Msualization of the Reliability inGlassified Remotely Sensed lmages

Peter F. Fisher

AbstractMuch research has been concentrated on studies of the na-ture and cause of unreliability in classifying remotely sensedimages, particularly those derived ftom the Landsat series ofsatellites. This paper presents a methodologt to allow q vq-riety of measwes of that accurocy (Overall Accuracy, Userand Producer Accuracy, and Classification Accuracy) to beembedded in the display of the classified image, The princi-ple is that, as the image is displayed on a computer screen,pixels are randomly selected and the cover type at that loca-tion is rc-displayed according to algorithms listed here. Theresulting displays are fundamentdly dynamic, althoughstatic images are used to illustrate the paper. It is believedthat the method gives a new dimension to the visuakzationof classified images, and makes appropriate use of computerresources.

IntroductionPerhaps the primary product from imagery gathered by Earthobservation satellites is currently the land-cover map. Eachpixel in the original image is assigned to one of a number ofland-cover classes based on reflectance from the piece ofland concerned in the various different bands of the electro-magnetic spectrum recorded by the sensor concerned. Theimages thus produced are widely recognized to be only ap-proximations to reality or ground truth, and a substantialbody of research has focused on identifying the nature andthe causes of the error tlat is present (Campbell, 1987, pp.334-365; Congalton, 1988; Congalton and Mead, 1983; Fi-tzpatrick-Lins, 1978; Story ef al., tgAE; Todd ef a1., 1980). Anumber of different descriptions of accuracy have been iden-tified, each taking different views of the confusion matrixwhich compares ground truth with classified information(Aronoff, 1982; Story and Congalton, 1986). No work isknown, however, which relates how this information may bedisplayed, other than in the usual tabular form. In the w6rkpresented here, three different algorithms are given, each en-abling different measures of classification accuracy to beembedded in the display of the classified image. One algo-rithm uses only a single figure summary of accuracy (theoverall accuracy, or percent correctly classified), one willwork with row or column values in the confusion matrix(user and producer accuracies), and the last displays accu-racy in the digital classification of the image.

The first section of the paper reviews the nature of errorin classified imagery, and the second outlines the basicmethod to be applied, Error Animation. The next outlinesthe study site. Then three algorithms are presented for ani-

Department of Geography and Midland Regional ResearchLaboratory, University of Leicester, University Road,Leicester LE1 7RH, Great Britain.

PE&RS

mating the different types of accruacy,'and discussion fol-lows. The basic method depends fundamentally upon anactive computer screen for a dynamic display. Thus, al-though figures are included here, the full effect of error ani-mation cannot be conveyed in print. Therefore, ttrepenultimate section describes how the reader may acquire acopy of a demonstration program which illustrates all themethods discussed here.

Errors in Glassification of lmageryIt is widely acknowledged that classification of remotelysensed imagery has variable and often poor quality. Thecauses and nature of the error have been the subject of exten-sive research in the past, and wiLl be into the foreseeable fu-ture, and are ably reviewed by Campbell (1987, especiallysee pp. 334-364) among others.

The primary method for determining classification erroris by comparing the cover type at sample locations to estab-lish the ground truth with ttre cover type for tle correspond-ing pixels i:r the classified i:r.rage. Various approaches aretaken to defining the sample, but, whichever method is used,the crosstabulation of the ground truth and classified covertypes is called the confusion matrix. For tle classified imageshown in Figure 1, it was possible to construct ttre confusionmatrix shown in Table 1. The dominant cover tyf)e per pixelwas used as the basis for judging ground truth (Fisher andPathirana, 1990; Pathirana, 1990).

The confusion matrix can be read in a number of ways.First, the sum of the values in the leading diagonal dividedby the total number of points sampled, gives the Overall Ac-curacy. This is a useful, simple, and understandable sum-mary figure for the whole table.

As various authors have pointed out, however, the con-fusion matrix includes errors of both omission and commis-sion, and each is different for each cover type. After Storyand Congalton (1980), and Aronoff (1982), the accuracy mea-sures derived from these errors (1 - [error]) are termed Pro-ducer (1 - [commission error]) and User (1 - [omissionerrorl), respectively. Essentially, these report ttre percent cor-rectly classified for each land cover type separately, and de-rive different values for the rows and columns of theconfusion matrix respectively (Table 2). Thus, it can be seenthat in Table 1 the frequency of other cover tJryes classifiedas water is zero, while the uset accuracy shows 1/11 pixelswhich are actuallv water have been classified as wetland.

Photogrammetric Engineering & Remote Seusing,Vol. 60, No. 7, July 1994, pp. 905-910.

0099-77721941600 1-000$03.00/0O1sS4 Americaa Society for Photogrammetry

and Remote Sensing

:

I;

:

ilffiil

Figure 1. The Ori$nal Classified lmage of a small area tothe southwest of Akron, Ohio, being a hardened classifica-tion from the unsupervised implementation of the Fuzy c-Means classifier (see Fisher and Pathriana, 1990).

FdWnt$

A$pfrElt

Op6$ lifld

ts6ru $r?Und

Woodlfl|d

lffetfdnd

Similarly, from the producer's view, 7128 of pixels classifiedas open land should be woodland, and Bl2B should be build-ings, while, from the user's point of view, 3/29 pixels classi-fied as woodland are actually buildings, and 1/29 areactually open land.

Finally, many image classification mettrods, includingminimum-distance-to-the-mean, maximum-likelihood (|en-sen, 1986; Mather, 1987), and fuzzy classifiers (Fisher andPathirana, 1990; Robinson and Thongs, 1985; Wang, 1990),assess the degree to which a pixel belongs to all cover types.Most implementations of the first two classifiers fail to reportthis information, although some report the reliability of themost important cover type (the one to which the pixel is as-signed). Fuzzy classifiers, on the other hand, all report thefuzzy membership of all land-cover types (Bedzek, 1981).Whichever classifier is used, however, the numerical valuesreport the reliability of the assignment of tle pixel to the pri-mary class, and the likelihood or the fuzzy membership of itbelonging to all others. This, then, presents a third dimen-sion to the reliability of classified imagery, or classificationaccuracy.

Error Animation to Visualize ReliabilityIt is, then, possible to derive several different measures ofthe accuracy or reliability of the classification of a remotelysensed image. The challenge addressed in this paper is theintegration and visualization of any of those measures of ac-curacy with the image.

A static image and an adjoining confusion matrix can beused to show the overall, user, and producer accuracy, As abasis for this research, however, it is assumed that the aver-age user of the image will do what is easiest, and, even whenthe confusion matrix exists, the easiest thing to do is acceptthat error exists, but ignore its amount and structure as re-vealed in the confusion matrix. Thus, the confusion matrixmight just as well not have been produced, and, what-is-more, many users are confused by the possible interpreta-tions of tle confusion matrix.

As noted above, it is sometimes possible to derive mea-

906

Taelr 1. Corurusrol MarRx ron rne Axnoru SuasET Usso rru Tnrs Pnpen(rnou PnrHrnnrue, 1990)

Classified Image

GroundTruth Water Buildings Asphalt

Open Bare Wood-land Ground land Wetland

WaterBuildingsAsphaltOpen LandBare GroundWoodlandWetland

'j

;

Overall Accuracy: 77 .lVo from 170 observations,

sures of ttre classification accuracy, and two visualizationmettrods may be used in standard image processing pack-a8es.

o A statistical test (chi-squared; Mather, 1986) may be used toidentify as a separate category all pixels where the classifica-tion accuracy is below a certain threshold.

o The likelihood (or fuzzy membership) of a pixel belonging tothe most likely cover type may be held as a secondary imageduring the classification process. It may then be used aseither a grey scale or a tlree-dimensional (en) backdrop tothe classified image, giviug an impression of the relative reli-ability of different areas.

Both methods, however, ignore the fact that the reliability ofa pixel's classification is only part of the information poten-tially contained in the precision information. Indeed, recentresearch has demonstrated that the relative proportions ofdifferent land-cover types within the pixel are related to themembership or likelihood values (Fisher and Pathirana,1990; Robinson and Thongs, 1985; Wang, 1990).

As an alternative to ttrese methods, a set of tlree algo-rithms is presented here that all integrate the visualization ofthe accuracy of the classification with the classified image. Anew cartographic method named enor animation is used toeffect this integration, and, when used, the original imagecannot be seen without also conveying reliability informatioa(Fisher, in press).

Study SiteThe details of the study site are somewhat immaterial to thetheme of this paper, but, for completeness they are men-tioned here. The demonstration software, and the figures inthis paper, all relate to work reported by Fisher and Pathir-ana (1990) and Pathirana (1990). Those studies showed thatthe fuzzy memberships derived from the Fuzzy c-Means clas-

Teeu 2, Pnooucen eruo UseR AccumcrEs DERvED FRoM tHe Mnrnx(rnou Parnrnarla, 1990)

Producer

Accuracies

-3 -1

\ -

,u :18

-1 -7 -5

t 7 1 119

1 - 2 02 3

, t2I

WaterBuildingsAsphaltOpen LandBare GroundWoodlandWetland

7017723134171797S/29201292512918/19

90.967.689.4o c . c

68.986.294.7

101102314017/2715128201222513018/19

100J / . J

80.967.868.986.294.7

PE&RS

sifier (Bedzek et a1.,7984) are proportional to different covertypes within a pixel in the suburban fringe southwest of Ak-ron, Ohio. All details of the analysis are presented in eitherof the citations. The work here simply uses the confusionmatrix for the hard classification given by Pathirana (1990),and the digital forms of the hard and fuzzy classifications ofthe area shown in both sources. The Fuzzy c-Means classifieryields a value for each pixel in each cover type, such thatthe sum of membership values for one pixel equals 1 (simi-larly to a likelihood classifier). The method given here couldwork therefore with the more widely available maximum-likelihood classifier, and, to avoid confusion or unnecessaryrepetition, the values are refered to as strengtls below, im-plyrng the use of either likelihoods or fuzzy memberships.

AlgorithmsThe Basic ApproaehThe various error animation procedures suggested share abasic framework for their operation. A classified image isread into computer memory as an integer coded anay. Thisis the classified image for which accruacy measurements areavailable, and for which visualization of the accuracy is de-sired. One value in the aray represents the cover type at thatpixel location. This image is displayed on the screen as a se-ries of colored pixels either at the same time as it is read intomemory or else subsequently (collections of pixels in asquare shape may represent a single entry in the array if thearray is small compared with the display space on ttre com-puter monitor). This is termed the original classified image(Figure 1). A user or viewer may then select which of thefour accuracy measures they wish to view.

In animating the accuracy (whatever measure is se-lected), two different phenomena may be randomized; theseare referred to as cover-type randomization and spatial ran-domization. Cover-type randomization is when the covertype to be displayed at a location is chosen at random by oneof the three methods discussed subsequently. Spatial ran-domization is the random selection of a pixel for which thecover type is to be changed.

The first step in animating the accuracy is when the dis-play is completely redrawn using the cover-type randomiza-tions rule appropriate to the accuracy measure beingdisplayed. This ensures that the image does not actuallyevolve into chaos which might otherwise occur, because theevolution would give an impression of change. By redrawingthe screen, tle viewer is prepared for something new. Then apixel in the classified image is selected either by spatial ran-domization or systematically (e.g., scanning through the ras-ter image). Experiment shows that both methods haveadvantages; for simplistic accuracy measures (Overall Accu-racy), the appropriate method is random selection, but for amore complex measure (Classification Accuracy), systematicselection may be more appropriate, although those who haveseen the demonstration programs usually prefer spatial ran-domization in this too. The color (cover typeJ to be displayedat the location is chosen using the appropriate randomizationrule, again. This random or systematic selection of a pixeland random change of the color is repeated until the user iu-tervenes to select either another accuracy measure, the original image, or to leave the display.

The method is referred to as animation because pixelsare continuously selected, and the cover tJrye display re-eval-uated, giving a constantly qlenging display. In a sufficientlylong period of viewing, the total length of time for displaying

PE&RS

the original cover t1pe is proportional to the accuracy of thecover type whether overall, user, producer, or classificationaccuracy is displayed. The higher the accuracy, the longerthe total lengtb of time for displaying the correspoldilgcolor, and the more stable the original cover type displayed.

The details of how cover types are randomized for thedifferent measures of accuracy are discussed in followingsections (cover-type randomization).

(herallAccuracyAs noted above, the overall accuracy is based on tle numberof times the cover type mapped actually occurs at the loca-tion mapped. What is either actually there or is classified asbeing there is unknown, and so if animation is to be used todisplay tle overall accuracy, it may be assumed that anycover type in the image space could be at any location.Therefore, the procedure requires either a calculated or esti-mated overall accuracy.

With respect to the location concerned (whether for ini-tial display of the image, or for continui+g animation), a ran--dom number is generated, between 0 and 1 (the maximum ofthe possible overall accuracy), and if that r^ndom number isless than the value of the overall accuracy, then the originalcover type at that location is displayed; otherwise, a secondrandom-number is used to choose between the other possiblecover t5pes that could be there. The same algorithm can beused wiih any value of accuracy, which could include theaverage producer or user accuracy'

A static realization of this randomization algorithm isshown in Figure 2. The disorganized nature of the accuracymeasure can be seen clearly.

Producer and User AccuracyThe algorithms for Producer and User Accuracy by covertype are very similar except in the actual accuracy valuesriJed. In thii case, a list of accuracy values are associatedwith each category, so ttrat there is some level of probabilitythat any pixel is associated with any cover type, dependingon the cover tJpe in the original image.

The fulI confusion matrix is used to animate both of

Figure 2. Randomization of the covertypes according to the Overall Accuracyderived from the confusion matrix (keyas in Figure 1).

TaeLE 3. MATRX FoR r{E AxRoN SuesEr Re-nnRANoeo to ENnetr Sruclor.ror New CovEn Types roR Vsueuzlnon or PRooucen AccuRacv

(See Tocr poR ilplrrueroru)

Classified Image

GroundTruth WaterBuildingsAsphdt

Figure 4. Randomization of the coverVpes according to the User Accuracyderived from the confusion matrix (keyas in Figure 1).

Openland

Bare Wood-Ground land Wetland

WaterBuildingsAsphaltOpen LandBare GroundWoodlandWetland

10 10 10 10 10 10 10o 2 3 2 4 3 1 3 6 3 9 4 0o 2 1 9 2 0 2 1 2 7 2 70 8 8 2 7 2 7 2 8 2 80 1 2 2 2 2 2 2 2 20 0 0 2 5 3 0 3 01 1 1 1 1 1 1 9

these accuracy measures. If the producer accuracy is to beanimated, then it is most convenient to re-arrange the confu-sion matrix so that the figures entered are cumulatve fromleft to right (Table g). A pixel is then chosen for randomiza-tion, and a random number is found between 1 and the rowtotal for the cover type in the original image at that pixel.Then the row in the re-arranged confusion matrix of thecover tJpe coucerned is scanned until the entr5r in the col-umn exceeds the value of ttre random number. The covertype correspoading to that column is then the cover typerepresented. For exa:nple, if when the pixel to be re-evalu-ated is identified as the cover tlpe building in the originalimage, and 27 is ttre value of the random number, then openland will be shown in the animation process. When the orig-inal cover type is bare ground and the random value is 20,then bare ground will be displayed.

If User Accuracy is to be animated, then ttre cumulativevalues in the columns is found and columns srs ssennsd,but otherwise the procedure is identical.

This procedure ensures that the amount of time a pixelis displayed as a particular cover tlpe is proportional to thefrequency of that cover type in the table, using row or col-umn precedence depending on whether Producer or User ac-curacy is to be displayed. Figures 3 and 4 show static

randomizations of the Producer and User accuracv from Ta-ble 1 (or Table 3 for Froducer accuracy). Note thai the areasshown as water in tle original image (Figure 1) are all shownas water when hoducer accuracy is displayed (Figure 3), be-ca-use no water pixels in the classified image are actually anyother cover types. Some pixels not shown as water in theoriginal image are shown as water when Producer accuracyis displayed {compare Figures 1 and 3), because water caroccut where ttre ground truth is wetland. Furthermore, whenUser accuracy is displayed, pixels shown as water in theoriginal appear as wetland, due to the 1/11 chance of this oc-curring (Table 1).

Classification AccuracyThe uncertalnty inherent in the assignment of a pixel to acategory is also amenable to display using error animation.The prerequisite for this is that there be a measure to thestrengttr of every pixel belonging to every cover type. Thisrequires rapid access to a massive three-dimensional arraywith (columns by rows by cover types) entries, and this il&s urein limiting factor which causes the demonstration pro-gram (see below) to use only a 50- by SO-pixel subset (Fig-ures 1 to 5).

To achieve randomization of the cover types for classifi-cation accuracy, it is most convenient to systematically addthe shengths of each cover type cumulatively, so that

-the

sbength in the last [seventl here) cover type is 1 for all pix-els, assuming that the strengths sum to 1, as they do in theFuzzy c-Means and maximum-likelihood classifiers. As apixel is chosen for evaluation of the cover type to be dis-played, a random number must be chosen between 0 and 1.The cumulative strengths for the pixel concerned are ttrenscanned, and if the random number is less than the value forthe current cover tJrpe, then the current cover type is dis-playqd. If we consider the strengths of an imaginary pixellisted in Table 4, a random number of 0.3S, for example,would cause bare ground to be selected. This is also ihe hardclass (greatest strength) for this pixel. A value of 0.1 wouldcaus-e the building cover type to be displayed. The period fordisplay of a cover type at a pixel is proportional to ihe

Figure 3. Randomization of the covertypes according to the Producer Accu-mcy derived from the matrix (key as inFigure 1).

TeeLE 4. lruverreo Srneruerxs (Fuzr MeMeensHrp oR UKEUHooD) oF APARTTcULAR Pxet rru reca or rne Snclt lmto-Coven Tvpes

(See Tocr roR Bpleneror)

Figure 5. RandomizaUon of the covertypes according to the Classification Ac-curacy, as reflected in the streng[h ofmembership of the fuzy sets of thecover types (key as in Figure 1).

OriginalStrengths

CumulativoSbengths

WaterBuildingsAsphaltOpen LandBare GroundWoodlandWetland

0.01o.200.050.040.60.040.06

0.01o.2ro.260.300.900.941.00

strength of that pixel in the cover type. A static version ofthe randomization procedure is shown in Figure 5.

DiscussionFigures 2 to 5 show frozen examples of an implementation ofaII three of the algorithrns discussed. Figure 2 shows imple-mentation of the Overall Accuracy, taking values from theconfusion matrix given in Table 1. In Figure 3 Producer Ac-curacy and in Figure 4 User Accuracy, derived from Tables1, 2, and 3, are presented. Figure 5 shows the classificationaccuracy. The full impact of the randomization is not appar-ent in these figures, and interested readers are encouraged toacquire a copy of the demonstration disk. The chaotic pat-terns that result from enor animation show clearly the insuf-ficiencv of Overall Accuracv as a measure of databaseaccuraiy. Interestingly, the-relatively ordered patterns of theIjser "-d Producer Accuracy in the static displays is fol-lowed by a more chaotic static display for Classification Ac-curacy. This is due to the increasing specificity of these lastthree accuracy measures. The animated display, however,does not retain the confused pattern in the last, due to thetemporal stability of well classified pixels.

Error anirration has a number of features that seem tomake it particularly attractive:

o The classified image is always apparent because prolongedviewing of any part of the image will reveal the primarycover tJrpe at a pixel because that is the color that will beused for most of the time.

r Prolonged viewing ofa group ofpixels will not only revealthe primary cover t5pes of those pixels, but also the covertypes that may be there but are not actually classified,

o The strengttr of different cover t5pes being at a pixel are re-lated to the time they are displayed.

The actual human perception of the display method re-quires research. The following questions occur to the author:

o What speed of s[nngs would be optimal in randomizing thedisplay?

o Is randomization or scanning preferable i.n classification ac-curacy?

o Do users understand fts msaniag of the image or are theyjust confused?

. Do users prefer static or dynamic images?o Is methodological information required for a user to under-

stand the display or is communication implicit?

Perceptual experiments are plnnned.

AvailabilityError Animation requires the use of a computer to deliver itsfull impact. Therefore, a computer disk with an implementa-tion of the algorithms described here is available to any in-

PE&RS

terested reader. The program runs on an IBM ec compatiblewith vca monitor. pssfsl nrashines with coprocessors willgive an improved effect over older and slower computers,but the software should work on any machine with us nos3.0 or higher. The program is available as both source code(Turbo Pascal version 6.0) and compiled. The progtam comeswith two other implementations of error animation, one il-lustrating statistical dot maps, and one showing its use topresent soil map reliability (Fisher, in press). Interested read-ers should send a 3.5-inch 1.44M floppy disk to the author.

The programs are available on the understanding thatthe ideas aad code remain the copyright of the author, andthat they are not guaranteed to work in any situation. Bugsmay be reported to ttre author, however, and attempts maybe made to fix the problem.

GonclusionError Animation is presented here as a method for embed-ding measures of ttre reliability or accuracy in the display ofa classified remotely sensed image. Measures of reliabilityfrom overall accuracy to classification accuracy are appliedin a set of three algorithms. Figures illustrating the methodare presented, but these give static, frozen views; the full im-pacf can only be defined in a dynamic computer display,and readers are encouraged to acquire the demonstrationsoftware. The method is presented in the firm belief that itenhances the visualization of the classification result byembedding measutes of reliability in the display, givingusers far more information than the normal display of aclassified image, without detracting from that classified im-age, and, furthermore, making the reliability information un-avoidable. Much work remnins to be done on evaluatinghuman perception of the display method, and expanding itinto other areas of mapping.

AcknowledgmentThe work described here owes much to various colleagues.Milton Harvev and Sumith Pathirana at Kent State Univer-sity, Ohio,

"oa Ul"ty Hearnshaw, BiII Hickin, and Mitchell

Langford at the University of Leicester, all contributed ideasto either data exbaction or to the methods proposed here.The work is directly related to an invitation to attend ttreNCGIA specialists mee'ing on the Visunlioalioo of Error inSpatial Data (Initiative 7), and thanks for that are extended toBarbara Buttenfield and Kate Beard. Encouragement from allattenders at that meeting and others who have seen the soft-ware described here nnning is gratefully acknowledged. Fi-nally the paper has improved considerably from theconstructive criticism of anon',rmous referees.

ReferencesAronoff, S., 1982. Classification accuracy: A user's approach, Pioto-

grcmm etric Engineerin g & Remote Sensrng, B(B) :1 299-1 3 0 7.Bedzek, I.C., 1981. Pattem Recognition with Fuzzy Objective Func-

tion Algorithms, Plenum, New York,Bedzek, I.C., R. Ehrlich, and W. Full, 1984. FCM: The fu2ry c-means

clustering algorithm, C omputers & Geo sciences, 10 : 19 1-2 03.Campbell, J.8., 1987. Introduction to Remote Sensing, Guildford,

New York,Congalton, R.G., 1988. Using spatial autoconelation analysis to ex-

plore the errors in maps genertated ftom remotely sensed data,Photogrammetric Engineering & Remote Sensing, 5a$):587 -592.

Congalton, R.G., and R.A. Mead, 1983. A quantitative method to testfor consistency and correctness in photointerpretation, Phofo-grammetic Engineering & Remote Sensing, 49:69-74.

Fisher, P.F., in press. Error Animation of reliability in soil maps,Cartographica,

Fisher, P.F., and S. Pathirana, 1990, The evaluation of fuzzy mem-bership ofland cover classes in the suburban zone, RemoteSensing of Enuironment, 34:727-732,

Fitzpatrick-Lins, K., 1978. Accuracy and consistency comparisons ofland use and land cover rnaps made from high-altitude photo-graphs and l,andsat multispechal imagery, Joumal of flesearchof the U.S. Geological Suruey,6(1):23-40.

Mather, P.M., 1987. Computer Processing of fremotely-Sensed Im-ages:,4n Introduction, Wiley, New York,

Pattrirana, S., 1990. Fuzzy Membership Appmach to the Mixed PixelPrcblem of Remotely Eensed Data: An Application in the Suburban Fringe Zone of Northeast Ohio, PhD thesis, Kent Stato Uni-versity,

Robinson, V.8., and D. Thongs, 1986. Fuzzy set theory applied to themixed pixel problem ofmultispectral landcover databases, Geo-graphic Information S;afems in Govemment (B. Opitz, editor),A. Deerpak pullishing, Hampton, Virginia, pp. 871-885.

Story, M.H., |.B. Campbell, and C. Best, 1984. An evaluation of theaccuracies of five algorithms for machine classification of re-motely sensod dala, Proceedings of the Ninth Pecora SWpo-srum, American Society for Photogrammetry and RemoteSensing, Falls Church, Virginia, pp. 399-405.

Story, M., and R.G. Congalton, 1986. Accuacy assessment: A user'sperspective, Photogrammetric Engineering & Remote Sensing,52:397-399.

Todd, WJ., D.G. Gehring, and |.F. Haman, 1980. Landsat wildlandmapping accuracy, Photogrammetric Engineefing & RemoteSensrhg, 46:509-520.

Wang, F., 1990. Improving remote sensiag image analysis throughfuzzy information representatiot, Photogammetic Engineefing& Remote Sensrhg, 56:1163-1168.

(Received 4May 1992; revisod and accepted 17 March 1993)

Peter FisherPeter Fisher is Lecturer in Geographical Infor-mation Systems at the University of Leicester.There he directs the M.Sc. in GIS, and is a re-searcher with the Midlands Regional Research

r'iir'he:tq*r* Laboratory. Previously, he spent 5 years as anAssistant Professor at Kent State University, Ohio, and beforettrat at Kingston University, England. His major areas of in-terest are in aII aspects of uncertainty in spatial data process-ing, and, for oue paper in tlis area, he won the 1992 ESnrprize from ASPRS.

HOW to LIE with MAPS

by: Mark Monmonier

1991. 184 pp. sofrcover. $17; ASPRS Members, $12. Stock # 5014.

A lively, cleverly illustrated essay on the use and abuse of maps that teaches us how to evaluate maps criticallyand promotes a healthy skepticism about these easy-to-manipulate models of reality. This book shows that mapscan not only point the way and provide information, maps lie. In fact, they have to lie. Chapters include:Elements of the Map t Map Generalization: I.ittle White Lies and Lots of Them i Blunders that Misleada Maps for Political Propaganda I Maps, Defense, and Disinformation: Fool Thine Enemy t DataMaps: Making Nonsense of the Census O And More!

From the people who make maps and do not want to mislead readers or clients - to the potential victims of badmaps: scientist, voters, politicians, planners, business managers, travelers, students, and all the rest of us -everyone will benefit from reading this book.

For ordering information, see the ASPRS Store in the back of this journal.

910