Features of derivative continuity in shape

Derivative continuity is a distributed invariant relationship between parts of flowing shapes. The original techniques presented here were developed f or making the behavioral dynamics of complex processes more recognizable, b ut are equally applicable to assisting in the recognition of shapes in imag es. Regularizing a sequence using a constraint of derivative continuity is equivalent to using a bimodal smoothing kernel, producing a distinct bias f or reducing variation on higher derivative levels, sharply defining shape w ith minimal suppression of shape. To help determine where reconstructing sh apes in this way is valid, a test was developed to help distinguish combina tions of noise and smooth flows from random walks. This helps distinguish b etween illusory and genuine, data shapes but also exposes a flair in using this and other measures of scaling behavior for diagnostic purposes. Gaussi an scale space techniques in use for some time in image recognition, for id entifying reliable landmarks in the shapes of outlines, are demonstrated fo r use in identifying key features of shape in time series.