We propose a graphical indexing of images to be exposed on the Web. This should be accomplished by "keypics", i.e. auxiliary,
simplified pictures referring to the geometrical and/or the semantic content of the indexed image. Keypics should not be rigidly standardized; they should be left free to evolve, to express nuances and to stress details. A mathematical tool for dealing with such freedom already exists: Size Functions. We support the idea of keypics with some experiments on a 498 images dataset.
The problem of completeness for invariant size functions is studied. Families of size functions are introduced, which allow recognition of some classes of plane curves up to transformations of increasing generality.
Size functions are a mathematical tool for comparing shapes represented as topological spaces. In this paper we introduce a method for describing a set of size functions corresponding to a given class of objects. An example of the application of this method for signature recognition is presented.
A method to construct new pseudo-distances for the size function space based on the formal series representation of size function is introduced. These new pseudo-distances allow to measure quantitatively the differences in shapes by comparing size functions. Some experiments on digital images are shown.
Inequalities involving size functions of a subset of the Euclidean plane, its dilation and its skeleton are given, which lead to new techniques of computation of size functions. Some experiments on digital images are shown.
We define the concept of size functions. They are functions from the real plane to the natural numbers which describe the `shape of the objects' (seen as submanifolds of a Euclidean space). We give two different techniques of computation of size functions and some actual examples of computation. Moreover, we present the concept of deformation distance between manifolds (i.e., curves, surfaces, etc.). It is a distance which measures the `difference in shape' of two manifolds. Finally we point out the link between deformation distances and size functions.