An Eigenstructure Approach to Edge Detection

A new procedure for detecting step edges in noisy signals is proposed. The procedure does not involve any pre-filtering of the data. It locates step edges in 1-D noisy signals as follows. First, it computes the eigenvectors corresponding to the three smallest eigenvalues of a matrix formed with the discrete Fourier transform of the given data. Next, it estimates the edge locations by finding the local minima in the sum of the spectra of the computed eigenvectors. The technique computes a point edge map for 2-D images by analyzing each row, column, 45° and 135° diagonal in the image. The computational complexity of the proposed procedure is for an image of size N × N with at most I_max edges per row, column, 45° or 135° diagonal.