gtravan@adam.ua.oz (george travan dentistry) (10/20/89)
could someone give me a pointer to an algorithm that may be able to 'fit' two meshes together. more specifically i have two regular meshes which represent iso-surfaces. i want to see how close 'in a lock and key' sense they fit together. i cant use least squares because there are no identifiable or corresponding landmarks on the two meshes, which are meshes generated through arbitrary data. you can imagine a mesh with a hill and another mesh with a trough, how can you determine how close they can be made to correspond? i hope this makes sense... --GeO George Travan University of Adelaide AUSTRALIA. e-mail: gtravan@adam.ua.oz george@frodo.ua.oz
finn@sunshine.cad.mcc.com (Chris Finn) (10/20/89)
In article <134@adam.ua.oz> gtravan@adam.ua.oz (george travan dentistry) writes: > >you can imagine a mesh with a hill and another mesh with a trough, how can >you determine how close they can be made to correspond? > >i hope this makes sense... > I tried to email a response but it bounced so I'll post this and maybe someone can add more concrete info. From what I understand you are trying to devise a measure of the similarity or dissimilarity of two shapes. For instance if you have two functions (or discrete samples of two functions) of one independent variable (y=f1(x) & y=f2(x) ) you don't want to just measure the vertical distance between them f1(x)-f2(x), and you don't want to measure the perpendicular distance between them. You want to first correlate the features you see in one function with the corresponding features in the other function and then measure the difference between them in the direction in which the correlation is a maximum. In a sense one function is a stretched or contracted, and possibly amplified version of the other. These kinds of similarity measures are used on one dimensional functions in speech recognition. The computer receives a digitized version of the spoken word and tries to match it against words in its vocabulary library. I think similar techiques are used for two dimensional signals when interpolating between two images. For instance, an artist draws a cartoon but doesn't want to draw all 24 frames per second (or whatever it is). He draws the picture at two instances which are seperated by a larger gap in time and the computer fills in the missing images. I think this would be more like your case, where, from what I understand, you want to measure the distance between z=f1(x,y) and z=f2(x,y). I don't have any references handy but if you have an engineering library at your disposal look up "speech recognition" and in particular "time warping" or "dynamic time warping" you can quickly hunt down these algorithms for the one-dimensional case. Hope this helps, Chris Finn MCC CAD Program, P.O. Box 200195, Austin, TX 78720 [512] 343-0978 ARPA: finn@mcc.com UUCP: {uunet,harvard,gatech,pyramid}!cs.utexas.edu!milano!cadillac!finn
keller@ethz.UUCP (Christoph Keller) (10/23/89)
George writes: > could someone give me a pointer to an algorithm that may be able to 'fit' > two meshes together. more specifically i have two regular meshes which > represent iso-surfaces. i want to see how close 'in a lock and key' sense > they fit together. i cant use least squares because there are no identifiable > or corresponding landmarks on the two meshes, which are meshes generated > through arbitrary data. > you can imagine a mesh with a hill and another mesh with a trough, how can > you determine how close they can be made to correspond? > --GeO George Travan > e-mail: gtravan@adam.ua.oz > george@frodo.ua.oz This is a common problem in solar physics. The Earth's atmosphere is distorting sequentially observed images through the randomly changing refractive index of the atmosphere. This distortion needs to be removed when comparing images of the same region on the sun obtained at different times. Here are some references: von der Luehe, O.: A study of a correlation tracking method to improve imaging quality of ground based solar telescopes, Astron.Astrophys. 119, p.85 November, L.J.: Measurement of geometric distortion in a turbulent atmosphere, Applied Optics, Vol.25,No.3, p.392 Keller, C.U.: Restoration of distorted images as a variational problem: A dynamic programming approach, NOAO Preprint No. 229 (I can mail this article by e-mail, but without figures) Hope this helps, Christoph ----------------------------------------------------------------------------- Christoph Keller keller@czheth5a.bitnet Institute of Astronomy ckeller@solar.stanford.edu ETH-Zentrum keller@ifa.ethz.ch CH-8092 Zuerich keller@bernina.ethz.ch.uucp Switzerland ----------------------------------------------------------------------------