Can think of our approach as edge curve detection where the operator geometry is adaptive.
When the hypothesis is false, the larger extent of averaging limits false positives
No smoothing is necessary prior to fitting
Noise does not influence fitted curves significantly -- the modelling power of the polynomial is limited: it can only model the most salient structures in a window.
- Multiple curves in the window are found with a single polynomial model (different level sets of the same polynomial)
  
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