Book contents
- Frontmatter
- Contents
- To the instructor
- Acknowledgements
- 1 Introduction
- 2 Review of mathematical principles
- 3 Writing programs to process images
- 4 Images: Formation and representation
- 5 Linear operators and kernels
- 6 Image relaxation: Restoration and feature extraction
- 7 Mathematical morphology
- 8 Segmentation
- 9 Shape
- 10 Consistent labeling
- 11 Parametric transforms
- 12 Graphs and graph-theoretic concepts
- 13 Image matching
- 14 Statistical pattern recognition
- 15 Clustering
- 16 Syntactic pattern recognition
- 17 Applications
- 18 Automatic target recognition
- Author index
- Index
7 - Mathematical morphology
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- To the instructor
- Acknowledgements
- 1 Introduction
- 2 Review of mathematical principles
- 3 Writing programs to process images
- 4 Images: Formation and representation
- 5 Linear operators and kernels
- 6 Image relaxation: Restoration and feature extraction
- 7 Mathematical morphology
- 8 Segmentation
- 9 Shape
- 10 Consistent labeling
- 11 Parametric transforms
- 12 Graphs and graph-theoretic concepts
- 13 Image matching
- 14 Statistical pattern recognition
- 15 Clustering
- 16 Syntactic pattern recognition
- 17 Applications
- 18 Automatic target recognition
- Author index
- Index
Summary
A man's discourse is like to a rich Persian carpet, the beautiful figures and patterns of which can be shown only by spreading and extending it out; when it is contracted and folded up, they are obscured and lost
PlutarchThe suffix “-ology” means “study of-,” so obviously, “morphology” is the study of morphs; answering critical questions like: “How come they only come out at night, and then fly toward the light?” and “Why is it that bug zappers only toast the harmless critters, leaving the 'skeeters alone?” and – HOLD IT! That's MORPH-ology, the study of SHAPE, not moths! Try again …
Binary morphology
We begin by considering ONLY BINARY images. That's important, remember it! Only binary! We will discuss a couple of operators first. Then, once you understand how they work, we'll explain how they are used in binary images. As an extension to binary morphology, we also describe gray scale morphology operations and the corresponding operators.
Dilation
First, the intuitive definition: The dilation of a (BINARY) image is that same image with all the foreground regions made just a little bit bigger.
Now, formally: We consider two images, fA and fB, and let A and B be sets of ordered pairs, consisting of the coordinates of each foreground pixel in fA and fB, respectively.
Consider one pixel in fB, and its corresponding element (ordered pair) of B, call that element b ∈ B.
- Type
- Chapter
- Information
- Machine Vision , pp. 144 - 180Publisher: Cambridge University PressPrint publication year: 2004