Yes, these are good points. If you want to replicate what would happen by merging labels and then running mris_annatomical_stats, then you would weight by number of vertices.

doug

Michael Harms wrote:

Hello, I also need to compute a weighted average thickness across some of the labels, so I went ahead and tested how FS empirically handles this issue.

Let me say first off that Doug's recommendation of weighting by the surface area (rather than number of vertices) is imminently reasonable and indeed seems to me the "correct" way to do it from a theoretical perspective. The one potential confound with weighting by surface area is the issue of which particular surface to use -- white? pial? some surface mid-way between the two?

That said, I just wanted to point out to the list that as a practical matter, within FS itself, average thicknesses seem to be computed by weighting by the number of vertices (effectively assuming that the area associated with each vertex is constant, which is fine assumption since the FS vertices are reasonably equally distributed across the surface). There are at least two examples where you can see this manifested:

1. The ThickAvg values in ?h.aparc.stats are the simple average of the

thickness values for the vertices associated with each label. [That is, within a label, ThickAvg is not computed as the average of the thickness at each vertex weighted by the area associated with each vertex. To see this, convert the annotation file to labels using mri_annotation2label, load a given label in Matlab (read_label.m), load the ?h.thickness map (read_curv.m), and compute the mean thickness across the indices in that label (remembering to add 1 to the indices since matlab is 1-based). The resulting mean (and std) will be identical to the values in ? h.aparc.stats].

Important caveat: The above assumes that the values in ?h.thickness are themselves not "pre-weighted" in some manner by the area of each vertex -- someone please correct me if I'm wrong about that!

2. Consistent with what you would expect based on (1), if you merge two

labels directly in FS (bin/mri_mergelabels), and then compute stats on that merged label (using mris_anatomical_stats), the result for ThickAvg is identical to weighting the results of the individual regions by the number of vertices.

cheers, Mike H.

On Tue, 2008-05-06 at 23:15 -0400, Doug Greve wrote:

...

Use the area.

doug

On Tue, 6 May 2008, Pierson, Ronald K wrote:

...

I apologize if this has been asked and answered before, but I wish to combine rostral and caudal middle frontal gyri for a summary measure. To find the average thickness of the entire region, will it be weighted by the surface area or by the number of vertices?

Avg_MidFront = ((CaudThick*NumVertsCaud) + (RostThick*NumVertsRost) / (NumVertsCaud + NumVertsRost))

Or

Avg_MidFront = ((CaudThick*SurfAreaCaud) + (RostThick*SurfAreaRost) / (SurfAreaCaud + SurfAreaRost))

Thanks,

Ronald Pierson

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