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			<revisedBy>Mona Zeftel</revisedBy>
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					<b>
						<c val="#008080">IMAGE PROCESSING EXTENSION PACK</c>
					</b>
				</p>
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						<b>
							<c val="#800080">Introduction to Image Processing</c>
						</b>
					</f>
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						<b>
							<c val="#800080">in Mathcad</c>
						</b>
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				<phrase>image processing, introduction</phrase>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Image processing is the science or art of taking images and transforming them into other images. Sometimes this makes a picture clearer, removing distortions and highlighting important features. Sometimes this makes a picture sharper or more aesthetically pleasing - artists use image filters all the time to enhance certain aspects of a picture or to make it fit into a larger design. Sometimes image processing is not concerned with the appearance of the final image at all, but rather with the levels of color or intensity components, which is useful in analysis.</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Image processing and analysis is also a means of extracting quantitative information from images as well as a means of detecting and measuring objects in images.</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The goal of this book is to give you some insight into what sorts of functions exist to perform image processing (in particular, the ones implemented in this Extension Pack), how they work, and what kind of output you can expect from a given image. There are also some application examples, showing you the variety of work which is done using these techniques.</p>
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					<b>
						<c val="#800000">Images in Mathcad</c>
					</b>
				</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Digitized images can be stored in many formats, but generally they all contain a matrix of numbers representing the gray level or color of each pixel in the image. Mathcad stores images in ordinary Mathcad matrices, with the position (row, column) in the matrix corresponding to the pixel position of the image, and the value in that position corresponding to the gray or color level of the image. <f family="Times New Roman" charset="0">
						<inlineAttr font-weight="normal" line-through="false">One advantage of Mathcad as an image-processing tool is that all of Mathcad's matrix operations and numerics are available for analyzing and transforming images stored in matrix form. There are many examples in this Extension Pack that illustrate the power of combining Mathcad</inlineAttr>
					</f>'s built-in functions with your new image-processing functions.</p>
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				<phrase>image matrix</phrase>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The eight-bit scale for levels of gray that is used in many bitmap images goes from 0 to 255; that is, using eight bits, there are 2<f family="Times New Roman" charset="0" size="12">
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							<sup>8</sup>
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					</f> = 256 possible intensity levels. For example, a grayscale image of a white square in a black square would be written as</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">For information on how to view this image in Mathcad, see the section on <f family="Times New Roman" charset="0">
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							<u>
								<inlineAttr line-through="false">The Mathcad Image Viewer</inlineAttr>
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						</b>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Color bitmap images work on the same principle, but there are three matrices contained within the image matrix. The first corresponds to the values (0 to 255) of the reds in the picture, the second to the greens, and the third to the blues. So, for example, if you wanted to construct the same white square in a black border out of colors, the matrix would be:</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Keep in mind that this image is in <b>24-bit color</b>. This means that each pixel requires a full 24 bits of information to record all the color information (red, green, and blue). If your screen is only displaying 8-bit color (a total of 256 colors) or 15-bit color (about 32 thousand colors), the monitor averages the exact 24-bit colors (there are over 16 million of them) to some (we hope) acceptable palette of 256.</p>
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				<phrase>24-bit color</phrase>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Many Mathcad functions and the Image Viewer can also handle grayscale and color images with other values in them besides 8-bit integers, including arbitrarily large, floating point, and even negative numbers. Keep in mind that they are converted to 8-bit integers for display (see section on the viewer for more information), and that you may not be able to write them out as image files.</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Armed with this information, and instructions on the viewer contained in the next section, you are ready to go exploring in this package. So, welcome to the Mathcad image-processing workshop. We hope you examine the included images, as well as some of your own, while learning about the functions and forms of image processing.</p>
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					<b>
						<c val="#800000">A Note </c>
					</b>
					<b>
						<c val="#800000">about Display Drivers</c>
					</b>
				</p>
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				<phrase>display drivers</phrase>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Your computer will do some palette adjustment if you are displaying less than full 24-bit color. You may actually need to set your video display driver for optimal viewing of images using the functions in this Extension Pack. We recommend that you set your display to at least 256 colors. Check Control Panel &gt; Display in your Start menu. </p>
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					<b>
						<c val="#800000">A Note </c>
					</b>
					<b>
						<c val="#800000">about Memory</c>
					</b>
				</p>
			</text>
			<indexes>
				<phrase>memory requirements</phrase>
			</indexes>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Keep in mind as you work that large matrices take a lot of storage space, and <f family="Times New Roman" charset="0">
						<inlineAttr font-weight="normal" line-through="false">Mathcad</inlineAttr>
					</f> needs to store these matrices in RAM while you are working on them. (For those of you who are interested, <f family="Times New Roman" charset="0">
						<inlineAttr font-weight="normal" line-through="false">Mathcad stores all matrix values in double floating-point precision.) Displaying images in the Mathcad</inlineAttr>
					</f> Image Viewer likewise places demands on memory. If you have the minimum amount of RAM required, we recommend that you increase the size of the swap space (consult your User's Guide for Microsoft Windows) to 12 MB - 20 MB, as much as your system will allow. If you are able also to increase the amount of RAM in your system, the performance will improve accordingly. The larger swap space and/or available RAM allows you to process larger images, view multiple images at one time, and do more extensive processing operations.</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Here is a hint for conserving memory while you use this Extension Pack:</p>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Where possible, avoid storing the results of intermediate image-processing calculations in separate matrices. Every matrix you create in <f family="Times New Roman" charset="0">
						<inlineAttr font-weight="normal" line-through="false">Mathcad</inlineAttr>
					</f> adds to the storage space required.</p>
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					<b>
						<c val="#800000">Production Staff</c>
					</b>
				</p>
			</text>
		</region>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The following individuals contributed to the creation of the <b>Image Processing Extension Pack</b>: Dan Slater, Leslie Bondaryk, Frank Purcell, David Blair, Paul Lorczak, Kelly Johnson, Bo Shen, Tino Lichauco, Dan Lepow, Vikram Chalana, Qin Cai, and Jennifer Hodgdon. Thanks to Greg Aharonian for his coding work. We thank Drs. Margaret Mortz, John Reid, Michael Wegener, and Martin Zombeck for reviewing early versions of this product and contributing to this E-book.</p>
			</text>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="9">
						<b>Copyright © 2007 Parametric Technology Corporation. All Rights Reserved.</b>
					</f>
				</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="9">User and training documentation from Parametric Technology Corporation and its subsidiary companies (collectively “PTC”) are subject to the copyright laws of the United States and other countries and is provided under a license agreement that restricts copying, disclosure, and use of such documentation. PTC hereby grants to the licensed user the right to make copies in printed form of this documentation if provided on software media, but only for internal/personal use and in accordance with the license agreement under which the applicable software is licensed. Any copy made shall include the PTC copyright notice and any other proprietary notice provided by PTC. This documentation may not be disclosed, transferred, modified, or reduced to any form, including electronic media, or transmitted or made publicly available by any means without the prior written consent of PTC and no authorization is granted to make copies for such purposes.</f>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="9">Information described herein is furnished for general information only, is subject to change without notice, and should not be construed as a warranty or commitment by PTC. PTC assumes no responsibility or liability for any errors or inaccuracies that may appear in this document.</f>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="9">The software described in this document is provided under written license agreement, contains valuable trade secrets and proprietary information, and is protected by the copyright laws of the United States and other countries. It may not be copied or distributed in any form or medium, disclosed to third parties, or used in any manner not provided for in the software licenses agreement except with written prior approval from PTC. </f>
				</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="9">UNAUTHORIZED USE OF SOFTWARE OR ITS DOCUMENTATION CAN RESULT IN CIVIL DAMAGES AND CRIMINAL PROSECUTION.</f>
				</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="9">
						<b>Important Copyright, Trademark, Patent, and Licensing Information</b>
					</f>
				</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="9">On the Reference Documents page at http://www.ptc.com/appserver/cs/doc/refdoc.jsp, select Legal for the product and PTC Copyright for the document type. Alternatively, click Help &gt; About on your product’s main menu. </f>
				</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="9">
						<b>UNITED STATES GOVERNMENT RESTRICTED RIGHTS LEGEND</b>
					</f>
				</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<f size="9">This document and the software described herein are Commercial Computer Documentation and Software, pursuant to FAR 12.212(a)-(b) (OCT’95) or DFARS 227.7202-1(a) and 227.7202-3(a) (JUN’95), and are provided to the US Government under a limited commercial license only. For procurements predating the above clauses, use, duplication, or disclosure by the Government is subject to the restrictions set forth in subparagraph (c)(1)(ii) of the Rights in Technical Data and Computer Software Clause at DFARS 252.227 7013 (OCT’88) or Commercial Computer Software-Restricted Rights at FAR 52.227 19(c)(1)-(2) (JUN’87), as applicable. 00002007</f>
				</p>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
					<b>
						<f size="9">Parametric Technology Corporation, 140 Kendrick Street, Needham, MA 02494 USA</f>
					</b>
				</p>
			</text>
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