The Manchester Computational Flora Project



Question:

Aspen

How do you describe the leaf shapes of Aspen trees?

  • broadly ovate to suborbicular or oblate-orbicular --- Flora of the British Isles
  • broadly ovate to orbicular --- New Britton and Brown illustrated Flora of the Northeastern United States and Adjacent Canada
  • kidney-shaped, reniform or oblate --- Gray's Manual of Botany
  • suborbicular --- New Flora of the British Isles
  • almost round --- The Wild Flower Key: A Guide to Plant Identification in the Field
  • ...

How do you integrate them into a uniform description and use it afterwards?

In order to integrate them into a formal ontology, or to check their compatibility, we need
  • an appropriate semantic model in which the semantics in such NL descriptions can be captured and the compatibility between descriptions can be measured;
  • a formal language which is expressive enough to represent the NL semantics and also compatible with the current ontology system;
  • a proper integration strategy for combining information from different sources.

Shape Modelling

There are several general ways to model shapes:
  1. Interpolation techniques and curve-fitting. For example, polygonal fitting (i.e. selecting points on the margin); simple interpolation using, say, polynomials, through to sophisticated curve-fitting techniques, e.g. using (elliptic) Fourier series, or using splines;
  2. Formulae for generating shapes, e.g. SuperFormula. Figure 2 gives some common leaf shapes generated from the SuperFormula.

Common Leaf Shapes

Figure 2. Common Leaf Shapes Generated by the SuperFormula
   3. Transformational methods, e.g. conformal maps or image morphing, or compositional methods
 
Here, we derived a special leaf shape model: Four-Feature Model
  • Length/width ratio
  • The position of the broadest part
  • Apex angle
  • Base angle
We have implemented a small tool to measure these features of a single leave (click here for more details)

Syntax of Shape Descriptions

Leaf Shape Description Pattern
Example
Single term ovate
Modified term broadly elliptic
Hyphenated expression linear-lanceolate
Range built by ``to'' oblong to elliptic
Multiple ranges connected by coordinators ("and", "or"), or punctuations linear, lanceolate or narrowly elliptic
ovate and cordate

Semantics Construction

The semantics of complex descriptions is constructed by applying certain operations on that of  basic terms, including modifying its length/width ratio to get "broadly" or "narrowly" shape, use an intermedia shape for hyphenated shape "A-B" while a "super-shape" representing a range for shape A to shape B, etc.


Distance and Integration

Parallel information is assumed to be complementary, possibly with a certain degree of overlap. It is not appropriate to simply mix information without careful studies of how similar or how different they are. However, measuring the distances between shapes --- especially non-geometric shapes --- is an inherently ill-defined problem, because what counts as "similar" or "different" --- how close is "close enough" ---  is dependent on the task and the domain. Distances between shape descriptions are therefore extremely difficult to measure.


References

  1. D'Arcy W. Thompson. On Growth and Form. Cambridge University Press, London, 1917.
  2. William T. Stearn, Botanical Latin: History, Grammar, Syntax, Terminology and Vocabulary, David & Charles, 2004
  3. E. Sharon and D. Mumford. 2D-Shape Analysis using Conformal Mapping, in Proceedings IEEE Conference on Computer Vision and Pattern Recognition, 350-357. Washington, DC, June 2004.
  4. Shimon Edelman. Representation, Similarity, and the Chorus of Prototypes, Minds and Machines, 5:45-68. 1995.




Links

Here are some useful links:


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