Stable Fitting of 2D Curves and 3D Surfaces by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
A representation of time series based on implicit polynomial curve
Pattern Recognition Letters
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A new concept and algorithm are presented for non-iterative robust estimation of piecewise smooth curves of maximal edge strength in small image windows - typically 8脳8 to 32脳32. This boundary-estimation algorithm has the nice properties that it uses all the data in the window and thus can find locally weak boundaries embedded in noise or texture and boundaries when there are more than two regions to be segmented in a window; it does not require step edges - but handles ramp edges well. The curve-estimates found are among the level sets of a d'th degree polynomial fit to 驴suitable驴 weightings of the image gradient vector at each pixel in the image window. Since the polynomial fitting is linear least squares, the computation to this point is very fast. Level sets then chosen to be appropriate boundary curves are those having the highest differences in average gray level in regions to either side. This computation is also fast. The boundary curves and segmented regions found are suitable for all purposes but especially for indexing using algebraic curve invariants in this form.