Matlab_UserGuide图像处理工具箱.pdf

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Preface

What Is the Image Processing Toolbox?

Related Products

Configuration Notes

About the Documentation

Structure of the Documentation

Image Credits

Terminology

MATLAB Newsgroup

Typographical Conventions

Image Processing Demos

Getting Started

Example 1 — Some Basic Topics

1. Read and Display an Image

2. Check the Image in Memory

3. Perform Histogram Equalization

4. Write the Image

5. Check the Contents of the Newly Written File

Example 2 — Advanced Topics

1. Read and Display an Image

2. Use Morphological Opening to Estimate the Background

3. Display the Background Approximation as a Surface

4. Subtract the Background Image from the Original Image

5. Adjust the Image Contrast

6. Apply Thresholding to the Image

7. Determine the Number of Objects in the Image

8. Examine the Label Matrix

9. Measure Object Properties in the Image

10. Compute Statistical Properties of Objects in the Image

Where to Go from Here

Online Help

Toolbox Demos

Introduction

Terminology

Images in MATLAB and the Image Processing Toolbox

Storage Classes in the Toolbox

Image Types in the Toolbox

Indexed Images

Intensity Images

Binary Images

RGB Images

Multiframe Image Arrays

Summary of Image Types and Numeric Classes

Converting Image Types

Working with Image Data

Reading a Graphics Image

Writing a Graphics Image

Querying a Graphics File

Converting Image Storage Classes

Converting Graphics File Formats

Image Arithmetic

Summary of Image Arithmetic Functions

Image Arithmetic Truncation Rules

Adding Images

Subtracting Images

Multiplying Images

Dividing Images

Nesting Calls to Image Arithmetic Functions

Coordinate Systems

Pixel Coordinates

Spatial Coordinates

Displaying and Printing Images

Terminology

Displaying Images

Displaying Indexed Images

Displaying Intensity Images

Displaying Binary Images

Displaying RGB Images

Displaying Images Directly from Disk

Special Display Techniques

Adding a Colorbar

Displaying Multiframe Images

Displaying Multiple Images

Setting Toolbox Display Preferences

Toolbox Preferences

Using the truesize Function

Zooming in on a Region of an Image

Zooming In or Out with the Zoom Buttons

Zooming In or Out from the Command Line

Texture Mapping

Printing Images

Troubleshooting

Spatial Transformations

Terminology

Interpolation

Image Types

Image Resizing

Specifying the Size of the Output Image

Specifying the Interpolation Method

Using Filters to Prevent Aliasing

Image Rotation

Specifying the Interpolation Method

Specifying the Size of the Output Image

Image Cropping

Performing General Spatial Transformations

Specifying the Transformation Type

Performing the Transformation

Advanced Spatial Transformation Techniques

Image Registration

Terminology

Registering an Image

Point Mapping

Example: Registering to a Digital Orthophoto

Types of Supported Transformations

Selecting Control Points

Using the Control Point Selection Tool

Starting the Control Point Selection Tool

Viewing the Images

Specifying Matching Control Point Pairs

Saving Control Points

Using Correlation to Improve Control Points

Neighborhood and Block Operations

Terminology

Block Processing Operations

Types of Block Processing Operations

Sliding Neighborhood Operations

Padding Borders

Linear and Nonlinear Filtering

Distinct Block Operations

Overlap

Column Processing

Sliding Neighborhoods

Distinct Blocks

Linear Filtering and Filter Design

Terminology

Linear Filtering

Convolution

Correlation

Filtering Using imfilter

Using Predefined Filter Types

Filter Design

FIR Filters

Frequency Transformation Method

Frequency Sampling Method

Windowing Method

Creating the Desired Frequency Response Matrix

Computing the Frequency Response of a Filter

Transforms

Terminology

Fourier Transform

Definition of Fourier Transform

Discrete Fourier Transform

Applications

Discrete Cosine Transform

The DCT Transform Matrix

The DCT and Image Compression

Radon Transform

Using the Radon Transform to Detect Lines

The Inverse Radon Transform

Morphological Operations

Terminology

Dilation and Erosion

Understanding Dilation and Erosion

Structuring Elements

Dilating an Image

Eroding an Image

Combining Dilation and Erosion

Dilation- and Erosion-Based Functions

Morphological Reconstruction

Marker and Mask

Pixel Connectivity

Flood-Fill Operations

Finding Peaks and Valleys

Distance Transform

Example: Marker-Controlled Watershed Segmentation

Step 1: Read in Images

Step 2: Create the Structuring Element

Step 3: Enhance the Image Contrast

Step 4: Exaggerate the Gaps Between Objects

Step 5: Convert Objects of Interest

Step 6: Detect Intensity Valleys

Step 7: Watershed Segmentation

Step 8: Extract Features from Label Matrix

Objects, Regions, and Feature Measurement

Connected-Component Labeling

Selecting Objects in a Binary Image

Finding the Area of Binary Images

Finding the Euler Number of a Binary Image

Lookup Table Operations

Analyzing and Enhancing Images

Terminology

Pixel Values and Statistics

Pixel Selection

Intensity Profile

Image Contours

Image Histogram

Summary Statistics

Region Property Measurement

Image Analysis

Edge Detection

Quadtree Decomposition

Image Enhancement

Intensity Adjustment

Noise Removal

Region-Based Processing

Terminology

Specifying a Region of Interest

Selecting a Polygon

Other Selection Methods

Filtering a Region

Filling a Region

Image Deblurring

Terminology

Understanding Deblurring

Causes of Blurring

Deblurring Model

Using the Deblurring Functions

Deblurring with the Wiener Filter

Deblurring with a Regularized Filter

Deblurring with the Lucy-Richardson Algorithm

Deblurring with the Blind Deconvolution Algorithm

Creating Your Own Deblurring Functions

Avoiding Ringing in Deblurred Images

Color

Terminology

Working with Different Screen Bit Depths

Determining Your Systems Screen Bit Depth

Choosing a Screen Bit Depth

Reducing the Number of Colors in an Image

Using rgb2ind

Reducing Colors in an Indexed Image

Dithering

Converting to Other Color Spaces

NTSC Color Space

YCbCr Color Space

HSV Color Space

Function Reference

Functions – By Category

Image Input, Output, and Display

Spatial Transformation and Registration

Image Analysis and Statistics

Image Enhancement and Restoration

Linear Filtering and Transforms

Morphological Operations

Region-Based, Neighborhood, and Block Processing

Colormap and Color Space Functions

Miscellaneous Functions

Functions – Alphabetical List

applylut

bestblk

blkproc

brighten

bwarea

bwareaopen

bwdist

bweuler

bwfill

bwhitmiss

bwlabel

bwlabeln

bwmorph

bwpack

bwperim

bwselect

bwulterode

bwunpack

checkerboard

cmpermute

cmunique

col2im

colfilt

colorbar

conndef

conv2

convmtx2

convn

corr2

cp2tform

cpcorr

cpselect

cpstruct2pairs

dct2

dctmtx

deconvblind

deconvlucy

deconvreg

deconvwnr

dicominfo

dicomread

dicomwrite

dilate

dither

double

edge

edgetaper

erode

fft2

fftn

fftshift

filter2

findbounds

fliptform

freqspace

freqz2

fsamp2

fspecial

ftrans2

fwind1

fwind2

getheight

getimage

getneighbors

getnhood

getsequence

gray2ind

grayslice

graythresh

histeq

hsv2rgb

idct2

ifft2

ifftn

im2bw

im2col

im2double

im2java

im2uint8

im2uint16

imabsdiff

imadd

imadjust

imapprox

imbothat

imclearborder

imclose

imcomplement

imcontour

imcrop

imdilate

imdivide

imerode

imextendedmax

imextendedmin

imfeature

imfill

imfilter

imfinfo

imhist

imhmax

imhmin

imimposemin

imlincomb

immovie

immultiply

imnoise

imopen

impixel

improfile

imread

imreconstruct

imregionalmax

imregionalmin

imresize

imrotate

imshow

imsubtract

imtophat

imtransform

imwrite

ind2gray

ind2rgb

iptgetpref

iptsetpref

iradon

isbw

isflat

isgray

isind

isrgb

label2rgb

makelut

makeresampler

maketform

mat2gray

mean2

medfilt2

montage

nlfilter

normxcorr2

ntsc2rgb

ordfilt2

otf2psf

padarray

phantom

pixval

psf2otf

qtdecomp

qtgetblk

qtsetblk

radon

reflect

regionprops

rgb2gray

rgb2hsv

rgb2ind

rgb2ntsc

rgb2ycbcr

rgbplot

roicolor

roifill

roifilt2

roipoly

std2

strel

stretchlim

subimage

tformarray

tformfwd

tforminv

translate

truesize

uint8

uint16

warp

watershed

wiener2

ycbcr2rgb

zoom

Index

Image Processing Toolbox For Use with MATLAB® Computation Visualization Programming User’s Guide Version 3

How to Contact The MathWorks: www.mathworks.com comp.soft-sys.matlab Web Newsgroup support@mathworks.com suggest@mathworks.com bugs@mathworks.com doc@mathworks.com service@mathworks.com info@mathworks.com Technical support Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 508-647-7001 The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 Phone Fax Mail For contact information about worldwide offices, see the MathWorks Web site. Image Processing Toolbox User’s Guide  COPYRIGHT 1993 - 2002 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro- duced in any form without prior written consent from The MathWorks, Inc. FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by or for the federal government of the United States. By accepting delivery of the Program, the government hereby agrees that this software qualifies as "commercial" computer software within the meaning of FAR Part 12.212, DFARS Part 227.7202-1, DFARS Part 227.7202-3, DFARS Part 252.227-7013, and DFARS Part 252.227-7014. The terms and conditions of The MathWorks, Inc. Software License Agreement shall pertain to the government’s use and disclosure of the Program and Documentation, and shall supersede any conflicting contractual terms or conditions. If this license fails to meet the government’s minimum needs or is inconsistent in any respect with federal procurement law, the government agrees to return the Program and Documentation, unused, to MathWorks. MATLAB, Simulink, Stateflow, Handle Graphics, and Real-Time Workshop are registered trademarks, and TargetBox is a trademark of The MathWorks, Inc. Other product or brand names are trademarks or registered trademarks of their respective holders. Printing History: August 1993 First printing Version 1 Second printing Version 2 May 1997 Online only January 1998 January 1999 Online only September 2000 Online only April 2001 June 2001 July 2002 Third printing Online only Online only Revised for Version 2.1 Revised for Version 2.2 (Release 11) Revised for Version 2.2.2 (Release 12) Revised for Version 3.0 Revised for Version 3.1 (Release 12.1) Revised for Version 3.2 (Release 13)

Contents Preface What Is the Image Processing Toolbox? . . . . . . . . . . . . . . . . . . xii Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Configuration Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv About the Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Structure of the Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . xv Image Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii MATLAB Newsgroup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii Typographical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Image Processing Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx 1 Getting Started Example 1 — Some Basic Topics . . . . . . . . . . . . . . . . . . . . . . . . 1-2 1. Read and Display an Image . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 2. Check the Image in Memory . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3 3. Perform Histogram Equalization . . . . . . . . . . . . . . . . . . . . . . 1-4 4. Write the Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7 5. Check the Contents of the Newly Written File . . . . . . . . . . . 1-7 Example 2 — Advanced Topics . . . . . . . . . . . . . . . . . . . . . . . . . 1-9 1. Read and Display an Image . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9 2. Use Morphological Opening to Estimate the Background . . 1-9 3. Display the Background Approximation as a Surface . . . . . 1-10 i

4. Subtract the Background Image from the Original Image . 1-12 5. Adjust the Image Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13 6. Apply Thresholding to the Image . . . . . . . . . . . . . . . . . . . . . 1-14 7. Determine the Number of Objects in the Image . . . . . . . . . 1-15 8. Examine the Label Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-16 9. Measure Object Properties in the Image . . . . . . . . . . . . . . . 1-18 10. Compute Statistical Properties of Objects in the Image . . 1-21 Where to Go from Here . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23 Online Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23 Toolbox Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23 2 Introduction Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Images in MATLAB and the Image Processing Toolbox . . . 2-4 Storage Classes in the Toolbox . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4 Image Types in the Toolbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Indexed Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Intensity Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7 Binary Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8 RGB Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8 Multiframe Image Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11 Summary of Image Types and Numeric Classes . . . . . . . . . . . 2-12 Converting Image Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12 Working with Image Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-15 Reading a Graphics Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16 Writing a Graphics Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17 Querying a Graphics File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-18 Converting Image Storage Classes . . . . . . . . . . . . . . . . . . . . . . 2-19 Converting Graphics File Formats . . . . . . . . . . . . . . . . . . . . . . 2-20 Image Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21 ii Contents

Summary of Image Arithmetic Functions . . . . . . . . . . . . . . . . 2-22 Image Arithmetic Truncation Rules . . . . . . . . . . . . . . . . . . . . . 2-22 Adding Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-23 Subtracting Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-24 Multiplying Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25 Dividing Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27 Nesting Calls to Image Arithmetic Functions . . . . . . . . . . . . . 2-27 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28 Pixel Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28 Spatial Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29 3 Displaying and Printing Images Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 Displaying Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3 Displaying Indexed Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3 Displaying Intensity Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4 Displaying Binary Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6 Displaying RGB Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10 Displaying Images Directly from Disk . . . . . . . . . . . . . . . . . . . 3-11 Special Display Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12 Adding a Colorbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12 Displaying Multiframe Images . . . . . . . . . . . . . . . . . . . . . . . . . 3-13 Displaying Multiple Images . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-17 Setting Toolbox Display Preferences . . . . . . . . . . . . . . . . . . . 3-23 Toolbox Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23 Using the truesize Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-24 Zooming in on a Region of an Image . . . . . . . . . . . . . . . . . . . 3-26 Zooming In or Out with the Zoom Buttons . . . . . . . . . . . . . . . . 3-26 Zooming In or Out from the Command Line . . . . . . . . . . . . . . 3-26 iii

Texture Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-28 Printing Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-29 Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-30 Spatial Transformations Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 Image Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4 Image Resizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5 Specifying the Size of the Output Image . . . . . . . . . . . . . . . . . . 4-5 Specifying the Interpolation Method . . . . . . . . . . . . . . . . . . . . . 4-6 Using Filters to Prevent Aliasing . . . . . . . . . . . . . . . . . . . . . . . . 4-6 Image Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8 Specifying the Interpolation Method . . . . . . . . . . . . . . . . . . . . . 4-8 Specifying the Size of the Output Image . . . . . . . . . . . . . . . . . . 4-9 Image Cropping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10 Performing General Spatial Transformations . . . . . . . . . . . 4-12 Specifying the Transformation Type . . . . . . . . . . . . . . . . . . . . . 4-12 Performing the Transformation . . . . . . . . . . . . . . . . . . . . . . . . 4-14 Advanced Spatial Transformation Techniques . . . . . . . . . . . . 4-15 Image Registration Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 4 5 iv Contents

Registering an Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4 Point Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4 Example: Registering to a Digital Orthophoto . . . . . . . . . . . . . . 5-6 Types of Supported Transformations . . . . . . . . . . . . . . . . . . 5-13 Selecting Control Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-15 Using the Control Point Selection Tool . . . . . . . . . . . . . . . . . . . 5-15 Starting the Control Point Selection Tool . . . . . . . . . . . . . . . . . 5-16 Viewing the Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-18 Specifying Matching Control Point Pairs . . . . . . . . . . . . . . . . . 5-22 Saving Control Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-30 Using Correlation to Improve Control Points . . . . . . . . . . . 5-33 Neighborhood and Block Operations 6 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2 Block Processing Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-3 Types of Block Processing Operations . . . . . . . . . . . . . . . . . . . . 6-3 Sliding Neighborhood Operations . . . . . . . . . . . . . . . . . . . . . . 6-5 Padding Borders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-6 Linear and Nonlinear Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . 6-6 Distinct Block Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-9 Overlap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-10 Column Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-12 Sliding Neighborhoods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-12 Distinct Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-13 v

7 8 Linear Filtering and Filter Design Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2 Linear Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-6 Filtering Using imfilter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7 Using Predefined Filter Types . . . . . . . . . . . . . . . . . . . . . . . . . 7-14 Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-16 FIR Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-16 Frequency Transformation Method . . . . . . . . . . . . . . . . . . . . . 7-17 Frequency Sampling Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-18 Windowing Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-19 Creating the Desired Frequency Response Matrix . . . . . . . . . 7-20 Computing the Frequency Response of a Filter . . . . . . . . . . . . 7-21 Transforms Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2 Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3 Definition of Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . 8-3 Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-8 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-11 Discrete Cosine Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-16 The DCT Transform Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-17 The DCT and Image Compression . . . . . . . . . . . . . . . . . . . . . . 8-18 Radon Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-20 Using the Radon Transform to Detect Lines . . . . . . . . . . . . . . 8-24 The Inverse Radon Transform . . . . . . . . . . . . . . . . . . . . . . . . . 8-26 vi Contents

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