Next: Object Relative Position Up: Describing 2D Shape with Previous: Primitive Shape

### Relative Size

Relative size can be represented qualitatively at the simplest level by the qualitative relations: bigger, smaller, and equal to. In the ASSF system, relative size of objects within a scene, features within subparts, and subparts within objects, are all expressed in terms of the lengths of different types of axes.

The two axes which are most often used as a reference for relative size are the major and minor axes of each distinct shape; such shapes can be either a complete object, a subpart, or an imple. Local relative size is expressed by comparing a given dimension to these axes. Five qualitative values are immediately available: there are three qualitative ranges (less than the minor axis, between the minor and major axes, and greater than the major axis) and two distinguished points (major and minor).

Section 4.1.4 above points out the ways in which this approach is unsatisfactory, and also some partial solutions. One partial solution is to further subdivide the quantity space, so that it is possible to make qualitative distinctions between sizes that are closer in magnitude. I have done this by introducing further ``distinguished'' points at one half and one quarter of the major and minor axis lengths. This results in a quantity space with six distinguished points and seven qualitative ranges, which can be used to construct a satisfactory representation of quite complex objects (especially where local complexity is treated using a local set of imple axes), but which still suffers from the limitations described in section 4.1.4 if there are essentially equal sizes that are accidentally separated into different quantity space ranges.

Individual features are measured along their own axis, which is usually a straight line between the points at either end of the feature. This is true of straight and curved edges, and also of imples, which are measured along the waist where the imple meets another convex part. Secondary axis measurements are used to define the shape of an imple, by specifying the size of imple major and minor axes relative to the axes of the main shape. All of these feature sizes are described by comparing them to the local quantity space defined from the major and minor axes of the main shape.

Next: Object Relative Position Up: Describing 2D Shape with Previous: Primitive Shape
Alan Blackwell
2000-11-17