Abstract

We show that the problem of detecting edges in a digital image is equivalent to the problem of estimating the wavenumber vectors of complex exponentials in the spatial frequency domain. This observation is then used to show that most of the known nonmodel based edge detection algorithms can be interpreted as variations of the per- iodogram method of spectral estimation. The variations include using data windows and smoothing of the resulting power spectral estimate. Next, the above observation is used to derive three new edge detection algorithms. The first algorithm is based on the fact that complex exponentials are the homogeneous solution of a difference equation with proper initial conditions. It derives estimates of the edge locations by performing a singular value decomposition of a Hankel matrix formed from the fast Fourier transform of the underlying image. The second and third approaches use the maximum likelihood spectral estimation method and various maximum entropy spectral estimation techniques on the fast Fourier transform of the underlying image to estimate the edge locations.

© 1989 Optical Society of America