By Peter W. Hawkes

ISBN-10: 0120147599

ISBN-13: 9780120147595

Advances in Imaging and Electron Physics merges long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The sequence positive factors prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, photo technological know-how and electronic photograph processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in a lot of these domain names.

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**Extra resources for Advances in Imaging and Electron Physics, Vol. 117**

**Sample text**

To show that the series converges, we need to show only that the sum from k0 to ∞ converges. Applying the preceding equation yields ∞ r r =1 k=1 λk−1 = μk ≤ = = k0 −1 ∞ r =1 k=1 ∞ k0 −1 r =1 k=1 k0 −1 λk−1 μk k=1 q 1−q λk−1 μk r k=k0 λk−1 μk λk−1 r −k0 +1 q μk ∞ q (37) r −k0 +1 r =1 k0 −1 k=1 λk−1 μk Convergence of the adaptive Þlter means it reaches a steady state, in which r is a random variable. Key characteristics are the steady-state mean and variance of r, given by μr = σr2 = ∞ r =0 ∞ r =1 r pr = ∞ r r p0 r =1 r r 2 p0 k=1 k=1 λk−1 μk λk−1 μk − μr2 (38) (39) Both mean and variance exist.

From the type-[I, 0] state diagram, we see that the steady-state distribution has a band of probability mass concentrated in a curve running internally to the transition diagram. Existence of such mass is reasonable since either an appropriate width or height of the structuring rectangle can discriminate signal from noise. Adaptation is likely to yield a suitable structuring rectangle whose dimensions lie along the concentration of steady-state probability mass. 5 and r1 ≤ 10. The numerically computed steady-state distribution for the type-[II, 1] model is shown in Figure 14.

Figure 20 shows discrete spectra for a triangle from three granulometries: (a) an opening by disks, (b) an opening by horizontal lines, and (c) a τ -opening using horizontal and vertical lines. , 1995). That theory applied only to specialized granular images and did not explicitly involve the GSD. Discrete bandpass approaches have been considered that involve the GSD (Dougherty, 1997; Sivakumar and Goutsias, 1997). Our interest here is in continuous spectra and representation of optimal bandpass Þlters in terms of the GSDs of the signal and the noise.

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