Derivative continuity is a distributed invariant relationship between parts of flowing shapes. The original techniques presented here were developed for making the behavioral dynamics of complex processes more recognizable, but are equally applicable to assisting in the recognition of shapes in images. Regularizing a sequence using a constraint of derivative continuity is equivalent to using a bimodal smoothing kernel, producing a distinct bias for reducing variation on higher derivative levels, sharply defining shape with minimal suppression of shape. To help determine where reconstructing shapes in this way is valid, a test was developed to help distinguish combinations of noise and smooth flows from random walks. This helps distinguish between illusory and genuine, data shapes but also exposes a flair in using this and other measures of scaling behavior for diagnostic purposes. Gaussian scale space techniques in use for some time in image recognition, for identifying reliable landmarks in the shapes of outlines, are demonstrated for use in identifying key features of shape in time series.
FEATURES OF DERIVATIVE CONTINUITY IN SHAPE
