Download e-book for kindle: 53.Robotics and Automation by John G. Webster (Editor)

By John G. Webster (Editor)

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The inverse transform of F(u, v) is defined as f (x, y) = 1 N N−1 N−1 F(u, v) exp[ j2π (ux + vy)/N] u=0 v=0 where 0 Յ x, y Յ N Ϫ 1. Several computational algorithms have been developed to calculate the two-dimensional DFT. The Fourier power, or amplitude, spectrum plays an important role in image processing. Since the Fourier transform of a real function produces a complex function, F(u, v) ϭ R(u, v) ϩ jI(u, v), the frequency spectrum of the image is the magnitude function F (u, v) = [R2 (u, v) + I 2 (u, v)]1/2 and the power spectrum (spectral density) is defined as P(u, v) ϭ ͉F(u, v)͉2.

Actually, this set of points forms a sinusoidal curve in the (r, ␸) plane. ] Since each point in the input image generates such a sinusoidal curve in HT, the whole of the input image generates a multitude of overlapping sinusoids in the HT image. In many instances, a large number of sinusoidal curves are found to converge on the same spot in the HT image. The (r,␸) coordinates of such a bright point indicates the slope ␸ and position r of a straight line that can be drawn through a large number of white spots in the input image.

Filling Holes. Consider a white bloblike figure containing a hole (lake) against a black background. The application of the hole-filling operator will cause all of the holes to be filled in by setting all pixels in the holes to white. Region Labeling. Consider an image containing a number of separate bloblike figures. A region-labeling operator will shade the output image so that each blob is given a separate intensity value. We could shade the blobs according to the order in which they are found, during a conventional raster scan of the input image.

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53.Robotics and Automation by John G. Webster (Editor)

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