How to crop coordinates within a (Delaunay) surface?

Hi everyone,

I hope that I am explaining this problem clearly. I need to be able to crop out lower-resolution voxel coordinates that lie within a surface derived from higher-resolution voxel coordinates.

The long story short here is that I have data that comes from two different imaging modalities (high res: anatomical MRI; low res: diffusion tensor imaging, DTI). The image sets are co-registered to one another so they are aligned, but the anatomical MRI is much higher-resolution than the DTI. I'm able construct a surface for a brain landmark of interest in MATLAB using a Delaunay Triangulation, derived from the higher-resolution coordinates. I need a way to find the lower-resolution coordinates that lie within that surface. There is no direct overlap between the actual coordinates, so I can't just use a "find" command to fix this.

Can anyone help? Thanks in advance!

[Sean de Wolski]

If the images are coregistered, do you have the transformation matrix?

[Layla]

Hi Sean,

Yes I do have the transformation matrix. I already apply it in advance to get the coordinates properly aligned. Even after applying the transformation, the actual coordinates won't have any perfect overlaps. For example, the higher-resolution image may have coordinates at (0.5, 0.5, 0.5) and (1, 0.5, 0.5) while the lower resolution image just has one at (0.6, 0.5, 0.5). Does that make sense?

[Layla]

A more simple explanation of this problem: how can I determine if some arbitrary point (Px, Py, Pz) lies within an irregular surface?

[Matt Kindig]

Oh, in that case, you can use the inpolygon() function, which is designed for this (in 2D). Although I prefer the inpoly ( http://www.mathworks.com/matlabcentral/fileexchange/10391-fast-points-in-polygon-test) for this purpose, as it is much faster than the built-in version.

[Layla]

Thanks! inpoly looks very promising. I assume this code would search within 2D slices of the shape in question. But the surfaces I work with are quite irregular--do you think that this code is robust enough for an oddly-shaped brain nucleus?

I'm currently messing around with a combination of creating a tesselation with delaunayn and using tsearchn to solve this problem also. See: http://www.mathworks.com/matlabcentral/newsreader/view_thread/33157

[Matt Kindig]

I think inpoly() would work for your purpose. In my experience tsearchn() can be rather slow, and if all you need is to identify whether points are within a (highly irregular) polygon, inpoly() should be fine.

[Layla]

That's terrific. Thank you so much!