An Optimal Frequency Domain Filter for Edge Detection in Digital Pictures

Abstract

Edge detection and enhancement are widely used in image processing applications. In this paper we consider the problem of optimizing spatial frequency domain filters for detecting edges in digital pictures. The filter is optimum in that it produces maximum energy within a resolution interval of specified width in the vicinity of the edge.We show that, in the continuous case, the filter transfer function is specified in terms of the prolate spheroidal wave function. In the discrete case, the filter transfer function is specified in terms of the sampled values of the first-order prolate spheroidal wave function or in terms of the sampled values of an asymptotic approximation of the wave function. Both versions can be implemented via the fast Fourier transform (FFT). We show that the optimum filter is very effective for detecting blufred and noisy edges. Finally, we compare the perfor-

Edge Detection and Feature Line Tracing in 3D-Point Clouds by Analyzing Geometric Properties of Neighborhoods

“…Generally, once edges are detected, a further step will be done for tracing feature lines from the detected edges. For edge detection in images, edges have been well defined, such as "the boundary element between two regions of different homogeneous luminance" [2] or "large or sudden changes in some image attribute, usually the brightness" [3]. An extensive review of the established edge detection methods can be found in the literature [1].…”

“…Then, the definition of 2D edges is extended by the literatures [1][2][3][4]11]. Specially, the literature [1] defines 2D edges as one-dimensional discontinuities in the intensity surface of the underlying scene.…”

“…The usual aim of edge detection is to locate edges belonging to boundaries of objects of interest [3]. Most edge detection techniques consist of two stages [11]: (1) converting an original image into features; and (2) assigning points to edges or non-edges.…”

Two-dimensional textural edge detection using ω-Gaussian filter

“…It was shown by Shanmugan et al 5 that the optimal frequency domain filter Hh(W) for tonal edge extraction is, under the constraints of band limitation and evenness of the function,…”

“…Nevertheless, an interesting filter capable of extracting the boundary between domains modulated by different spatial frequencies has recently been proposed and demonstrated in 1-D simulations. 4 This filter is an extrapolation of an optimum tonal edge extraction filter previously described by Shanmugan et al 5 An approximate form of this filter, which is similar to the difference in two Gaussians (DOG) 6 and the Laplacian of a Gaussian 7 filter, was found to perform particularly well in extracting the blurred or noisy edges. The optimum performance of the filter was demonstrated under the constraint of even symmetry, which was necessary to extend operation of the filter to a 2-D case.…”