Measuring the Performance of Algorithms for Generating Ground Slope

Transcription

1 This file was created by scanning the printed publication. Errors identified by the software have been corrected; however, some errors may remain. Measuring the Performance of Algorithms for Generating Ground Slope William H. Ryder' and Demetra E. Voyadgis2 Abstract. - Calculation of ground slope is a fundamental geographic information system (GIs) utility. While accurate slope prediction is acknowledged to be a fundamental capability, reality is that users normally apply the slope utility in their GIs without considering accuracy of the product. As the Army's center of expertise for digital topographic data, the Digital Concepts and Analysis Center at the U.S. Army Topographic Engineering Center (TEC) has conducted a study of the accuracy of several slope generation algorithms. This study was designed to field test existing slope generation algorithms, to identify one or more that performed satisfactorily, and to recommend incorporation of those into Army systems. Several Army source algorithms as well as algorithms embedded in commercial off the shelf (COTS) software packages were tested. Rapid field collection of point slope data, a key aspect of this study, was made possible through Global Positioning System (GPS) and laser range finding technology. To assess slope algorithm accuracy, field slope measurements were compared with computer generated slope values. INTRODUCTION Detailed mapping of the Earth's surface configuration (slope) has always been time intensil-e. Traditional slope compilation methods are very labor intensive, requiring anal!-sis of contour line information by a human interpreter. Compilation time can be dramatically reduced by using a computer to generate slope from digital elevation data. Key ingredients in this process are elevation data with adequate resolution and an algorithm that performs satisfactorily. This study was commissioned to examine algorithms for slope generation from elevation data. Automated slope generation has been a topic of research for many years. Efforts h!- the Defense Mapping Agency (DMA) and the U.S. Army Topographic Engineering Center (TEC) during the 1970's were abandoned due to the lack of accurate Digital Terrain Elevation Data (DTED). Since then, source data has! Ph~~sical Scientlsr. U.S. Arm)' Topographic Engineering Center, Alexandria. VA ' Geograplwr. I '. S..lrmy Topographic Engineering Center, Alexandria, VA.

2 improved and new algorithms have been written. Problems also existed because users wanted a product that resembled a traditional, manually compiled slope overlay and slope generated from gridded elevation data was blocky and disjointed. This is less of a problem today because slope is mainly used in computer models and seldom as a stand-alone product. With higher spatial resolution elevation data and faster computers, automated slope generation is a reality. The question remains, given identical elevation data inputs, which algorithm creates the best representation of the Earth's surface configuration? APPROACH The approach used by this study was to review literature on algorithms used currently, and to select candidates based on the availability and acceptance by the users. Three grid-based algorithms were examined. Also examined were two manually compiled slope overlays. (See Table 1). Table 1.--Slope Generation Methods. Svstem/Author ERDAS IMAGINE C.S. Arnly Waterways Experiment Station (b-e S) Method used Uses the average maximum technique. Calculates slope from the third order finite difference method as described by Horn, Doubles the weight of the nearest neighbors in the cardinal directions. Similar to ARC/INFO, but weighs all neighbors equally. Calculates slope from normal vectors and the second order finite difference method. 1 : Slope Overlay Manually compiled from the contours of a 1 :24,000 USGS Quadrangle. Tactical Terrain Anal~~sis Data Base Slope 01.erlay Manually compiled by DMA from the contours of a 1:50,000 Topographic Line Map. The algorithms were tested using a high spatial resolution elevation data set. Els-ation postings for this data set were collected at five meter spacings. Besides generating slope using the five meter data, spacings were thinned to 30 and 100 rnaers. This was done to approximate the elevation post spacing of DTED Levels 2 and 1 respectively. The slope values that resulted from the different algorithms and resolutions were satcgorized according to the ranges used on a DMA Tactical Terrain Analysis Data Bass (TTADB) (See Table 2). An TTADB is a collection of six overlays (obstacles,

3 soils, slope, surface drainage, transportation and vegetation) used by the military for tactical planning. The categorized results were compared statistically against field data to calculate the overall accuracy. Table 2.--TTADB Slope Categories Slope category Range (percent slope) A 01 3 B > C > D >20 s 30 E > F >45 DATA Data Used To meet study objectives, data used had to be accurate and have high spatial resolution. Spatial resolution had to be at least equal to that of DTED Level 2 ( 30 meters). Data that met these requirements were available over the Yakima Training Ccnter, Washington. An elevation matrix was created on a digital stereo photogrammetric workstation using GPS controlled 9" by 9" imagery. The Yakima Training Center was chosen for this study because of the variety of slope categories found there. Additionally, the road network throughout the area allowed for easier access to site locations. To conserve computer resources, a four kilometer by four kilometer area was used as the test area. This area contained the required variety of terrainlslope categories. Collection of Field Data The procedure for collection of data consisted of two parts, test point selection and slope measurement in the field. Test Point Selection Field objectives of this study required that each point visited in the field meet the f;zl!o\ving conditions: points had to be separated by at least 125 meters (this was to ensure that the longest distance measured, 100 meters, did not fall into area covered by other points), and the 125-meter radius circle surrounding the point had to be totally contained within a slope category, not crossing over into another category. To meet these conditions, approximately 50 points from each slope category were preselected on the slope overlay. The actual number of points visited was lcwsr because of firing range restrictions at Yakima.

4 Once in the field, personnel navigated to the preselected coordinates using a Precision Lightweight Global Positioning System Receiver (PLGR). When using the military key, the PLGR is accurate to within ten meters. This amount of accuracy is sufficient for measuring slope values at thirty and one hundred meter post spacings, but higher accuracies were needed to measure slope at five meter spacings. To achieve higher accuracies, differential GPS was used. After reaching a point using the PLGR, readings were taken using the differential GPS unit. This unit took position readings every five seconds until sixty positions were recorded. These positions were later differentially corrected by comparing them with readings taken by a GPS base station set up over a known point. The average of the corrected readings provided a coordinate that was accurate to approximately two and one-half meters. Field Measurement of Slope Values Slope was measured in the field using laser ranging equipment. Once a point was found using the PLGRs, and its actual position was recorded with the differential GPS. one analyst remained on the point while the other analyst paced-off a distance of five meters in the direction of the steepest slope. The exact distance was measured using the range gun, and the analyst's position was adjusted accordingly. When using the range guns, care was taken to ensure that the measurement point on the anal!-st was at the same height as the gun itself. Maximum slope, when not readily apparent, was determined by measuring in several directions. The laser ranging equipment is ideal for this work, instantly giving slope percent and horizontal distance as well as azimuth. After recording the readings, the analyst moved to thirty meters from the start point, again making sure to be on the maximum slope, and the measurements were taken. This procedure was repeated at 100 meters from the start point. Maximum slope was determined for each distance. The maximum was not alu ays in the same direction for all distances. MANUALLY GENERATED SLOPE METHODOLOGY The slope overlay was manually compiled in-house, using the contours from a United States Geological Survey 1:24,000 topographic map and a slope \\-edge. The slope wedge uses a series of circles whose sizes correspond to the slope categories. The category is determined by the largest circle that can fit between two contours. As the distance between the two contours increases or decreases, the slope catsgory changes. A minimum polygon size of 250 meters by 250 meters (ground disrance) was used in accordance with DMA specifications. This is the same method thar DMA used to compile the TTADB from the contours of a 150,000 Topographic Line Nap.

5 COMPUTER GENERATED SLOPE METHODOLOGY Three methods were used for generating the slope thematic maps: an ARCIINFO method, a WES method, and an ERDAS IMAGINE method. The ARCDNFO Method A matrix of the elevations points was output in ASCII format. The ARC generate command was used to generate a point coverage, which was brought into the GRID module through the pointgrid function. Next, the field locations were downloaded from the differential GPS in ASCII format. Again, the generate command was used to create a point coverage, the pointgrid command used to create a grid coverage. The original elevation data set, at 5-meter spacing, was thinned to 30 meters and 100 meters using the resample command. For each of these three data sets, the following procedures were performed: define the projection calculate the slope classify the data extract the slope category values for the field locations. The projectdefine command was used to set the projection, datum, and units of measure to match those used during data extraction. (This was also performed on the field location data set.) The slope was calculated using the slope command. A r-enlop table of values, using the TTADB slope categories, was created and used with the reclass function to produce the thematic map. Finally the combine command was used to extract the slope category values. The combine command combines two or more coverages and outputs a coverage of unique values. The database table associated with the resulting coverage contains the values from each of the original coverages. Therefore, when the reclassified slope grid and the field location grid are input to the combine function, the resulting grid coverage contains only those grid cells that are common to both input grids. The database table for the resulting grid contains the slope category value and the field location number. These numbers were then used in the statistical comparisons. The M7ES Method The WES algorithm is a stand-alone utility that generates slope values directly from a matrix of elevation points, and returns the results as a matrix in ASCII format. Therefore, a software suite was needed to classify the slope values and to extract the values for the field locations. ARCIINFO was used for these purposes. Using the ARCIINFO commands stated above, the following procedures were performed on the algorithm at all three resolutions (5, 30, 100 meters):

6 define the projection classify the data extract the slope category values for the field locations. These slope category values for the field locations were then used in the statistical con~parisons. The ERDAS IMAGINE Method The original 5-meter point file generated in ARC/INFO from the ASCII output, was imported into IMAGINE. An image file was created at a 5-meter cell size and the resanlple function was used to thin the data set to 30 and 100-meter resolutions. Also imported was the field location point file generated in ARCIINFO. The same procedures as in ARCmJFO were used for the elevation data sets at all three resolutions. Using the image info utility, the projection, datum, and units of measure were defined for the elevation data sets (as well as the field location data set) in accordance with those parameters used during the extraction process. The raster recode function was used to reclassify the data into TTADB slope categories. Finally, a spatial model was created with the model utility using the conditional function. Using the slope data and field points as input, the conditional function outputs the pixel value of the first input grid for every pixel value existing in the second input grid. Therefore, a slope 17alus was output for every field location. The pixel to table function was used on the resulting image file to create an ASCII file that contained the x, y, z values for each pixel. A z value of zero indicated that the pixel was not a field location point. To extract the field location points, the UNIX awk command was used to output the x, y, z mlues for each pixel with a non-zero z value. These values were then used in the statistical comparisons. STATISTICAL ANALYSIS The slops iralues generated by the algorithms at the selected points were compared with the values obtained in the field by using a confusion matrix. The generated values wrs matched against the known (field measurement) values, allowing an assessment of slope category accuracy and overall accuracy. These results were used to judge the performance of the algorithm.

7 Table 3.--Sample confusion matrix. 1 I The bold numbers in the sample above are the number of points correctly classified. This means that at a given point, the generated value matched the field measurements. In the sample, 32 points had the correct "A" value. Eleven points were classified as "B" values by the algorithm while they were actually "A" values according to field measurements. To calculate the percent correct in any given category, divide the total correctly classified for the category by the row total (i.e., 32/43 = or 74.4% correctly classified as "A" slope). To calculate the overall accuracy, the total correctly classified for the matrix (sum of the diagonals) is divided by the total of all the values in the matrix (i.e., ( )/201 = or 63.2% of the values were correctly classified by this algorithm). RESULTS The prediction accuracies of the methods tested are shown in Table 4. DISCUSSION The slope generation algorithm embedded in ARCIINFO outperformed all others at 5 and 100-meter resolutions. At 30-meter resolution, the ARCIINFO algorithm also performed well though was slightly less accurate than the WES algorithm (74.6% I-ersus 76.1%). The WES algorithm was a consistently good performer, but failed to classify any "B" slopes at 5 meters, indicating a possible flaw in the software. Further testing must be done before any recommendation can be made. All of the algorithms tested, except the WES tended to underestimate slope. The WES algorithm overestimated slope, especially in the "B" category. The manually

8 Table 4.--Results of testing - I CATEGORVACCURACY (%) I OVERALL ( - - ELEVATION - RESOLUTION METHOD ACCURACY A B C D E F (%) IMAGINE 5 Meters WES TTADB IMAGINE 30 Meters WES TTADB IMAGINE 100 Meters WES 1 :24,000 TTADB compiled overlaps also overestimated slope. Overall. accuracy of the algorithms at 30 and 100-meter resolutions was better than the accuracy achieved at 5 meters, when compared with the field collected data. A possible reason for this lies in the accuracy of the coordinates obtained using differential GPS. Although the method produced ground coordinaies with an accuracy of +/- 2.5 meters, this may not have been sufficient accuracy for comparisons to the 5-meter grid. Due to the 2.5-meter uncertainty in the location of the measuring point, exact correlation with the automated slope prediction grid was not possible. This discrepancy may be responsible for misclassification of some points. As shown in Table 4, the manually compiled overlays at 1 :24,000 and 150,000 scale (TTADB) were less accurate slope predictors than all of the algorithms. As expected. the larger scale overlay (1 :24,000) did predict better than the smaller scale 01-erlay (1 :50,000). Part of the reason for the observed lower accuracy of these o\-erlays is the minimum compilation size of each polygon. For this study, the

9 smallest area retained during compilation was 250 by 250 meters on the ground. This minimum size affects the prediction accuracy though the overriding factor is that manual compilation is clearly less accurate than automated approaches. All algorithms tested to this point are grid-based. The need to examine algorithms utilizing triangulated irregular networks (TINs) to compute slope still exists. Additionally, TINs using geomorphic data (such as drainage networks) must be tested to see if this additional data improves the accuracy of the slope predictions. CONCLUSIONS 1. Use of grid-based slope algorithms alone will produce point slope predictions that match the TTADB slope categories approximately 75% of the time. 2. The WES Maximum slope and the ARC/INFO algorithms performed similarly except for the "B" slope anomaly for the WES Maximum slope algorithm noted earlier in the discussion. 3. The ERDAS IMAGINE algorithm produced slightly lower prediction accuracies than the WES Maximum slope and the ARCIINFO algorithms. 4. All of the automated slope prediction algorithms outperformed the manual slope compilation approach. 5. Use of TIN-based algorithms with and without geomorphic data may increase prediction accuracy. ACKNOWLEDGMENTS The authors of this paper would like to thank Louis Fatale and James Ackeret for their excellent field support, and Patrick Nguyen for his system support. We also greatly appreciate the leadership and support of Mr. Jeffrey Messmore. REFERENCES Burrough. P.A Principles of Geographical Information Systems for Land Resources Assessment, New York, NY: Oxford University Press. pp En~k-omlental Systems Research Institute Help documentation for ARC/INFO 7.0.2, Redlands. CA. ERDAS Inc ERDAS Field Guide, Atlanta, GA. pp Horn, B.K.P Hill shading and the reflectance map, Proceedings of the I.E.E.E. pp Skidmore. A.K A comparison of techniques for calculating gradient and aspect from a gridded digital elevation model, International Journal of Geographical Information Systems, Vol. 3, No. 4. pp