2D-discontinuity detection from scattered data
The paper describes a numerical approach for the detection of discontinuities of a 2D function distorted by noise. The proposed method is based on the 2D continuous wavelet transform and follows some previously obtained results of the author. Section 2 introduces the 2D wavelet transform, defines the wavelet transform modulus maxima, and gives a characterization of the wavelet transform behaviour in the neighbourhood of a maximum corresponding to a function value discontinuity. Section 3 performs a statistical test to detect the discontinuity curve in the presence of noise. Section 4 provides a detection algorithm from scattered and noisy data. This kind of problems arises in many applications within computer vision, geology, signal processing, etc. Section 5 contains numerical results supporting the proposed approach.
scientific article; zbMATH DE number 1233903