A one-dimensional slope detection approach

This paper extends the scale-invariant edge detector to the one-dimensional slope. It can accurately detect the slope and estimate its parameters. The method has been verified with several mathematical functions, sample sizes, and noise levels. A contrast-invariant operator is proposed to suppress noise. The inter-sample localization and interpolation greatly improve the accuracy. The proposed slope detector is also suitable for real-world signals. In additional to above-mentioned, a threshold formula is developed for the first derivative slope detector, and the upper-bound of the filterable noise level is also explored.