Blurred segments [Debled06] were introduced in discrete geometry to address possible noise along discrete contours. The noise is not really detected but is rather canceled out by thickening digital straight segments. The thickness is tuned by a user and set globally for the contour, which requires both supervision and non-adaptive contour processing. To overcome this issue, we propose an original strategy to detect locally both the amount of noise and the meaningful scales of each point of a digital contour. Based on the asymptotic properties of maximal segments, it also detects curved and flat parts of the contour. From a given maximal observation scale, the proposed approach does not require any parameter tuning and is easy to implement. We demonstrate its effectiveness on several datasets. Its potential applications are numerous, ranging from geometric estimators to contour reconstruction.