2.2 can be modified by assigning more weight to the regions of interest. For example, in language studies interested in activation in the temporal lobe and Broca's area we can increase the weights wn
in Eq. 3
for STS, ITS, SF, abSF, hbSF, IFS. Our method would then favor the aforementioned sulci and produce different sets of optimal curves than the ones displayed in .
In this paper, we have used a registration method which constrains the endpoints of the sulci to match. While allowing sulcal curves to slide as opposed to uniformly sampling them can lead to slightly better results (Leow et al., 2005
), uniform sampling with matching endpoints has been used in a number of publications and has led to useful and important results. e.g. (Gogtay et al., 2004
; Thompson and Toga, 1996
; Thompson et al., 2003
; Sowell et al., 2003
; Thompson et al., 2001a
). This approximation makes the analysis tractable as opposed to letting the sulcal curves slide. The error in the sulcal curves was normalized and weighted by the area surrounding each curve. Consequently the error does not depend on the length of the curve but rather the area surrounding the curve.
Errors and variability in identifying cortical landmarks are a common problem concerning all landmark based techniques and can affect the registration error. However, they are beyond the scope of this paper. For this particular study the curves were identified and cross-checked by an expert neuroanatomist. Inter- and intra-rater variability is typically minimized by appropriate training and cross checking of traces. A possible extension of our method could allow modeling of intra/inter-rater variability in identifying sulci, so that sulci with high rater variability are penalized in the protocol selection process.
Even though we used 2D flat maps, other registration approaches are also possible with our method, such as spherical registrations used in FreeSurfer and BrainVoyager. Our methodology readily extents to other landmark based registration methods in which the goal is to select an optimal subset of landmarks for large scale studies, from a set of candidate landmarks. Finally, it can possibly be applied to other problems of computer vision such as robotics (Madsen and Andersen, 1998
; Wang and Song, 2009
; Greiner and Isukapalli, 1994
), terrain matching (Olson, 2000
), face recognition (Beumer et al., 2006
), etc. for aiding optimal landmark selection.