By Peter W. Hawkes (Eds.)

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 aspects prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, photograph technology and electronic photo processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in these kind of domain names.

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PE i1... i8 L**1 F/F L2 F/F CONTROL UNIT b9 b1 r0 MODE L11 ... k . . r1 t 1 L**4 . . r8 t 8 L**11 o1 PE o8 L*4 . . o9 L*11 pi : image data si : structuring element data di :dummy numbers Figure 10. Systolic array hardware structure implementing the majority gate technique for soft morphological filtering. L*12 o 42 M. I. VARDAVOULIA, A. GASTERATOS, AND I. ANDREADIS TABLE 1 Use of Dummy Numbers in the Computation of Weight Order Statistics k Sequence of numbers Dummy numbers 1 2 3 4 9 10 11 12 8 7 6 5 latches (L∗ 1) store the structuring element, and latch (L∗∗ 1) stores the number k.

GASTERATOS, AND I. 5 Antiextensivity–Extensivity Fuzzy soft opening is not antiextensive. If it were antiextensive, then μ A ◦ [B1 ,B2 ,k] (x) ≤ μ A (x), ∀x ∈ Z 2 . The following example shows that ∃x ∈ Z 2 | μ A ◦ [B1 ,B2 ,k] (x) > μ A (x). 3 Consider the image A and the structuring element B for k = 2. 2 which means that fuzzy soft opening is not antiextensive. Similarly, it can be shown that, in general, fuzzy soft closing is not extensive: ∃x ∈ Z 2 and A,B ⊂ Z 2 |μ A•[B1 ,B2 ,k] (x) < μ A (x).

The central value corresponds to its core and it is equal to 30. Additionally, it denotes the origin. The four remaining values belong to its soft boundary and they are equal to 20. From both Figures 1a and b it is obvious that the greater the value of the order index, the better the fitting. D. Vector Soft Morphology for Color Image Processing In this section an approach to soft color image mathematical morphology is presented. E in the same way that gray-scale soft morphology extends the grayscale standard morphology theory.

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