GEN RE: Types of Quantitative Data - Outline Methods

[Stuart G. Poss]

Gregor wrote:

>
> > Does anybody know about good parameterization of shapes, so they can
> > be stored in more objective forms?
>

To which Don responded:

>
> Wouldn't the most objective representation of shape be given by a set of
> coordinates for points placed around the outline? If orientation of the
> object is important, then give landmark coordinates too eg. mark the organ
> base and apex. From that info, parameters such as object area, perimeter
> length, circularity (perimeter length*perimeter length/area), centroid,
> longest and shortest axes, aspect ratios etc. can be calculated.
>
> You'd also be able to standardise your outlines (eg. using Bookstein's
> transformation) and compare against reference shapes (eg elliptic fourier
> analysis), pairwise comaprisons using (thin plate splines) or fit to average
> shape using Procrustes metric.
>
> Feature extraction from digital images (eg defining the object outline,
> sampling of points around outline)and calculation of the shape parameters
> and export to spreadsheet is virtually automatic in packages like OPTIMAS.
> James Rolf's NTsysPC will perform the basic standardisations, thin plate
> splines and EFA.
>
> don

Approaches to evaluating OUTLINES include:

Freeman Chain Code Encoding

Chris Meacham's MorphoSys package uses a Freeman Chain Code to automatically
identify and encode points along the perimeter of a target object using video
digitization, as well as along the edge of holes within it.  There is a
published citation for this, but I can not find it at the moment.  This is not
a parametric technique since it generates a point set for which no parameters
must be either calculated.

Median or Symmetrical Axis

Blum,  H.  1967.  A transformation for extracting new descriptors of shape, pp.
362-380, In: Whaten-Dunn, E,  Models for the perception of speech and visual
form, MIT Press, Cambridge, MA, 470 pp.

Straney, D. O.  1990.  Median Axis Methods in Morphometrics, pp. 179-200, In:
Rohlf, F. J. and F. L. Bookstein,   Proceedings of Michigan Morphometrics
Workshop.  Special Publication Number 2, The University of Michigan Museum of
Zoology,  Ann Arbor, 380 pp.


Fourier Analysis using Polar Coordinates

Kaesler, R. L. and J. A. Waters.  1972.  Fourier analysis of the ostracode
margin.  Geol. Soc. Amer. Bull., 83:1169-1178.

Younker, J. L. and R. Ehrlich.  1977.  Fourier biometrics: harmonic amplitudes
as multivariate shape descriptors: Syst. Zool., 26:336-342.


Elliptical Fourier transforms

Kuhl, F. P.  and C. R. Giardina.  1982.  Elliptic Fourier features of a closed
contour.  Computer Graphiccs and Image Processing.  18:236-258.

Rohlf, F. J. and J.  W. Archie.  1984.  A Comparions of Fourier methods for the
description of wing shape in mosquitos (Diptera: Culicidae).  Syst. Zol.,
33:302-317.


Eigenshape analysis:

Lohmann, G. P.  1984.  Eigenshape analysis of microfossils: A general
morphometric procedure for describing changes in shape.  Math. Geol.,
15(6):659-672.

Lohmann, G. P. and P. N. Schweitzer.  1990.  On Eigenshape Analysis, pp.
147-166, In: Rohlf, F. J. and F. L. Bookstein,   Proceedings of Michigan
Morphometrics Workshop.  Special Publication Number 2, The University of
Michigan Museum of Zoology,  Ann Arbor, 380 pp.


Bezier Curves

Engles, H.  1986.  A least squares methods for estimation of Bezier curves and
surface and its applicability to multivariate analysis.  Mathemaical
Biosciences, 79:155-170.


Cubic Splines

Evans,  D. G., P. N. Schweitzer, and M. S. Hanna.  1985.  Parametric cubic
splines and geological shape descriptions.  Mathematical Geology, 17:611-624.


Fractals

Barnsley,  M.  F. , V. Ervin, D. Hardin, and J. Lancaster.  1986.  Solution of
an inverse problem for fractals and other sets.  Proceedings of the National
Academy of Sciences USA, 83:1975-1977.