# Image Processing and Mathematical Morphology: Fundamentals and Applications

## Frank Y. Shih

Language: English

Pages: 439

ISBN: 1420089439

Format: PDF / Kindle (mobi) / ePub

In the development of digital multimedia, the importance and impact of image processing and mathematical morphology are well documented in areas ranging from automated vision detection and inspection to object recognition, image analysis and pattern recognition. Those working in these ever-evolving fields require a solid grasp of basic fundamentals, theory, and related applications―and few books can provide the unique tools for learning contained in this text.

**Image Processing and Mathematical Morphology: Fundamentals and Applications** is a comprehensive, wide-ranging overview of morphological mechanisms and techniques and their relation to image processing. More than merely a tutorial on vital technical information, the book places this knowledge into a theoretical framework. This helps readers analyze key principles and architectures and then use the author’s novel ideas on implementation of advanced algorithms to formulate a practical and detailed plan to develop and foster their own ideas. The book:

- Presents the history and state-of-the-art techniques related to image morphological processing, with numerous practical examples
- Gives readers a clear tutorial on complex technology and other tools that rely on their intuition for a clear understanding of the subject
- Includes an updated bibliography and useful graphs and illustrations
- Examines several new algorithms in great detail so that readers can adapt them to derive their own solution approaches

This invaluable reference helps readers assess and simplify problems and their essential requirements and complexities, giving them all the necessary data and methodology to master current theoretical developments and applications, as well as create new ones.

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= (X • B) ° B. (5.2) or Another type of AF is defined as AFB(X) = ((X ° B) • B) ° B (5.3) 57 Basic Morphological Filters or AFB(X) = ((X • B) ° B) • B. (5.4) An ASF is an iterative application of AFB(X) with increasing size of structuring elements, denoted as ASF(X) = AFBN(X)AFBN-1(X) · · · AFB1(X), (5.5) where N is an integer and BN, BN-1, . . . , B1 are structuring elements with decreasing sizes. The BN is constructed by BN = BN-1 B1 for N ≥ 2. (5.6) The ASF offers a method of

Since an OSSM dilation on f at location x, OSSM( f, B, A, k, l)(x), is to choose the lth largest value from f within domain Bx, we can write the descending sort list as [f U, k ‡ f(x), f L], where f U and f L represent upper [greater than f(x)] and lower parts, respectively. It is found that as long as l £ k is satisfied, either a greater value in f U or f(x) will be picked out. Thus, we always have f £ OSSM( f), "x. ᮀ Property 5.11: The OSSM erosion is antiextensive if l £ k, and the origin of

Uniform 3B1A 5B1A MF — — — — k=3 MF — — — — — — 0.9092 0.9357* 1.0071+ 2.4889 2.6974* 2.6974+ 0.3849 0.3468* 0.3766+ 1.031* 1.031+ 0.9092 0.8831* 0.990+ 3.1368* 3.1368+ 2.4889 2.4805* 2.4805+ 0.3374* 0.3374+ 0.3849 0.3111* 0.368+ 0.8831* 2.4805* 2.4805+ 2.2557 2.6075* 2.3886+ 0.368+ 0.8545 0.9009* 0.9276+ 0.964* 1.0376+ 0.8545 0.8691* 0.8912+ 2.7233* 2.8006+ 2.2557 2.5911* 2.2649+ 0.3884* 0.5035+ 0.505 0.3893* 0.4588+ 2.4085* 2.4085+ 2.2557 2.2494* 2.2494+ 0.445+ k=2

pixel and 0 the background pixel. In the first step of applying the erosion by È-2 -1 -2˘ Í ˙ g(1) = Í-1 0 -1˙ , ÍÎ-2 -1 -2˙˚ 146 Image Processing and Mathematical Morphology we have È0 Í0 Í Í0 Í Í0 Í0 Í d = Í0 Í0 Í Í0 Í Í0 Í0 Í Î0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 255 255 255 255 255 1 0 0 0 0 0 0 0 0 0 0˘ 0 0 0 0 0 0 0 0˙˙ 1 1 1 1 1 1 0 0˙ ˙ 255 255 255 255 255 1 0 0˙ 255 255 255 1 1 1 0 0˙ ˙ 255 255 255 1 0 0 0 0˙ 255 2 1 1 0 0 0 0˙ ˙ 255 1 0 0 0 0 0 0˙ ˙ 1 1 0 0 0 0 0

there are n possibilities when dividing ds(p, q). If p is derived from H1, ds(H1, q) should be equal to (Imax - 1)2 + (Imin)2 or (Imax)2 + (Imin - 1)2. Similarly, If p is derived from H3, ds(H3, q) should be equal to (Imax - 1)2 + (Imin)2 or (Imax)2 + (Imin - 1)2. If p is derived from H2, ds(H2, q) should be equal to (Imax - 1)2 + (Imin - 1)2. ᮀ 161 Distance Transformation q FIGURE 6.17 H2 H3 H1 p The relation between p and its parents. 6.6.4 TS1—A Two Scan–Based EDT Algorithm for