Edge detection using spectral estimation techniques

Summary form only given. It has been shown that the problem of detecting edges in a digital image is equivalent to the problem of estimating the wave number vectors of complex exponentials in the spatial frequency domain. This observation has been used to show that most of the known non-model-based edge detection algorithms can be interpreted as variations of the periodogram method of spectral estimation. The variations include using data windows and smoothing of the resulting power spectral estimate. The above observation has also been used to derive three 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. The main advantage of the three approaches is that they do not involve the use of a smoothing filter (and thus do not introduce additional blurring of the edges) or gradient operations. Hence, they have no problem dealing with sharp corners in the underlying scene.