An eigenstructure approach to edge detection
A procedure for detecting step edges in noisy signals that does not involve any prefiltering of the data is proposed. 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, and 45 degrees and 135 degrees diagonal in the image. The computational complexity of the proposed procedure is determined.