JOHN R. JENSEN, PH.D. Department of Geography

Uniuersity of Georgia Athens, GA 30602

Computer Graphic Feature Analysis and Selection

A graphic method of analyzing training class statistics is presented which allows the analyst to view parallelepipeds in three-dimensional space.

INTRODUCTION

S UPERVISED LAND-COVER classification using multispectral remotely sensed data

requires systematic collection of training statistics for classes of interest. Once spectral statistics for each class and channel are col- lected, a judgment is made to determine those channels which are most effective in discriminating each class of information from all others. This process is commonly called feature selection. Feature selection may involve both statistical and/or graphical

techniques? The reason is simple. An analyst may base a decision solely on the statistic yet obtain no fundamental under- standing of the spectral nature of the data being analyzed. In effect, without ever visu- alizing where the spectral measurements cluster in n-dimensional space, each new supervised classification finds the analyst beginning anew, relying totally on the abstract statistical analysis. Many of the practitioners of remote sensing are by neces- sity "graphically literate" (Balchin, 1976).

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KEY WORDS: Analyzing; Azimuth; Classification; Elevation angles; Feature analysis; Graphic methods; Ground cover; Parallelepipeds; Spatial distribution; Training class ABSTRACT: Analysts conducting supervised land-cover classification often rely solely on statistical divergence or separability measures for feature selection. Consequently, they may fail to appreciate the relatively consistent spatial clustering and degree of overlap among training class spectra. A graphic method of analyzing training class statistics is presented which allows analyst anlyst to view parallelepipeds in three-dimensional space and interactively vary viewing azimuth and elevation angles for optimum visual examination. Up to three channels may be examined at one time. It is hoped that the graphic method will supplement statistical measures, resulting in improved feature analysis and selection. REFERENCE: Jensen, John R., "Computer Graphic Feature Analysis and Selection," Photogrammetric Engineering and Remote Sensing, Journal of the American Society of Photogrammetry, ASP, Vol. 45, No. APl l , November, 1979

analysis t o de t e rmine t h e deg ree of between-class separability. By using statisti- cal methods, combinations of channels are normally ranked according to their ~otent ial ability to discriminate each class from all others using n channels at a time. Statistical measures such as separability and di- vergence are adequately discussed in the literature (Lindenlaub, 1973; Tou and Gon- zalez, 1974).

If statistical techniques provide all the information necessary to select features for classification, then why use graphical meth- ods alone or in conjunction with statistical

Therefore, a graphic display of the statistical data might be considered useful and often necessary for a thorough analysis of multi- spectral training data and feature selection. Several graphic feature selection methods have been developed for this purpose.

Graphic methods generally may be grouped as being either two-dimensional or synthetic three-dimensional displays of training class statistics. One method of two- dimensional display is the "spectral plots" available in LARSYS and other image process- ing systems (Coggeshall et al., 1973; Anuta, 1977) where statistics are displayed in a bar

PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSING, Vol. 45, No. 11, November 1979, pp. 1507-1512.

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1979

graph format for each channel (Figure 1). The "radiometric interpretive legend" de- veloped by Robinove (1977) is another at- tempt to communicate visually the relative and absolute location of training class statis- tics. This method simply rearranges the data displayed in the spectral plots (Figure 2). A final two-dimensional portrayal involves the plotting of "ellipses" of training class statis- tics. Two channels are compared a t one time u n t i l a l l p o s s i b l e c o m b i n a t i o n s a r e exhausted (Figure 3). This may be done manually (Heaslip, 1975) or digitally (Smith,

Radiometric Legend

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FIG. 2. The radiometric interpretive legend, al- though originally developed as a thematic map key (Robinove, 1977), is useful for assessing the separability of training class statistics. The re- lationship between spectral channel and land- cover training statistics is shown by a two- dimensional polygon with the Landsat channels plotted on the ordinate and reflectance values on the abscissa. Data are the same as shown in Figure 1.

1977; Downs and Faust, 1978). Unfortu- nately, the analyst must overlay one set of graphs onto another in order to visualize the feature separability of three or more chan- nels.

Graphic displays of training class statistics which facilitate analysis of three channels at once often take the form of parallelepipeds d isplayed in three-dimensional fea ture space (Figure 4). Numerous image process- ing papers display these parallelepipeds for illustrative purposes yet do not include in- structions concerning their creation or use of t h e m a s analytical tools du r ing fea ture .- - "- *-

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FIG. 1. Spectral plots of Santa Barbara, Califor- nia, land-cover training statistics derived from Landsat data. Training statistics (mean *I stan- dard deviation) for six land-cover classes are dis- played for three Landsat channels. The display emphasizes between-class separation for each channel.

FIG. 3. Two-dimensional ellipse envelopes showing the distribution of forest and cotton Landsat training statistics for an area in north Alabama (Downs and Faust, 1978). Such graphics are very useful but necessitate manual overlay of one graph onto another when working with more than two bands.

COMPUTER GRAPHIC FEATURE ANALYSIS AND SELECTION

Band 4 L Frc. 4. A simple parallelepiped displayed in three-dimensional space. Each of the eight cor- ners represents a unique X, Y, Z coordinate corre- sponding to a lower or upper threshold value. For example, the original coordinates of point #4 are associated with (1) the upper threshold value of band 4, (2) the lower threshold value of band 5, and (3) the lower threshold value of band 6. Rota- tion matrix transformations cause the original coordinates to be rotated about the Y, Z axis some 9 degrees and the X, Z axis some + degrees.

selection (G. E. Space Division, 1975; Jen- sen, 1978; Taranik, 1978). This paper discuss- es a method of displaying ~arallelepipeds in synthetic three-dimensional space and of interactively varying viewpoint azimuth and elevation angles to enhance feature analysis and selection.

In order to display three-dimensional par- allelepipeds in feature space, the analyst must obtain fundamental statistical data and make several important decisions. First, the mean and standard deviation of training class statistics for each class, i, and channel, j, are required. These data are routinely pro- vided by image processing systems. Using the mean and standard deviation statistics, the analyst determines the lower and upper threshold values for each class and channel as if selecting them for a traditional paral- lelepiped classification (Addington, 1975). Next, the analyst selects which combination of three channels to portray initially because it is not possible to use all four channels at once in a three-dimensional display. Landsat channels 4,5, and 6 are used in the following example; however, the method is applicable to any multispectral data set. Using this in- formation, a parallelepiped for each land- cover class may be derived. Each corner of a parallelepiped is identifiable by a unique set of X, Y, Z coordinates corresponding to

FIG. 5. Three-dimensional parallelepipeds based on training class statistics presented in Fig- ure 1. Using 15 degree azimuth, 8, and 12 degree elevation, I$, viewing angles, it is visually appar- ent that the first three classes are separable using Landsat channels 4, 5, and 6 while the last three classes experience signature overlap. Additional viewpoints might provide a more effective as- sessment of the degree of overlap (see Figure 7). Depending upon rotations selected, the paral- lelepipeds often fall on the Z axis. Consequently, the Z axis is not annotated because additional an- notation tends to obscure the parallelepipeds.

either the lower or upper threshold value for the three channels under investigation (Fig- ure 4).

By applying rotation matrix transforma- tions to the original X, Y, Z coordinates de- fined as transpose matrix PT, it is possible to provide a synthetic three-dimensional view of parallelepipeds for numerous land-cover classes (Figure 5). A viewing azimuth rota- tion, A, causes the parallelepipeds to be ro- tated about the Y, Z axis some e radians (Figure 4) by using the formula

0 0 X X' 0 cos (t) i n 1:) = lz:l 0 sin (t) cos(t) I

A viewing elevation rotation, B, causes the parallelpiped to be rotated about the X, Z axis some C#J radians by using the formula

In practice, these two matrix transforma- tions, A and B, are concatenated (Newmann and Sproull, 1973; Hungerford, 1978) using matrix algebra to provide a final matrix transformation, C , which is applied to the original PT matrix values, yielding PT':

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1979

B C 0 0 A' B' C'

( ) 1: cos't' s i n = 1:: cos(s) 0 sin(t) cos(t)

C PT PT ' A' B' C' X' 1:: ;: ;;I = I::I

This transformation causes the original X, Y, and Z coordinates of PT to be shifted about and contain depth information as vector PT' (MacDougall, 1976). Display devices are normally two-dimensional (e.g., a plotter surface or cathode-ray-tube screen); con- sequently, only the X, Y elements of the transformed matrix PT' are used to draw the

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parallelepipeds. Manipulation of the trans- formed coordinates using vector drawing software (Tektronix, 1976) yields a striking presentation (Figure 5). Figure 6 is a listing of the FORTRAN statements used to transform coordinates and display parallelepipeds.

Drawings made in this fashion are isomet- ric rather than perspective views. In an

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COMPUTER GRAPHIC FEATURE ANALYSIS AND SELECTION

Zb 2i-----i;"/ Band 6

Band 4 Band 4 Bond 4

FIG. 7. Three-dimensional parallelepipeds rotated about the Y, Z axis, 8, some 0, 1530 60, 90, and 120 degrees while maintaining an X, Z axis rotation, 4, of approximately 12 degrees. At zero and 90 degrees, 7A and 7E respectively, one is actually looking at only two bands analogous to the ellipses previously discussed. Between such extremes it may be possible to obtain optimum viewing angles for visual analysis of training class statis- tics using three bands at once. If desired, it is also possible to view the back of the parallelepipeds (7F). The reader should note that only the azimuth viewing angle, 8, was systematically manipulated in this example. A change in elevation angle, 4, might also improve one's understanding.

isometric view sides which are parallel on the object remain parallel, but in a perspec- tive view all lines converge at infinity along the Z axis. The difference is minor as the observer still perceives a three-dimensional object in most cases (Jenks and Brown, 1966).

By systematically specifying various azimuth and elevation angles, it is possible to display the parallelepipeds for optimum visual examination. For example, Figure 7 displays training statistics for six classes of land cover using a 12 degree viewing eleva- tion angle (0.20 radians) and azimuth rota- tion angles ranging from 0 degrees to 15,30, 60, and 120 degrees. At zero degrees rota- tion, the analyst actually views bands 4 and 5 only, as band 6 (the Z axis) is seen edge-on (Figure 7A). This view is analogous to the two-dimensional "ellipses" previously dis- cussed (Figure 3). Rotation by 15 degrees causes band 6 class statistics to contribute to the feature display along the Z axis (Figure 7B). The addition of band 6 information pro- vides valuable insight concerning the rela- tive and absolute separability of the paral- lelepipeds in three dimensions. Care must be taken when measuring down and across the X and Y axes, however, because the par- allelepipeds are now shifted along the Z axis.

By continuing the rotation to 30 and then 60 degrees (Figure 7C and 7D, respectively) the separation between classes 2 and 3 be-

comes more apparent. At this time the analyst might also conclude that there exists an unfortunate amount of overlap among the urban classes (4, 5, and 6) when using the three Landsat channels. Separation between multiple family residential (5) and commer- cial complex/barren (6) is very poor, sug- gesting the selection of new training statis- tics or a grouping of land-cover classes. Ro- tation by 90 degrees allows one to measure the absolute difference between band 5 and 6 statistics if desired (Figure 7E). This could be very useful when evaluating the urban class signatures just discussed. Rotation of 120 degrees presents the back or rear of the parallelepipeds to the viewer (Figure 7F). The process could be continued through 360 degrees returning to the starting point.

In order to use these graphics effectively, one should remember that the optimum viewpoint for analyzing the separability between any two classes may be unique. Iterative evaluation should isolate optimum views which enhance visual communication of between-class separability.

What is the significance of graphically displaying training class statistics in this manner? First, and potentially most impor- tant, is the insight which an analyst might obtain concerning the consistent location of spectra in three-dimensional feature space. Previously, only two dimensions could be

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1979

analyzed simultaneously without bother- some overlays. Addition of a third feature a l lows t h e u s e r t o cons t ruc t t h r e e - dimensional displays which may provide the basis for the development of an accurate three-dimensional "mental map" of training class spectra (Downs and Stea, 1977). As new spectra are obtained, it may be possible to update the mental map. In this manner, anomalies should be more intuitively appar- ent and subject to careful attention. Second, analysis of such graphics in conjunction with conventional divergence or separability statistics may provide more thoughtful fea- ture selection.

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System: System Description. General Elec- hic, Daytona Beach, 150 p.

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(Received 11 January 1979; accepted 1 May 1979)

Forthcoming Articles

A Century of Progress in USGS Mapping Alfred 0. Quinn, Introduction. Gerald FitzGerald, USGS Mapping: A Historical Review. Morris M. Thompson, USGS Mapping: The Last Three Decades. Dr. Wallace W . Hagan, Observations on USGS-State Cooperative Mapping. Charles H. Andregg, Military-USGS Mapping Cooperation. Radm. Allen L. Powell, Relationship of USGS and NOS. Jerome A. Gockowski, Mapping Cooperation among Civilian Agencies. Russell L. Voisin, A Commercial Mapmaker Views the USGS.

Francis H . Moffitt, Photogrammetric Mapping Standards.