Polynomial Degree Selection for Noisy Signal Approximation Using Multicriteria Filtering: Application to Boundary Detection in Infrared Images
Abstract
This article proposes a two-stage algorithm and presents the mathematical rationale for selecting the degree of polynomial approximation of a noisy digital signal to extract its component of interest. In the first stage, the signal is decomposed into components, and multicriteria filtering is used to isolate the slowly varying component, identify outliers, and locate abrupt changes in the signal profile. The detected change points define the boundaries of the segments used in the second stage. A polynomial is then fitted to each segment of the input sequence, with the degree selected according to the characteristics of the signal component being approximated. The article explains how the detected change points guide segmentation and how the characteristics of each segment inform the choice of polynomial degree. The algorithm is demonstrated on a line of pixel intensities extracted from an infrared image, where abrupt changes in the intensity profile are used to locate object boundaries along the sampled line.
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