Reconstructing a function from scattered points

A demanding test of a time series shape recognition method is provided by sin curves that are 'disguised' by superimposition and then sampled to see if the components can then be reconstructed. Derivative reconstruction (DR) performs admirably in this task as shown below. Time has not yet allowed displaying the comparable performance of what seems to be the current state of the art computer vision method, curvature scale space (CSC). CSC performs admirably on many other tests. Investigation has shown it to be reasonably effective in identifying the two longer period curves, but to lose the higher frequency curve entirely. This is a function of the amount of information present in the sampled data, and the smoothing 'kernel' that fundamentally distinguishes the two methods.

The full size figures display the steps of DR shape reconstruction in12 steps, from:

• 1. Selecting three regular mathematical sin curves,


• 2. Combining and sampling them to simulate the normal complexity of data


• 3. Comparing the continuities identified with the original.


• for more detail see the intermediate steps at full size by opening the links in the table below

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