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AI-GEOSTATS: analysis of bone surfaces- SUMMARY of responses

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    Last week I wrote to the list asking for advice about testing for differences between surfaces, especially surface rugosity (original message at the end of
    Message 1 of 1 , Jun 30, 2003
      Last week I wrote to the list asking for advice about testing for differences between surfaces, especially surface rugosity (original message at the end of this email). The responses are listed below. Thank you to all of you who responded! It has been very helpful.


      Hi Ann,
      Approaches would somewhat depend on the scale of the rugosity relative
      to the "global" curvature of the bone surface. If you can regard the
      surface as effectively flat (i.e. approximately a plane) then one aspect
      that could be revealing is the two-dimensional spectrum.

      However, if the scale of a "bump" is appreciable and the bone/specimen
      is curved, then you may have to fit a 2-D "smooth surface" to the overall
      shape of the bone, and then evaluate the rugosity say in terms of
      perpendicular distance from the fit. You would also then have the problem
      of defining position on the fitted surface in order to use say the

      Ted Harding <Ted.Harding@...>


      Though our software was developed primarily for Earth Science applications,
      Arizona State University is using our EVS-PRO software to animate fetal
      mouse embryo development based on scanned photomicrographs of tissue
      structures. One (of many) challenge they face is finding reference points
      to tie spatial anchors as they evaluate different stages of development.
      This common frame of reference is important if you're trying to evaluate
      spatial variations between objects rather than spectral analysis of surface
      roughness (rugosity).

      In your case it would be helpful to know what measures of similarity you are
      seeking. Are you trying to get a single number (scalar) that represents
      similarity or disimilarity? OR, are you wanting to map surface deviations
      between best-fit comparisons between similar bones? OR something else?

      Reed Copsey <reed@...>

      One possible suggestion: topographic roughness is often quantified by the power spectrum of the elevation plotted on a log-log scale as a function of the wavenumber (the cycles per km, or in your case, cm) in the horizontal direction along a profile. (The power law that this exhibits is often, but is not always, a self-affine fractal.) The roughness is characterized by the slope and the intercept (at some reference wavenumber) of a least-squares linear fit to the power spectrum. The measurement is repeated for multiple transects at regular horizontal spacing; in your case, this would correspond to profiles measures a few degrees apart as the bone is rotated about its axis. Examples of the application of this technique to topographic profiles are given in, e.g., "Fractals and chaos in geology and geophysics" by Donald Turcotte (Cambridge University Press, 1992). Once a quantitative measure is
      assigned (some way or another!) to the bones, then discriminant analysis can be applied
      to determine the separation (if any) between the populations ("exercised" vs. "no exercise").

      Wilmer Rivers <Wilmer@...>

      Hi Ann, this paper by Mark McCormick dealt with ways of
      summarising how bumpy coral reefs were, and might be a useful
      starting point. There's some fairly complex stuff in the geostats lit;
      this might be a gentle intro.

      McCormick MI (1994) Comparison of field methods for measuring
      surface topography and their associations with a tropical
      reef fish assemblage. Marine ecology progress series

      Russell Cole <r.cole@...>

      You might want to look at some of the work being done "shape analysis",
      see for example


      There are several very active groups in England (Dryden and Mardia are
      at different institutions).

      You might also want to look at the two volume set
      "Image Analysis and Mathematical Morphology" by J. Serra (Academic Press)

      If you do a search on Google for "shape analysis" you will find a lot of
      links that are likely to be interesting.


      You can use too the local standard deviation or correlation coefficient,
      obtained by moving windows. It can let you see de local variations of the
      roughness. In relation with the size of the window you ca display more local
      o global roughness. If exist more information ore variables you can use
      local correlations too.

      Later (knowing closing the local roughness) you can use more complex
      analysis as fractals.

      Adrian Martínez Vargas <amvargas@...>

      Hello Ann,

      I have worked on the same problem during my phD on one dimensional laser profile. Profiles corresponded to canopy rugosity and the goal was to see wether forest type affects canopy profile. I don't have solution for your problem but I can suggest you articles on that problems. I can eventually send you some of them if you are interested.

      Pachepsky, Y. A., J. C. Ritchie, et al. (1997). "Fractal modelling of airbone altimeter laser altimetry data." Remote Sensing of Environment 61: 150-161.
      Ollier, S., D. Chessel, et al. (2003). "Comparing and classifying one-dimensional spatial patterns: an application to laser altimeter profiles." Remote Sensing of Environment 85(4): 453-462.
      Drake, J. B. and J. Weishampel (1990). Multifractal analysis of laser altimeter and ground-based canopy height measures of a longleaf pine savanna.
      Pachepsky, Y. A. and J. C. Ritchie (1998). "Seasonal changes in fractal landscape surface roughness estimated from airbone laser altimetry data." International Journal of Remote Sensing 19(13): 2509-2516.
      Couteron, P. (2002). "Quantifying change in patterned semi-arid vegetation by Fourier analysis of digitised aerial photographs." International Journal of Remote Sensing 23(17): 3407-3425.
      Lark, R. M. and R. Webster (1999). "Analysis and elucidation of soil variation using wavelets." European Journal of Soil Science 50: 185-206.
      Nielsen, B., F. Albregtsen, et al. (1999). "The use of fractal features from the periphery of cell nuclei as a classification tool." Analytical Cellular Pathology 19: 21-37.

      These articles give an idea to methods (wavelet analysis, fourier analysis, multiscale analysis, fractal and multifractal) that could help you.
      ollier <ollier@...-lyon1.fr>

      > Hello-
      > I am a graduate student studying the functional morphology of bones. Part
      of my thesis entails characterizing the shape of a relatively complex 3D
      bone surface. I am testing to see whether exercise affects the morphology of
      this surface, so am looking for a way to test for differences between
      shapes/specimens. I am especially interested in testing for differences in
      the rugosity (ie, "bumpiness") of the surfaces, but am interested in *any*
      method that would help me analyze these surfaces.
      > I have 3D grid data (x,y,z) that represents the surfaces (I am scanning
      the bones with a 3D laser scanner to obtain this data). Can any of you
      suggest methods to analyze this data that will allow me to differentiate
      surfaces that are morphologically dissimilar?
      > Thank you,
      > Ann Zumwalt
      > Center for Functional Anatomy & Evolution
      > Johns Hopkins University

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