Stereo topography
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I am looking at SEM images of sandstones, and would like
to quantify the fractal dimensionality of this surface at this scale. One way I have thought to do this is to take two or more images, Tilted relative to one another, to create a stereo pair. From there, And given the scale of the image, there should be a way to reconstruct The surface topography as topographic slices or even a digital elevation map. This could then be used to calculate the "3-D" fractal dimension. I know this is done for satellite topographic mapping, so it should be do-able From an SEM image. Does anyone know if plugins/macros for such a project are available. Thanks. --Larry P.S. I know from scattering data that, at least at finer scales, these surfaces are fractal. -- Dr. Lawrence M. Anovitz MS 6110 PO Box 2008 Geochemistry and Interfacial Chemistry Group Oak Ridge National Laboratory Oak Ridge, Tennessee 37831-6110 [hidden email] |
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On Monday 12 October 2009 21:53:27 Anovitz, Lawrence {Larry} M. wrote:
> I am looking at SEM images of sandstones, and would like > to quantify the fractal dimensionality of this surface at this scale. > One way I have thought to do this is to take two or more images, > Tilted relative to one another, to create a stereo pair. From there, > And given the scale of the image, there should be a way to reconstruct > The surface topography as topographic slices or even a digital elevation > map. This could then be used to calculate the "3-D" fractal dimension. An easy way to achieve that once you determined the elevation map, is to 'flood' it at various levels and determine the dimension D of the 3d coastlines of the islands or lakes. The dimension in 3d is D+1. You can do the 2d analysis with the built in box counting method. However stereo pairs do not give you the whole 3d structure (some caves and overhangs might not be possible to image). Cheers G. |
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Gabriel
thanks. A few questions 1. most importantly, do you have any idea how do I get the elevation map ? 2. what's the best way to try the flooding ? 3. are you sure the 3d dimension is D(2)+1 ? Could it be (3/2)D(2), or even not necessarily directly related ? 4. I agree wrt the limitations of the stereo pairs. I may be able to improve this by making and combining several stereo pairs at different tilts. --Larry On 10/12/09 5:49 PM, "Gabriel Landini" <[hidden email]> wrote: On Monday 12 October 2009 21:53:27 Anovitz, Lawrence {Larry} M. wrote: > I am looking at SEM images of sandstones, and would like > to quantify the fractal dimensionality of this surface at this scale. > One way I have thought to do this is to take two or more images, > Tilted relative to one another, to create a stereo pair. From there, > And given the scale of the image, there should be a way to reconstruct > The surface topography as topographic slices or even a digital elevation > map. This could then be used to calculate the "3-D" fractal dimension. An easy way to achieve that once you determined the elevation map, is to 'flood' it at various levels and determine the dimension D of the 3d coastlines of the islands or lakes. The dimension in 3d is D+1. You can do the 2d analysis with the built in box counting method. However stereo pairs do not give you the whole 3d structure (some caves and overhangs might not be possible to image). Cheers G. |
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On Monday 12 October 2009 22:56:31 Anovitz, Lawrence {Larry} M. wrote:
> 1. most importantly, do you have any idea how do I get the elevation map I read a paper long ago on this. I think it is this one, but I cannot access it from here: http://www.mrs.org/s_mrs/bin.asp?CID=7589&DID=186904&DOC=FILE.PDF > 2. what's the best way to try the flooding ? You do a 'cut' at certain height. So everything higher than a value is set to the foreground value (island) and evertyhing lower is set to the background (water). Then, extract the edges and compute the box dimension. One could do a heightmap with pixel values and then threshold it. Actually this is an intersection of your object with a plane. One might try different orientations of the cutting plane. > 3. are you sure the 3d dimension is D(2)+1 ? I seem to remember that there is a theorem on this in Tamas Vicsek's book Fractal Growth Phenomena. So one reduces 1 the dimension by intersecting the 3d structure with a 2d plane. I just tried to find that theorem and found this instead: Chemical Physics Letters. Volume 433, Issues 1-3, 29 December 2006, Pages 248-252. which seems to argue that the relation does not always hold for some objects. (I have not read the whole paper, just the abstract). > Could it be (3/2)D(2), or even not necessarily directly related ? Where is 3/2 coming from? if the 2D dimension of the zero set (the section) is 1, (e.g. a plane intersected by another plane) in 3d this would mean D(3)=1.5 instead of 2. > 4. I agree wrt the limitations of the stereo pairs. I may be able to > improve this by making and combining several stereo pairs at different > tilts. Depends on the object. If too irregular I think you will not get all the detail, but perhaps your specimens are not that complex. Cheers G. |
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Gabriel
got the paper. It seems, on a quick look, to be exactly what I'm trying to do. Is there a plug-in out there that can do this ? --Larry On 10/12/09 7:07 PM, "Gabriel Landini" <[hidden email]> wrote: On Monday 12 October 2009 22:56:31 Anovitz, Lawrence {Larry} M. wrote: > 1. most importantly, do you have any idea how do I get the elevation map I read a paper long ago on this. I think it is this one, but I cannot access it from here: http://www.mrs.org/s_mrs/bin.asp?CID=7589&DID=186904&DOC=FILE.PDF > 2. what's the best way to try the flooding ? You do a 'cut' at certain height. So everything higher than a value is set to the foreground value (island) and evertyhing lower is set to the background (water). Then, extract the edges and compute the box dimension. One could do a heightmap with pixel values and then threshold it. Actually this is an intersection of your object with a plane. One might try different orientations of the cutting plane. > 3. are you sure the 3d dimension is D(2)+1 ? I seem to remember that there is a theorem on this in Tamas Vicsek's book Fractal Growth Phenomena. So one reduces 1 the dimension by intersecting the 3d structure with a 2d plane. I just tried to find that theorem and found this instead: Chemical Physics Letters. Volume 433, Issues 1-3, 29 December 2006, Pages 248-252. which seems to argue that the relation does not always hold for some objects. (I have not read the whole paper, just the abstract). > Could it be (3/2)D(2), or even not necessarily directly related ? Where is 3/2 coming from? if the 2D dimension of the zero set (the section) is 1, (e.g. a plane intersected by another plane) in 3d this would mean D(3)=1.5 instead of 2. > 4. I agree wrt the limitations of the stereo pairs. I may be able to > improve this by making and combining several stereo pairs at different > tilts. Depends on the object. If too irregular I think you will not get all the detail, but perhaps your specimens are not that complex. Cheers G. |
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In reply to this post by Gabriel Landini
Gabriel
just fyi, here are a couple of more recent articles on the same problem Three-dimensional reconstruction of cleavage fracture surface for duplex stainless steel T. Kuroda, K. Ikeuchi, K. Nakade, K. Inoue and Y. Kitagawa Vacuum Volume 65, Issues 3-4 , 27 May 2002, Pages 541-546 Reconstruction of surface topographies by scanning electron microscopy for application in fracture research J. Stampfl1 , S. Scherer2 , M. Gruber2 and O. Kolednik Applied Physics A: Materials Science & Processing Volume 63, Number 4 / October, 1996 I think these may directly yield DEM's - I'm looking them over. A Google search on "digital elevations from scanning electron microscope" Turns up quite a bit. Hopefully I can find a plug-in that will do this (I have no experience at writing one) --Larry On 10/12/09 7:07 PM, "Gabriel Landini" <[hidden email]> wrote: On Monday 12 October 2009 22:56:31 Anovitz, Lawrence {Larry} M. wrote: > 1. most importantly, do you have any idea how do I get the elevation map I read a paper long ago on this. I think it is this one, but I cannot access it from here: http://www.mrs.org/s_mrs/bin.asp?CID=7589&DID=186904&DOC=FILE.PDF > 2. what's the best way to try the flooding ? You do a 'cut' at certain height. So everything higher than a value is set to the foreground value (island) and evertyhing lower is set to the background (water). Then, extract the edges and compute the box dimension. One could do a heightmap with pixel values and then threshold it. Actually this is an intersection of your object with a plane. One might try different orientations of the cutting plane. > 3. are you sure the 3d dimension is D(2)+1 ? I seem to remember that there is a theorem on this in Tamas Vicsek's book Fractal Growth Phenomena. So one reduces 1 the dimension by intersecting the 3d structure with a 2d plane. I just tried to find that theorem and found this instead: Chemical Physics Letters. Volume 433, Issues 1-3, 29 December 2006, Pages 248-252. which seems to argue that the relation does not always hold for some objects. (I have not read the whole paper, just the abstract). > Could it be (3/2)D(2), or even not necessarily directly related ? Where is 3/2 coming from? if the 2D dimension of the zero set (the section) is 1, (e.g. a plane intersected by another plane) in 3d this would mean D(3)=1.5 instead of 2. > 4. I agree wrt the limitations of the stereo pairs. I may be able to > improve this by making and combining several stereo pairs at different > tilts. Depends on the object. If too irregular I think you will not get all the detail, but perhaps your specimens are not that complex. Cheers G. |
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