[Freesurfer] Making a patch of area A
Hi. I have a graph theory question: I would like to make a definition of a particular patch of cortex, that has a centroid at position (x,y,z) and has a total area of A. I thought that this was going to be somewhat hard, but I soon learned that it is very hard. First, I found some code for the Dijkstra algorithm, which can quickly tell me what is the minimum number of jumps needed from one vertex to another. IF the freesurfer surface triangles were all of EXACTLY the same euclidean distances on each side, then this alone could solve my problem. I could simply take all vertices which have a jump distance less than some number. However, because the side lengths of the triangles in a freesurfer surface are NOT the same, I need to get more sophisticated. Ideally, what I would like is the following: If I were an ant, walking along on the surface of the folded brain, I could walk from the centroid in any direction for a certain distance, and still be within my "patch." Knowing that distance (radius), I could just use pi*r^2 and call that the area of the patch. But how do I find this idealized patch in real life? Thanks Daniel Goldenholz ___ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Re: [Freesurfer] Making a patch of area A
You might try starting off with the ?h.sphere. It's easy to parameterize these things on the sphere. The sphere, of course, has some metric distortion, but if the patch is small, it might not be to bad. Once you've identified the vertices in the patch (or maybe a slightly bigger patch), then you can refine it in the folded space. doug Daniel Goldenholz wrote: > > Hi. I have a graph theory question: > > I would like to make a definition of a particular patch of cortex, that > has a centroid at position (x,y,z) and has a total area of A. > > I thought that this was going to be somewhat hard, but I soon learned that > it is very hard. > > First, I found some code for the Dijkstra algorithm, which can quickly > tell me what is the minimum number of jumps needed from one vertex to > another. IF the freesurfer surface triangles were all of EXACTLY the same > euclidean distances on each side, then this alone could solve my problem. > I could simply take all vertices which have a jump distance less than > some number. > > However, because the side lengths of the triangles in a freesurfer surface > are NOT the same, I need to get more sophisticated. > > Ideally, what I would like is the following: > If I were an ant, walking along on the surface of the folded > brain, I could walk from the centroid in any direction for a certain > distance, and still be within my "patch." > Knowing that distance (radius), I could just use pi*r^2 and call > that the area of the patch. > > But how do I find this idealized patch in real life? > > Thanks > Daniel Goldenholz > ___ > Freesurfer mailing list > Freesurfer@nmr.mgh.harvard.edu > https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer -- Douglas N. Greve, Ph.D. MGH-NMR Center [EMAIL PROTECTED] Phone Number: 617-724-2358 Fax: 617-726-7422 ___ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Re: [Freesurfer] Making a patch of area A
Hi Daniel - Well it seems to me that you're almost there already. A Dijkstra algorithm is the ideal engine to determine radial paths from a central node - I suspect you just need to tune the graph cost function to take the Euclidean distance between nodes (as opposed to the logical distance) into account. --R -- Rudolph Pienaar, M.Eng, D.Eng / email: [EMAIL PROTECTED] MGH/MIT/HMS Athinoula A. Martinos Center for Biomedical Imaging 149 (2301) 13th Street, Charlestown, MA 02129 USA ___ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Re: [Freesurfer] Making a patch of area A
Doug I was thinking of trying something like that. If I took all vertices which are a radius M or less from my centriod, aren't I basically done? (M is defined as the maximum euclidean distance between the centroid on the sphere and the ring of outer vertices. If my surface distance max is called R, I can use some geometry to figure out the relation between R and M) What tweaks would I need to do at the folded surface level? On Tue, 8 Mar 2005, Doug Greve wrote: You might try starting off with the ?h.sphere. It's easy to parameterize these things on the sphere. The sphere, of course, has some metric distortion, but if the patch is small, it might not be to bad. Once you've identified the vertices in the patch (or maybe a slightly bigger patch), then you can refine it in the folded space. doug Daniel Goldenholz wrote: Hi. I have a graph theory question: I would like to make a definition of a particular patch of cortex, that has a centroid at position (x,y,z) and has a total area of A. I thought that this was going to be somewhat hard, but I soon learned that it is very hard. First, I found some code for the Dijkstra algorithm, which can quickly tell me what is the minimum number of jumps needed from one vertex to another. IF the freesurfer surface triangles were all of EXACTLY the same euclidean distances on each side, then this alone could solve my problem. I could simply take all vertices which have a jump distance less than some number. However, because the side lengths of the triangles in a freesurfer surface are NOT the same, I need to get more sophisticated. Ideally, what I would like is the following: If I were an ant, walking along on the surface of the folded brain, I could walk from the centroid in any direction for a certain distance, and still be within my "patch." Knowing that distance (radius), I could just use pi*r^2 and call that the area of the patch. But how do I find this idealized patch in real life? Thanks Daniel Goldenholz ___ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer -- Douglas N. Greve, Ph.D. MGH-NMR Center [EMAIL PROTECTED] Phone Number: 617-724-2358 Fax: 617-726-7422 -- Daniel Goldenholz - Cell: 617-935-9421 http://people.bu.edu/danielg/ ___ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Re: [Freesurfer] Making a patch of area A
Hi Daniel, don't use Euclidean distance. Use the length of the great circle connecting each point to the central vertex on the ?h.sphere surface. Bruce On Tue, 8 Mar 2005, Daniel Goldenholz wrote: Doug I was thinking of trying something like that. If I took all vertices which are a radius M or less from my centriod, aren't I basically done? (M is defined as the maximum euclidean distance between the centroid on the sphere and the ring of outer vertices. If my surface distance max is called R, I can use some geometry to figure out the relation between R and M) What tweaks would I need to do at the folded surface level? On Tue, 8 Mar 2005, Doug Greve wrote: You might try starting off with the ?h.sphere. It's easy to parameterize these things on the sphere. The sphere, of course, has some metric distortion, but if the patch is small, it might not be to bad. Once you've identified the vertices in the patch (or maybe a slightly bigger patch), then you can refine it in the folded space. doug Daniel Goldenholz wrote: Hi. I have a graph theory question: I would like to make a definition of a particular patch of cortex, that has a centroid at position (x,y,z) and has a total area of A. I thought that this was going to be somewhat hard, but I soon learned that it is very hard. First, I found some code for the Dijkstra algorithm, which can quickly tell me what is the minimum number of jumps needed from one vertex to another. IF the freesurfer surface triangles were all of EXACTLY the same euclidean distances on each side, then this alone could solve my problem. I could simply take all vertices which have a jump distance less than some number. However, because the side lengths of the triangles in a freesurfer surface are NOT the same, I need to get more sophisticated. Ideally, what I would like is the following: If I were an ant, walking along on the surface of the folded brain, I could walk from the centroid in any direction for a certain distance, and still be within my "patch." Knowing that distance (radius), I could just use pi*r^2 and call that the area of the patch. But how do I find this idealized patch in real life? Thanks Daniel Goldenholz ___ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer -- Douglas N. Greve, Ph.D. MGH-NMR Center [EMAIL PROTECTED] Phone Number: 617-724-2358 Fax: 617-726-7422 ___ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Re: [Freesurfer] Making a patch of area A
Hi Bruce Yes, I'm sorry I wasn't clear in my previous posting. I think that you and I are talking about the same thing... The surface distance along the sphere from my vertex point... let's call that arc length. So I want to have all freesurfer points which are less than or equal to an arc length of R. Lets now consider the boundary condition, where I am looking at only locations that are arc length R. Now I could calculate the euclidean distance from vertex to any point on the sphere which has exactly arc length R. It turns out that a circle is formed on the sphere surface. The euclidean distance that I measure is a constant value - M. Therefore, I could identify that boundary in another way. I could get the intersection of two spheres: 1 the original freesurfer sphere, and 2, a sphere with my vertex at the origin, and the radius M. Intersecting these two spheres gives me that same boundary. Indeed, if I take all the points from the freesurfer ?h.sphere which are inside the second sphere, then I should now have my patch. Whew. Now the question is this: if I do all that (which I believe is equivalent to Bruce's suggestion) then do I correctly generate a patch which: a. has a centroid at my vertex b. has an area given approximately by pi*R^2 c. from a surface point of view, has radial symmetry (meaning an ant could walk in any direction from the centroi along the surface, and until he reaches distance R, he is still inside the patch) ? Thanks Daniel On Tue, 8 Mar 2005, Bruce Fischl wrote: Hi Daniel, don't use Euclidean distance. Use the length of the great circle connecting each point to the central vertex on the ?h.sphere surface. Bruce On Tue, 8 Mar 2005, Daniel Goldenholz wrote: Doug I was thinking of trying something like that. If I took all vertices which are a radius M or less from my centriod, aren't I basically done? (M is defined as the maximum euclidean distance between the centroid on the sphere and the ring of outer vertices. If my surface distance max is called R, I can use some geometry to figure out the relation between R and M) What tweaks would I need to do at the folded surface level? On Tue, 8 Mar 2005, Doug Greve wrote: You might try starting off with the ?h.sphere. It's easy to parameterize these things on the sphere. The sphere, of course, has some metric distortion, but if the patch is small, it might not be to bad. Once you've identified the vertices in the patch (or maybe a slightly bigger patch), then you can refine it in the folded space. doug Daniel Goldenholz wrote: Hi. I have a graph theory question: I would like to make a definition of a particular patch of cortex, that has a centroid at position (x,y,z) and has a total area of A. I thought that this was going to be somewhat hard, but I soon learned that it is very hard. First, I found some code for the Dijkstra algorithm, which can quickly tell me what is the minimum number of jumps needed from one vertex to another. IF the freesurfer surface triangles were all of EXACTLY the same euclidean distances on each side, then this alone could solve my problem. I could simply take all vertices which have a jump distance less than some number. However, because the side lengths of the triangles in a freesurfer surface are NOT the same, I need to get more sophisticated. Ideally, what I would like is the following: If I were an ant, walking along on the surface of the folded brain, I could walk from the centroid in any direction for a certain distance, and still be within my "patch." Knowing that distance (radius), I could just use pi*r^2 and call that the area of the patch. But how do I find this idealized patch in real life? Thanks Daniel Goldenholz ___ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer -- Douglas N. Greve, Ph.D. MGH-NMR Center [EMAIL PROTECTED] Phone Number: 617-724-2358 Fax: 617-726-7422 -- Daniel Goldenholz - Cell: 617-935-9421 http://people.bu.edu/danielg/ ___ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Re: [Freesurfer] Making a patch of area A
The sphere-based patch will change size and shape a little when you map it back to the folded surface due to metric distortion. So you could refine it some, eg, run your Dijstra algorithm on just the patch. I would not expect the distortion to make much of a difference, so it's probably not worth the trouble. dougx Daniel Goldenholz wrote: > > Doug > > I was thinking of trying something like that. > If I took all vertices which are a radius M or less from my centriod, > aren't I basically done? > (M is defined as the maximum euclidean distance between the centroid on > the sphere and the ring of outer vertices. If my surface distance max is > called R, I can use some geometry to figure out the relation between R and > M) > > What tweaks would I need to do at the folded surface level? > > On Tue, 8 Mar 2005, Doug Greve wrote: > > > > > You might try starting off with the ?h.sphere. It's easy to parameterize > > these things on the sphere. The sphere, of course, has some metric > > distortion, but if the patch is small, it might not be to bad. Once > > you've identified the vertices in the patch (or maybe a slightly bigger > > patch), then you can refine it in the folded space. > > > > doug > > > > > > Daniel Goldenholz wrote: > >> > >> Hi. I have a graph theory question: > >> > >> I would like to make a definition of a particular patch of cortex, that > >> has a centroid at position (x,y,z) and has a total area of A. > >> > >> I thought that this was going to be somewhat hard, but I soon learned that > >> it is very hard. > >> > >> First, I found some code for the Dijkstra algorithm, which can quickly > >> tell me what is the minimum number of jumps needed from one vertex to > >> another. IF the freesurfer surface triangles were all of EXACTLY the same > >> euclidean distances on each side, then this alone could solve my problem. > >> I could simply take all vertices which have a jump distance less than > >> some number. > >> > >> However, because the side lengths of the triangles in a freesurfer surface > >> are NOT the same, I need to get more sophisticated. > >> > >> Ideally, what I would like is the following: > >> If I were an ant, walking along on the surface of the folded > >> brain, I could walk from the centroid in any direction for a certain > >> distance, and still be within my "patch." > >> Knowing that distance (radius), I could just use pi*r^2 and call > >> that the area of the patch. > >> > >> But how do I find this idealized patch in real life? > >> > >> Thanks > >> Daniel Goldenholz > >> ___ > >> Freesurfer mailing list > >> Freesurfer@nmr.mgh.harvard.edu > >> https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer > > > > -- > > Douglas N. Greve, Ph.D. > > MGH-NMR Center > > [EMAIL PROTECTED] > > Phone Number: 617-724-2358 > > Fax: 617-726-7422 > > > > -- > Daniel Goldenholz > - > Cell: 617-935-9421 http://people.bu.edu/danielg/ -- Douglas N. Greve, Ph.D. MGH-NMR Center [EMAIL PROTECTED] Phone Number: 617-724-2358 Fax: 617-726-7422 ___ Freesurfer mailing list Freesurfer@nmr.mgh.harvard.edu https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer
Re: [Freesurfer] Making a patch of area A
Hello, You may prefer to write your own code for calculating the patch, but I thought I would just mention that this functionality is implemented in Caret (http://brainmap.wustl.edu/resources/caretnew.html). Caret can read FreeSurfer surfaces. It will calculate the distance of all nodes from a given seed node, along your chosen surface. Then it is easy to select all nodes at or within a certain radius. best, Rutvik On Wed, 9 Mar 2005, Daniel Goldenholz wrote: > Hi Bruce > > Yes, I'm sorry I wasn't clear in my previous posting. I think that you and > I are talking about the same thing... > > The surface distance along the sphere from my vertex point... let's call > that arc length. So I want to have all freesurfer points which are less > than or equal to an arc length of R. Lets now consider the boundary > condition, where I am looking at only locations that are arc length R. Now > I could calculate the euclidean distance from vertex to any point on the > sphere which has exactly arc length R. It turns out that a > circle is formed on the sphere surface. The euclidean distance that I > measure is a constant value - M. Therefore, I could identify that boundary > in another way. I could get the intersection of two spheres: 1 the > original freesurfer sphere, and 2, a sphere with my vertex at the origin, > and the radius M. Intersecting these two spheres gives me that same > boundary. Indeed, if I take all the points from the freesurfer ?h.sphere > which are inside the second sphere, then I should now have my patch. > > Whew. Now the question is this: if I do all that (which I believe is > equivalent to Bruce's suggestion) then do I correctly generate a patch > which: > a. has a centroid at my vertex > b. has an area given approximately by pi*R^2 > c. from a surface point of view, has radial symmetry > (meaning an ant could walk in any direction from the centroi > along the surface, and until he reaches distance R, he is > still inside the patch) > > ? > > > Thanks > > Daniel > > On Tue, 8 Mar 2005, Bruce Fischl wrote: > > > Hi Daniel, > > > > don't use Euclidean distance. Use the length of the great circle connecting > > each point to the central vertex on the ?h.sphere surface. > > > > Bruce > > > > On Tue, 8 Mar 2005, Daniel Goldenholz wrote: > > > >> Doug > >> > >> I was thinking of trying something like that. > >> If I took all vertices which are a radius M or less from my centriod, > >> aren't I basically done? > >> (M is defined as the maximum euclidean distance between the centroid on > >> the sphere and the ring of outer vertices. If my surface distance max is > >> called R, I can use some geometry to figure out the relation between R and > >> M) > >> > >> What tweaks would I need to do at the folded surface level? > >> > >> On Tue, 8 Mar 2005, Doug Greve wrote: > >> > >>> > >>> You might try starting off with the ?h.sphere. It's easy to parameterize > >>> these things on the sphere. The sphere, of course, has some metric > >>> distortion, but if the patch is small, it might not be to bad. Once > >>> you've identified the vertices in the patch (or maybe a slightly bigger > >>> patch), then you can refine it in the folded space. > >>> > >>> doug > >>> > >>> > >>> Daniel Goldenholz wrote: > > Hi. I have a graph theory question: > > I would like to make a definition of a particular patch of cortex, > that > has a centroid at position (x,y,z) and has a total area of A. > > I thought that this was going to be somewhat hard, but I soon learned > that > it is very hard. > > First, I found some code for the Dijkstra algorithm, which can quickly > tell me what is the minimum number of jumps needed from one vertex to > another. IF the freesurfer surface triangles were all of EXACTLY the > same > euclidean distances on each side, then this alone could solve my > problem. > I could simply take all vertices which have a jump distance less than > some number. > > However, because the side lengths of the triangles in a freesurfer > surface > are NOT the same, I need to get more sophisticated. > > Ideally, what I would like is the following: > If I were an ant, walking along on the surface of the folded > brain, I could walk from the centroid in any direction for a certain > distance, and still be within my "patch." > Knowing that distance (radius), I could just use pi*r^2 and > call > that the area of the patch. > > But how do I find this idealized patch in real life? > > Thanks > Daniel Goldenholz > ___ > Freesurfer mailing list > Freesurfer@nmr.mgh.harvard.edu > https://mail.nmr.mgh.harvard.edu/mailman/listinfo/freesurfer > >>> > >>> -- > >>> Douglas N. Greve, Ph.D. > >>> MGH-NMR Center > >>> [EMAIL PROTECTED] > >>> Phone Number: 617-724-23
