-Ann

----------------------------------------

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

spectrum.

Ted Harding <Ted.Harding@...>

--

Ann,

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@...>

http://www.ctech.com

--

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

http://www.maths.nottingham.ac.uk/personal/ild/book/.

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.

DEMyers

http://www.u.arizona.edu/~donaldm

--

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 MartÃnez 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.

Sincerly.

Sebastien.

ollier <ollier@...-lyon1.fr>

ORIGINAL REQUEST:> Hello-

of my thesis entails characterizing the shape of a relatively complex 3D

>

> I am a graduate student studying the functional morphology of bones. Part

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.>

the bones with a 3D laser scanner to obtain this data). Can any of you

> I have 3D grid data (x,y,z) that represents the surfaces (I am scanning

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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