Digital Image Processing Methods

Edward R. Dougherty

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9781000148862
• Edition: 1
• Topic: Computer Science
• Subtopic: Digital Media
• Index: Computer Science

This unique reference presents in-depth coverage of the latest methods and applications of digital image processing describing various computer architectures ideal for satisfying specific image processing demands.

1

Nonlinear Filters

Jaakko Astola

Tampere University of Technology
Tampere, Finland

Edward R. Dougherty

Rochester Institute of Technology
Rochester, New York

I. Median Filtering

Semantically, nonlinear filtering concerns all image-to-image operators that are nonlinear, and since digital images do not form a vector space, all image filtering. Nonetheless, insofar as classical linear techniques are adapted to image filtering, linear methods do compose a large segment of image filtering. Moreover, certain types of inherently nonlinear filters have been studied extensively and these concern us in the present chapter.

Linear filters are attractive for several reasons: they possess useful algebraic properties; their operation is easy to understand; via Fourier transform they have a direct relation to frequency representation; their statistical properties are well understood; and there exist elegant, closed-form solutions for finding statistically optimal linear filters. Yet requiring linearity imposes a strong constraint on filter design. Although the linear constraint might be appropriate for some image models, for many it is certainly disadvantageous. The example cited most often is the manner in which linear filters blur edges, which in images often contain key information; on the other hand, median filters, which are nonlinear, leave edges invariant. There any many other instances where linearity is a poor filter requirement, albeit one that is mathematically attractive. As a result, more recently much attention has been focused on the analysis and design of nonlinear filters for accomplishing various image-processing tasks.

The present chapter is broken into two parts. The first considers median filters, and the second, morphological filters. As intuitively conceived, median filters are numerically based, and morphological filters are shape based. Median filters arise from classical maximum-likelihood estimation and from certain operations on logical variables; morphological filters arise from fitting shape probes within larger shapes. Nevertheless, there is a close relation between the types of filtering and they form a unified, coherent theory. We begin with median filters, proceed to stack filters, then to shape-based morphological filters, and...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Series Introduction
• Preface
• Table of Contents
• Contributors
• Introduction
• 1. Nonlinear Filters
• 2. Morphological Segmentation for Textures and Particles
• 3. Multispectral Image Segmentation in Magnetic Resonance Imaging
• 4. Thinning and Skeletonizing
• 5. Syntactic Image Pattern Recognition
• 6. Heuristic Parallel Approach for 3D Articulated Line-Drawing Object Pattern Representation and Recognition
• 7. Handwritten Character Recognition
• 8. Digital Image Compression
• 9. Image-Processing Architectures
• 10. Digital Halftoning
• 11. Glossary of Computer Vision Terms
• Index