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
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
- 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.
There are several general ways to model shapes:
- 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
- Formulae for generating shapes, e.g. SuperFormula. Figure 2 gives some common leaf
shapes generated from the SuperFormula.
Figure 2. Common Leaf Shapes
Generated by the SuperFormula
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
|Range built by ``to''
||oblong to elliptic
|Multiple ranges connected
by coordinators ("and", "or"), or punctuations
||linear, lanceolate or
ovate and cordate
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.
W. Thompson. On Growth and Form.
Cambridge University Press, London, 1917.
T. Stearn, Botanical
Latin: History, Grammar, Syntax, Terminology and Vocabulary, David & Charles, 2004
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
Edelman. Representation, Similarity,
and the Chorus of Prototypes, Minds
and Machines, 5:45-68. 1995.
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