# Principles of Digital Image Processing, Volume 2: Core Algorithms

## Wilhelm Burger, Mark J. Burge

Language: English

Pages: 337

ISBN: 2:00260319

Format: PDF / Kindle (mobi) / ePub

This easy-to-follow textbook is the second of three volumes which provide a modern, algorithmic introduction to digital image processing, designed to be used both by learners desiring a firm foundation on which to build, and practitioners in search of critical analysis and concrete implementations of the most important techniques. This volume extends the introductory material presented in the first volume (Fundamental Techniques) with additional techniques that form part of the standard image-processing toolbox.

Features and topics:

* Practical examples and carefully constructed chapter-ending exercises drawn from the authors' years of experience teaching this material

* Real implementations, concise mathematical notation, and precise algorithmic descriptions designed for programmers and practitioners

* Easily adaptable Java code and completely worked-out examples for easy inclusion in existing (and rapid prototyping of new) applications

* Uses ImageJ, the image processing system developed, maintained, and freely distributed by the U.S. National Institutes of Health (NIH)

Provides a supplementary website with the complete Java source code, test images, and corrections – www.imagingbook.com

* Additional presentation tools for instructors including a complete set of figures, tables, and mathematical elements

This thorough, reader-friendly text will equip undergraduates with a deeper understanding of the topic and will be invaluable for further developing knowledge via self-study.

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of holes NL (R) in those regions. NL (R) can be easily computed while finding the inner contours of a region, as described in Sec. 2.2.2. A feature that can be derived from the number of holes is the so-called Euler number NE , which is the diﬀerence between the number of connected 46 2. Regions in Binary Images Figure 2.20 Example of the horizontal projection Phor (v) (right) and vertical projection Pver (u) (bottom) of a binary image. regions NR and the number of their holes NH , NE (R) =

decreases false negatives at the expense of introducing false positives, the reasoning being that it is much simpler to remove false positives during higher-level processing than it is to, in essence, fill in the missing elements eliminated during low-level processing. W. Burger, M.J. Burge, Principles of Digital Image Processing, Undergraduate Topics in Computer Science, DOI 10.1007/978-1-84800-195-4_3, © Springer-Verlag London Limited, 2009 50 3. Detecting Simple Curves Figure 3.1 The

function g¯(x) consists of a single pulse at position 0 whose height corresponds to the original function value g(0) (at position 0). Thus, by multiplying the function g(x) by the impulse function, we obtain a single discrete sample value of g(x) at position x = 0. If the impulse function δ(x) is shifted by a distance x0 , we can sample g(x) at an arbitrary position x = x0 , g¯(x) = g(x) · δ(x−x0 ) = g(x0 ) 0 for x = x0 otherwise. (7.32) Here δ(x−x0 ) is the impulse function shifted by x0 ,

to the angular frequency m ωm = 2π . M 148 7. Introduction to Spectral Techniques As an example, Figs. 7.11 and 7.12 show the discrete basis functions (with integer ordinate values u ∈ Z) for the DFT of length M = 8 as well as their continuous counterparts (with ordinate values x ∈ R). For wave number m = 0, the cosine function C M 0 (u) (Eqn. (7.54)) has the constant value 1. The corresponding DFT coeﬃcient GRe (0)—the real part of G(0)—thus specifies the constant part of the signal or the

multiplication in frequency space requires M 2 operations, independent of the filter size. In addition, certain types of filters are easier to specify in frequency space than in image space; for example, an ideal low-pass filter, which can be described very compactly in frequency space. Further details on filter operations in frequency space can be found, for example, in [28, Sec. 4.4]. 8.5.2 Linear Convolution versus Correlation As described already in Vol. 1 [14, Sec. 5.3], a linear