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<p>The authors study the location error of curved edges in two- and three-dimensional images after analog and digital low-pass filtering. The zero crossing of a second derivative filter is a well-known edge localization criterion. The second derivative in gradient direction (SDGD) produces a predictable bias in edge location towards the centers of curvature while the linear Laplace filter produces a shift in the opposite direction. Their sum called PLUS (PLUS=Laplace+SDGD) leads to an edge detector that finds curved edges one order more accurately than its constituents. This argument holds irrespective of the dimension. The influence of commonly used low-pass filters (such as the PSF originating from diffraction limited optics using incoherent light (2-D), the Gaussian filter with variable cutoff point (D-D), and the isotropic uniform filter (D-D)) is studied.</p>
edge detection; low-pass filters; location error; curved edges; low-pass filtered 2-D images; 3-D images; digital low-pass filtering; analog low-pass filtering; zero crossing; second derivative filter; edge localization criterion; second derivative in gradient direction; edge location; centers of curvature; linear Laplace filter; edge detector; PSF; diffraction limited optics; incoherent light; Gaussian filter with variable cutoff point; isotropic uniform filter

L. van Vliet and P. Verbeek, "On the Location Error of Curved Edges in Low-Pass Filtered 2-D and 3-D Images," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 16, no. , pp. 726-733, 1994.
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