An alternative to representing curves at a single scale or a fixed number
of multiple scales is to represent them only at their **natural**
(i.e. most significant) scales. This allows all the important information
concerning the different sized structures contained in the curve to be
explicitly represented without the overhead of redundant representations of
the curve.

Our earlier work developed techniques for determining global natural scales of curves, and found that the normalised number of points of inflection worked well. More recently we have looked at the more difficult task of estimating local natural scales of curves. Since these estimates are more sensitive to noise and other variations merging across and within scales is applied to reduce fragmentation.

Examples of the overlapping sections of the curve represented at their natural scales are shown below:

Koch snowflake

the Queen

More details are given in:

- P.L. Rosin, "Determining local natural scales of curves", Pattern Recognition Letters vol. 19, no. 1, pp. 63-75, 1998.
- P.L. Rosin and S. Venkatesh, "Extracting natural scales using Fourier descriptors", Pattern Recognition, vol. 26, pp. 1383-1393, 1993.
- P.L. Rosin, "Representing curves at their natural scales", Pattern Recognition, vol. 25, pp. 1315- 1325, 1992.

You can download code to implement the extraction of global natural scales.

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