Hi Frederic,
To amplify, are you are talking about vertex by vertex analyses in the context of between group comparisons? As Doug says, the optimal tools are not there yet.
As you know, you can always drop the threshold on the other side and see if activations/thickness blobs emerge in the same areas on the contralateral side though this is not a formal statistical test of laterality.
Of course there are the other simpler approaches if you are not talking vertex by vertex. If you have a result based on an mean thickness or fMRI activation in an aprior cortical parcellation (say, parsorbitalis) or an amalgam of such parcellations, then you are free to compare this with mean value from the same area in contralateral hemisphere, and formally test for a laterality interaction using a repeated measures GLM.
But depending on what you want to do, even with vertex by vertex data there are some ways to interrogate your data more formally for laterality effects. Suppose you have a label/subregion/blub in one hemisphere (could be functional or structural) and you want to test formally for laterality ( formal two way interaction with side). You could draw by hand the mirror image of the blob in the other hemisphere either by anatomical landmarks or perhaps better, by recording the min and max tal coordinates in x,y,z (and some additional control points) for the hemisphere where you have your activation, flipping the sign of the x coordinate, and then marking the vertex in the other hemisphere that corresponds to the flipped tal coordinate. Then make a label of the mirror image blob, extract mean signal for each subject within boundries of said blob, AND run a glm on this with dx, gender or whatever else you are interested in. Notice if you do this, you are not biased in the same way you would be if you ran your test statistics based on individual subjects values extracted form the original hemisphere blob which would be circular. And I dont think, but you can check with Doug, that you are biased if you included a term for side and compare the original label with the mirror label as a repeated within subject factor, as long as you are not using the outcome of the analysis to test for the significance of the between group difference in the original hemisphere (which you KNOW HAS to be significant because thats how you defined the original label). But that bias would seem to be absent for the contralateral label.
Carl