Digital Image Processing - University of Cyprus

1 Rafael C. GonzalezUniversity of TennesseeRichard E. WoodsMedData InteractiveSteven L. EddinsThe MathWorks, Saddle River, NJ 07458 Digital ImageProcessingUsing MATLAB Library of Congress Cataloging-in-Publication Data on FileVice President and Editorial Director, ECS:Marcia HortonVice President and Director of Production and Manufacturing, ESM:David W. RiccardiPublisher:Tom RobbinsEditorial Assistant:Carole SnyderExecutive Managing Editor:Vince O BrienManaging Editor:David A. GeorgeProduction Editor:Rose KernanDirector of Creative Services:Paul BelfantiCreative Director:Carole AnsonArt Director:Jayne ConteCover Designer:Richard E.

2 WoodsArt Editor:Xiaohong ZhuManufacturing Manager:Trudy PisciottiManufacturing Buyer:Lisa McDowellSenior Marketing Manager:Holly Stark 2004 by Pearson Education, Prentice-HallPearson Education, Saddle River, New Jersey 07458 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means,without permission in writing from the Prentice Hall is a trademark of Pearson Education, is a registered trademark of The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098 The author and publisher of this book have used their best efforts in preparing this book.

3 These efforts include the development, research, and testing of the theories and programs to determine their author and publisher shall not be liable in any event for incidental or consequential damages with, or arising out of, the furnishing, performance, or use of these in the United States of America10987654321 ISBN 0-13-008519-7 Pearson Education Ltd.,LondonPearson Education Australia Pty., Ltd.,SydneyPearson Education Singapore, Pte. Education North Asia Ltd.,Hong KongPearson Education Canada, Inc.,TorontoPearson Education de Mexico, de Education Japan,To ky oPearson Education Malaysia, Pte.

4 Education, Inc.,Upper Saddle River, New Jersey653 Intensity Transformationsand Spatial FilteringPreviewThe term spatial domainrefers to the Image plane itself, and methods in this cat-egory are based on direct manipulation of pixels in an Image . In this chapter wefocus attention on two important categories of spatial domain Processing :intensity(or gray-level) transformationsand spatial filtering. The latter approachsometimes is referred to as neighborhood Processing , or spatial following sections we develop and illustrate MATLAB formulations repre-sentative of Processing techniques in these two categories.

5 In order to carry aconsistent theme, most of the examples in this chapter are related to Image en-hancement. This is a good way to introduce spatial Processing because enhance-ment is highly intuitive and appealing, especially to beginners in the field. As willbe seen throughout the book, however, these techniques are general in scope andhave uses in numerous other branches of Digital Image noted in the preceding paragraph, spatial domain techniques operate di-rectly on the pixels of an Image . The spatial domain processes discussed in thischapter are denoted by the expressionwhere is the input Image ,is the output (processed) Image , andTis an operator on defined over a specified neighborhood about pointIn addition,Tcan operate on a set of images, such as performing the ad-dition of Kimages for noise principal approach for defining spatial neighborhoods about a pointis to use a square or rectangular region centered at as Fig.

6 Center of the region is moved from pixel to pixel starting, say, at the top, left1x, y2,1x, y21x, ,g1x, y2f1x, y2g1x, y2=T3f1x, 3 Intensity Transformations and Spatial FilteringyxOrigin(x, y) Image f(x, y)FIGURE ofsize about apoint in , y23*3corner, and, as it moves, it encompasses different neighborhoods. Operator Tisapplied at each location to yield the output,g, at that location. Only thepixels in the neighborhood are used in computing the value of gat .The remainder of this chapter deals with various implementations of thepreceding equation.

7 Although this equation is simple conceptually, its compu-tational implementation in MATLAB requires that careful attention be paidto data classes and value Transformation FunctionsThe simplest form of the transformation Tis when the neighborhood inFig. is of size (a single pixel). In this case, the value of gat de-pends only on the intensity of at that point, and Tbecomes an intensityorgray-leveltransformation function. These two terms are used interchangeably,when dealing with monochrome ( , gray-scale) images.

8 When dealing withcolor images, the term intensityis used to denote a color Image component incertain color spaces, as described in Chapter they depend only on intensity values, and not explicitly on intensity transformation functions frequently are written in simplified form aswhere rdenotes the intensity of and sthe intensity of g, both at any corre-sponding point in the imadjustFunction imadjustis the basic IPT tool for intensity transformations of gray-scale images. It has the syntaxg = imadjust(f, [low_in high_in], [low_out high_out], gamma)As illustrated in Fig.

9 , this function maps the intensity values in Image fto new values in g, such that values between low_inand high_inmap to1x, y2fs=T1r21x, y2,f1x, y21* , y21x, Intensity Transformation Functions67low_inhigh_inlow_outhigh_outl ow_inhigh_inlow_inhigh_ingamma 1gamma 1gamma 1 FIGURE mappingsavailable :Using between low_outand high_out. Values below low_inand abovehigh_inare clipped; that is, values below low_inmap to low_out, and thoseabove high_inmap to high_out. The input Image can be of class uint8,uint16, or double, and the output Image has the same class as the input.

10 Allinputs to function imadjust, other than f, are specified as values between 0and 1, regardless of the class of f. If fis of class uint8,imadjustmultipliesthe values supplied by 255 to determine the actual values to use; if fis of classuint16, the values are multiplied by 65535. Using the empty matrix ([]) for[low_in high_in]or for [low_out high_out]results in the default values[0 1]. If high_outis less than low_out, the output intensity is gammaspecifies the shape of the curve that maps the intensityvalues in fto create g. If gammais less than 1, the mapping is weighted towardhigher (brighter) output values, as Fig.