Advances in Imaging and Electron Physics, Vol. 126 by Peter W. Hawkes

By Peter W. Hawkes

The 4 surveys contained during this quantity illustrate greatly various facets of imaging and electron physics. the 1st chapters tackle purposes of electron microscopy, together with the function of this system in mineralogy and a research of the excessive- answer electron microscopy of quasicrystals. The latter is admittedly a quick monograph featuring the underlying crystallography and explaining intimately how the corresponding photos and diffraction styles can be interpreted. The 3rd contribution is an account of a brand new method of deconvolution in photograph processing within which the writer, by means of associating a polynomial with the gray-level values of (discrete) pictures, indicates that it truly is attainable to invert the convolutional relation that describes many types of picture formation. the amount ends with a close dialogue of the twin de Broglie wave, together with a severe account of latest advancements within the debate over the lifestyles and position of any such wave.

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ARNE impressive: for Áx > supða1 ; a2 Þ, the magnitudes of BH ¼ 1=3 (x) are found uncorrelated. D. Using the 2D WTMM Method to Perform Image Processing Tasks We now want to discuss the ability to use the WTMM method for specific purposes in image processing. We refer the reader to previous work [108] for edge detection and image denoising applications, and also to the work of Levy-Vehel [168,169] for previous attempts to use multifractal concepts for image analysis. In this subsection, we want to address a specific image processing segmentation problem that will be helpful when dealing with medical applications in Section VI.

15) from those that satisfy Eq. (17) and that are wavelet dependent. This is done by increasing the order of the analyzing wavelet; for n large enough, the spurious maxima lines are suppressed by a simple thresholding on M at the smallest scale amin . Their roots are definitely rejected as misleading singularity locations.  Step 3: Computation of the multifractal spectrum. According to Eq. (21), one uses the wavelet transform skeleton to compute the partition function Zðq; aÞ on the discrete set of considered scales amin a amax .

18). (a) f2 ðxÞ as coded using 32 gray levels from white (min f2 ) to black (max f2 ). The maxima chains (solid line) and the WTMMM () are shown for the following values of the scale parameter a ¼ 2 (b), 28 (c), and 211 (d) in w units. Same first-order analyzing wavelet as in Figure 3. Example 2. Anisotropic singularity. Let us illustrate with a specific example, the possibility for a function f2 ðxÞ to display anisotropic local scale invariance with respect to isotropic dilations. In Figure 7a the following function is represented: f2 ðxÞ ¼ f2 ð; Þ ¼ ÀhðÞ ð18Þ hðÞ ¼ 0:3 sin ð À 2=3Þ þ 0:5 ð19Þ with The exponent hðÞ is nothing but the Ho¨lder exponent at  ¼ 0 of the 1D profile obtained when intersecting the image in Figure 7a along the direction .

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