By Peter W. Hawkes (Eds.)

ISBN-10: 0120147610

ISBN-13: 9780120147618

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, picture technological know-how and electronic snapshot processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in most of these domain names.

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**New PDF release: Aspects of Image Processing and Compression**

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

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**Extra resources for Aspects of Image Processing and Compression**

**Example text**

X−y)∈B1 (x−z)∈B2 f (x − z) + μn (z)} ⎛ ⎞ {k ♦ ( f (x − y) + λ1 (y))} ∪ { f (x − z) + μ1 (z)}, ⎜{k ♦ ( f (x − y) + λ2 (y))} ∪ { f (x − z) + μ2 (z)},⎟ ⎟ = max(k) ⎜ ⎠ (x−y)∈B1 ⎝. . (x−z)∈B2 {k ♦ ( f (x − y) + λn (y))} ∪ { f (x − z) + μn (z)} n ⎛ = max(k) [{k ♦ ( f (x − y) + λi (y))} ∪ { f (x − z) + μi (z)}] (x−y)∈B1 (x−z)∈B2 i=1 26 M. I. VARDAVOULIA, A. GASTERATOS, AND I. ANDREADIS This equation can be expressed in terms of order statistics of the multiset as follows: f ⊕ [α, β, k](x) n = max(k) [max(N) ({k ♦ ( f (x − y) + λi (y))} ∪ { f (x − z) + μi (z)}), i=1 (x−y)∈B1 (x−z)∈B2 (N−1) max (x−y)∈B1 (x−z)∈B2 ({k ♦ ( f (x − y) + λi (y))} ∪ { f (x − z) + μi (z)}), ..

This agrees with the notion of fuzzy ﬁtting, because the structuring element ﬁts better only at these points than at the rest points of the image. Fuzzy erosion quantiﬁes the degree of structuring element ﬁtting. The larger the number of pixels of the structuring element, the more difﬁcult the ﬁtting. Furthermore, fuzzy soft erosion shrinks the image. If fuzzy image A is considered as a noisy version of a binary image (Sinha and Dougherty, 1992), then the object of interest consists of points (0, 1), (0, 2), (0, 3), (0, 4), (1, 1), (1, 2), (1, 3), (1, 4), (2, 1) and (2, 2), and the rest is the background.

D 34 x(16) ... x(1) (a) Maximum k=1 d 33 .. d1 d 69 ... ... d 23 x(28) x(27) ... x(1) d22 .. d1 19th-order statistic k=2 d 57 ... d 12 x(40) x(39) x(38) ... x(1) d 11 .. d1 d 45 ... d1 x(52) x(51) x(50) x(49) ... ... ... x(1) d 57 ... d 47 x(40) ... x(3) x(2) x(1) d 46 ... x(52) ... ... ... x(4) x(3) x(2) x(1) d 45 ... 26th-order statistic k=3 33th-order statistic k=4 (b) 45 d 81 ... d 49 x(12) ... x(1) d 48 ... ... d1 d 69 ... d 48 x(20) ... Minimum k=1 x(2) x(1) d47 ... ...

### Aspects of Image Processing and Compression by Peter W. Hawkes (Eds.)

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