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.