Open Access Research

A one-dimensional slope detection approach

Xiaochun Zhang* and Chuancai Liu

Author Affiliations

School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

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SpringerPlus 2013, 2:474  doi:10.1186/2193-1801-2-474

Published: 20 September 2013

Abstract

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.

Keywords:
Slope; Gaussian; Threshold; Error function; Sub-sample; Localization; Interpolation; Noise suppression; The first derivative operator