Accuracy analysis of remote sensing change detection by rule-based rationality evaluation with post-classification comparison

INT. J. REMOTE SENSING, 10MARCH, 2004, VOL. 25, NO. 5, 1037 1050 Accuracy analysis of remote sensing change detection by rule-based rationality evaluation with post-classification comparison H. LIU Department of Geography, Beijing Normal University, Beijing 100875, PR China; e-mail: hpliu@bnu.edu.cn and Q. ZHOU Department of Geography, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong, PR China; e-mail: qiming@hkbu.edu.hk (Received 8 April 2002; in final form 24 March 2003 ) Abstract. Accuracy assessment for remote sensing classification is commonly based on using an error matrix, or confusion table, which needs reference, or ground truthing, data to support. When undertaking change detection using numerous multi-temporal images, it is often difficult to make the accuracy assessment by the traditional method, which typically requires simultaneous collection of reference data. In this study, we propose a new approach by arguing change rationality with post-classification comparison. Multi-temporal Landsat TM images were classified for land use in an urban fringe area of Beijing, China and the post-classification comparison of these classified images shows change trajectories through the time series. These change trajectories were then analysed by assessing their rationality against a set of logical rules to separate cases of real land use change and possible classification errors. The analysis results show that the overall accuracy for land use change in the urban fringe area was 86%, with a fuzziness of 7%. Although it is argued that the uncertainty still exists on classification accuracy assessed by this method, it nevertheless provides an alternative approach for more reasonable assessment when ideal simultaneous ground truthing is not available. 1. Introduction In urban fringe areas, land use and land cover changes take place rapidly as a consequence of economic development and population growth. The characteristics of spatial land use patterns are multiform, miscellaneous and changing (Charbonneau et al. 1993). The geography of urban growth offers a graphic depiction of the interplay between economics, political systems and the environment (Masek et al. 2000). Thus, it becomes important to monitor change in this area frequently at time periods determined by various stages of economical development. Remote sensing images from Landsat and SPOT satellites have been used in land use and land cover change detection for years (Green et al. 1994, Kwarteng and Chavez 1998, Li and Yeh 1998, Masek et al. 2000, Ji et al. 2001, Weng 2001, Zhang 2001). Numerous remote sensing change detection methods have been International Journal of Remote Sensing ISSN 0143-1161 print/issn 1366-5901 online # 2004 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/0143116031000150004

1038 H. Liu and Q. Zhou developed, such as image differencing, vegetation index differencing, selective principal components analysis, direct multi-date unsupervised classification and post-classification comparison (Gong 1993, Lunetta and Elvidge 1999). Remote sensing change detection in urban fringe areas has two aspects, namely monitoring the urban growth area, or urban expansion, and detecting the land use and land cover type shifting. Many remote sensing applications for urban growth detection are based on the method that uses images acquired at the beginning and end of study periods (Fung and Ledrew 1988, Green et al. 1994, Kwarteng and Chavez 1998, Li and Yeh 1998, Ridd and Liu 1998, Mas 1999, Morisette et al. 1999, Chan et al. 2001, Ji et al. 2001, Weng 2001). We may call this the two-time comparison method, by which the classification accuracy is typically assessed using an error matrix against simultaneous reference data, such as aerial photographs and field checking (Li and Yeh 1998). Some studies analyse the overall accuracy in more detail (Pilon et al. 1988, Green et al. 1994, Mas 1999, Kwarteng and Chavez 1998), some with alternative methodological approaches such as consistency checking (Gong and Mu 2000). Beyond the two-time comparison method, multi-temporal comparison studies were also reported (i.e. use of more than two multi-temporal images; Martin 1989, Charbonneau et al. 1993, Michener and Houhoulis 1997, Petit et al. 2001). Charbonneau et al. (1993) used Landsat MSS images of 1972, 1979 and 1982 to monitor the urbanization process in Montreal, Canada. To study the dynamics of urban growth in Washington, DC metropolitan area, Masek et al. (2000) used MSS data of 1973, TM images of 1985, and SPOT images of 1991 and 1996 together. The traditional error matrix and kappa coefficient method were used in assessing these multi-temporal comparison studies where the reference data were available. Mertens and Lambin (2000) estimated classification accuracy for each image, using an independent sample of 262 observations from the field campaigns and the low-altitude aerial photographs. They reported high classification accuracy results of 97%, 97% and 98% for 1973, 1986 and 1991 images, respectively. When the simultaneous reference data were not available, some supporting methods were proposed (Masek et al. 2000, Petit et al. 2001). Most traditional accuracy assessment methods are developed for the one point in time (OPIT) thematic mapping (Biging et al. 1999). When multi-temporal classification results are assessed, it would be difficult to confirm the overall accuracy of the whole study period. For change detection based on the multitemporal classification method, the accuracy of each classified image has to be somehow aggregated as the overall assessment on accuracy of the whole-period result, typically by simple statistics such as average, or through an error propagation model (Martin 1989, Charbonneau et al. 1993, Michener and Houhoulis 1997, Mertens and Lambin 2000, Carmel et al. 2001, Petit et al. 2001). When the number of multi-temporal images increases, analysis on derived time-series data has been reported (Alves and Skole 1996), but without the accuracy assessment on the result. The objectives of this study, therefore, are (a) to develop an alternative approach to assess accuracy of remote sensing change detection in an urban fringe area by analysing change rationality in post-classification comparison according to given land use shifting rules; and (b) analysing the overall accuracy of the whole study period when only limited simultaneous reference data are available. Five multi-temporal Landsat TM images were classified for land use in an urban fringe area of Beijing, China and the post-classification comparison of these classified

Accuracy analysis of remote sensing change detection 1039 images shows change trajectories through the time series. These change trajectories were then analysed by assessing their rationality against a set of logical rules to separate cases of real land use change and possible classification errors. 2. Study area and data This study was undertaken at Chaoyang District located in the eastern part of Beijing (figure 1). The district covers an area of 455.2 km 2, with a population over 1.3 million the highest of all districts in Beijing. The majority of the district is characterized as urban fringe with the most rapid urban expansion in the past two decades. From 1978, the area of agricultural land decreased sharply: 18.8% from 1982 to 1989 and 6.5% from 1989 to 1992. Residential and industrial land, on the other hand, increased about 28.2% from 1982 to 1989, and 14.9% from 1989 to 1992 (Cao and Cai 1993). Landsat TM images were acquired on 2 October 1984, 21 April 1988, 6 May 1991, 28 August 1994 and 16 May 1997. The land use map, compiled in 1991 and Figure 1. The study area (Chaoyang District), located in the urban fringe area of Beijing, China.

1040 H. Liu and Q. Zhou based on field surveys at the scale of 1 : 50 000, was used for the accuracy assessment. The master scene (1991) was geometrically corrected and registered to the land use map, using 36 selected Ground Control Points (GCP) and secondorder polynomial transformation with nearest neighbour resempling. The other scenes were then registered to the master scene by image-to-image registration. 3. Methodology In order to achieve the objectives of this research, our approach towards accuracy assessment of change detection is based on the widely used postclassification comparison method (Lillesand and Kiefer 2000). Using the postclassification comparison, land cover change is identified where the classification categories are found to be different between two or more image dates. The comparison results (i.e. pixels with change status) are then assessed by a rule-based analysis based on both change/no change and from-to (land use shift) rationality. The methodology can be outlined as below: 1. The master scene (1991) image was selected and independently classified using two classifiers. 2. The one-time accuracy assessment on both of the classified images was undertaken using the common error matrix analysis with simultaneous reference data (land use map). By comparing the assessment results, the preferred classifier was then selected for image classification of other multitemporal images. 3. Using the preferred image classifier, the four other multi-temporal images were classified and integrated with the master image. The pixels with the change status through the study period were then identified by the postclassification comparison. 4. A test for sampling was conducted to determine the number of samples required for the rule-based rationality analysis. 5. The rule-based rationality analysis was then applied to the change pixels to separate the real change, fuzzy and classification error pixels so as to derive statistics as the basis for the accuracy assessment of the change detection. 3.1. Image classification Two classifiers were employed in this study, namely, the maximum likelihood (MLC) and artificial neural network (NNC) classifiers, of which the former is the most commonly used. One major difference between the two classifiers is the number and purity requirement on the training areas (Atkinson and Tatnall 1997, Kanellopoulos and Wilkinson 1997). The NNC needs fewer and less pure seeding data in comparison to that of MLC. PCI 6.0 remote sensing image processing software was used to accomplish the classifications. 4835 pixels were selected as the training data on the 1991 TM image. The BP model of NNC was applied in the classification, with a structure of 6, 32 and 7, which refer to input, nods number and output, respectively. After classification, the post process was applied to both results from MLC and NNC to aggregate classified categories in order to match those of the land use map. Five land cover classes were finally mapped, namely water, vegetable garden, forest, farmland, and built-up area.

Accuracy analysis of remote sensing change detection 1041 3.2. One-time accuracy assessment on the image classification The one-time classification error matrix was constructed for the land cover classification on the 1991 image with the 1991 land use map as the reference data. A total of 1212 samples were randomly selected over the study area on the land use map. With a higher overall accuracy of 3% than that of MLC, NNC was chosen to be the preferred classifier with an overall accuracy of 79.6% and the kappa coefficient of 0.696 (table 1 and table 2). 3.3. Multi-temporal image classification and change trajectory establishment Thus NNC was applied to classify the remaining four multi-temporal images. Together with the 1991 image, the five multi-temporal classified images were used to establish the land cover change trajectory for each pixel from 1984 to 1997. For each pixel, therefore, a change trajectory can be identified as either no change, or shifting between the interested cover types. 3.4. Sampling test Before taking samples from the classified images for analysing the change rationality, the reliability of sampling was tested. Two tests were undertaken, namely the number of samples and checking of the wrap points. Samples were taken from randomly generated locations and wrap points were checked. The frequency distribution of the cover type change times during the five monitoring dates was employed to check the stability of the sampling. When the frequency distribution became stable with increasing sampling points, a total of Table 1. Accuracy assessment of the artificial neural network classification of the 1991 TM image. Land use categories Producer accuracy (%) User accuracy (%) Average accuracy (%) Kappa Farmland 79.9 88.0 84.0 0.80 Water 53.5 72.9 63.2 0.70 Vegetable garden 64.2 53.0 58.6 0.48 Forest 75.0 34.1 54.6 0.33 Built-up area 89.0 84.6 86.8 0.74 Overall accuracy: 79.6%; kappa coefficient: 0.7%. Table 2. Confusion matrix of the artificial neural network classification of the 1991 TM image. Categories Farmland Water Reference data (land use map) Vegetable garden Forest Built-up area Total pixels Farmland 374 21 12 3 15 425 Water 13 62 2 2 6 85 Vegetable garden 25 10 70 0 27 132 Forest 12 8 3 15 6 44 Built-up area 44 15 22 0 445 526 Total pixels 468 116 109 20 449 1212

1042 H. Liu and Q. Zhou Table 3. Results of the sampling stability test. Changing times Random samples 3171 points 2500 points 2000 points 1000 points 500 points Pixels % Pixels % Pixels % Pixels % Pixel % 0 1362 43.0 1067 42.7 864 43.2 430 43.0 207 41.4 1 746 23.5 604 24.2 471 23.6 228 22.8 119 23.8 2 342 10.8 265 10.6 206 10.3 106 10.6 59 11.8 3 535 16.9 420 16.8 345 17.3 181 18.1 86 17.2 4 186 5.9 145 5.8 114 5.7 55 5.5 29 5.8 3171 samples, which constitute about 0.6% of the total study area, were then selected (table 3). 3.5. Rule-based rationality evaluation The spatio-temporal land use shifting pattern has been an active research field of land use change detection (Roy and Tomar 2001, Weng 2001). While the landscape is regularly monitored by remote sensing, the concept and methodology of change trajectory has been developed. From the point of view of change detection, the change trajectory was defined as trends over time among the relationships between the factors that shape the changing nature of human environment relations and their effects within a particular region (Kasperson et al. 1995). The trajectory of land cover change refers to successions of land cover types for a given sampling unit over more than two observations (Mertens and Lambin 2000, Petit et al. 2001). In an urban fringe area, most land use and land cover changes are the consequence of urban growth. Based on this understanding, an assumption can be made that change to built-up area from other land use types is irreversible. A set of rules, therefore, can be made to evaluate the rationality of detected change trajectory over every sample so that cases of real change, fuzzy or classification error can be identified. If we let t denote the number of detected categorical changes over the five monitoring dates from 1984 to 1997, we have: 0 t 4 ð1þ where the extreme case of t~0 refers to no change, while t~4 refers to the fact that the category of the sample has changed for every detection period. Six rules have been applied to determine the rationality of the change trajectory for each sample. Let A denote the case that the pixel is correctly classified, and B denote the case that the pixel is in a fuzzy state. When A is rejected, it means the pixel is not correctly classified, thus it is the classification error. Land cover types are represented as C i (where C 1 ~ water, C 2 ~ vegetable garden, C 3 ~ forest, C 4 ~ farmland, and C 5 ~ built-up area ). The detected change trajectory between the cover types is denoted as T(C i ) where, for example, T(C 4, C 5 ) means change from farmland to built-up area. For each sampled pixel, the rules are applied in the sequential order as below and their overall logic flow structure is shown as in figure 2.

Accuracy analysis of remote sensing change detection 1043 Figure 2. The structure of the rule-based rationality evaluation. Rule I: IF t~0 THEN accept A. Rule II: IF t~1 AND T(C a,c b ) THEN accept A. (a b; a 5) Rule III: IF t~1 AND T(C 5,C b ) THEN reject A. (b 5) Rule IV: IF t~2 AND T(C a,c b,c a ) THEN accept A. (a b) Rule V: IF t~2 AND T(C a,c b,c c ) THEN accept B (a b c; a 5; b 5) Rule VI: IF tw2 AND dƒ1 THEN accept A ELSE reject A. where d denotes the distance between the sample and the nearby unchanged area identified by Rule I, measured by the number of pixels. The meaning of Rule I is obvious. If the pixel is classified as the same land cover type for all monitoring dates, then there is no change and the pixel is regarded as correctly classified. The built-up area of Beijing doubled from 1984 to 1997. This happened when the other land cover types were transformed to built-up area and this process could not be reversed. Rule II, therefore, states that if once-only change is detected from one cover type (except built-up area) to another, then the change is regarded as a true case so that the pixel is correctly classified. Rule III, on the other hand, defines that if the reverse process were detected (i.e. once-only change from built-up area to another cover type), the change would be unlikely so that the pixel is not correctly classified. Rule IV addresses one-time error of multi-temporal remote sensing image

1044 H. Liu and Q. Zhou classification. If a pixel was found changed from one cover type (C a ) to another (C b ) and then back to its origin (i.e. C a ), it is regarded as one-time classification error case (i.e. C b was the incorrect class). This one-time error does not affect the final result of change detection, so that the pixel is regarded as correctly classified as C a. Rule V specifies the case where the land cover changed two times to different cover types during the study period. This is possible where land cover could shift from, for example, farmland to vegetable garden to built-up area. On the other hand, it is also uncertain whether the trajectory shows the true multiple land cover change or it is simply caused by classification error. We therefore consider this pixel as a fuzzy case with an uncertain land cover class. Note that we exclude the cases of the reverse change (i.e. from built-up area to another cover type) from Rule V as it is regarded as error (Rule III). Rule VI considers the marginal pixels that changed frequently between cover types and located adjacent to unchanged areas. This is most likely the consequence of misregistration in geometric image rectification (Townshend et al. 1992, Stow 1999). The distance from the sample to the nearby unchanged area (d ) is therefore measured. If d is within one pixel, then the sample is the marginal pixel, thus it is regarded as a correct case and has the same cover type as that of adjacent unchanged area. Finally the error state (i.e. reject A) is assigned to those that fail to pass every given rule. 4. Results 4.1. Image classification Figure 3 shows the results of classification for each acquisition date. During the entire study period from 1984 to 1997, the built-up area expanded from 26.7% to 55.9% of the total district, i.e. doubling in 14 years. On the other hand, farmland and vegetable garden decreased from 51.1% and 15.5% to 26.3% and 6.7%, respectively. Forest area decreased slightly but the area of water bodies increased sharply, mainly due to the increase of commercial fish ponds in the district (table 4). By overlapping the multi-temporal classified images, we derived an urban expansion map shown as figure 4. 4.2. Change trajectory test: stage 1 The rule-based assessment of change trajectory over the five-time multitemporal image classification results can be categorized into two stages. Stage 1 is composed of Rule I and II, providing an initial assessment on the classification accuracy. The application of these rules distinguishes samples into two groups, namely, correct and uncertain (table 5). Among 3171 tested samples, 1362 samples remained unchanged during the entire study period, accounting for 43% of the total; while 704 samples were found changed irreversibly (i.e. only once) from other cover types to built-up area, constituting 22% of the total. Thus, the results show that the overall classification accuracy was at least 65%, leaving 35% of samples remaining as uncertain to be further tested. 4.3. Change trajectory test: stage 2 The objective of the Stage 2 test is to further identify correct, incorrect and fuzzy classification samples among the remaining 1105 uncertain samples from

Accuracy analysis of remote sensing change detection 1045 Figure 3. Table 4. Land cover classification of the 1984, 1988, 1991, 1994 and 1997 images. The percentage of land use categories for each image acquisition date. Acquisition date Built-up area Farmland Forest Vegetable garden Water 1984 26.7 51.1 3.7 15.5 3.0 1988 39.8 39.9 2.7 10.7 6.8 1991 46.0 34.9 2.7 8.2 8.2 1994 49.9 32.0 3.0 6.9 8.3 1997 55.9 26.3 2.9 6.7 8.2 Stage 1 test, by applying Rules III, IV, V and VI (table 6). The results show that 43 (3.9%) of uncertain samples were found as reverse change cases (i.e. true for Rule III), so that they are identified as incorrect. Rule IV (one-time error cases) has found 100 samples accounting for 9% of total uncertain samples. Rule V (multiple changes between cover types other than built-up area) identified 242 samples (21.8%) indicating the fuzzy cases. For the marginal pixel cases (Rule VI), 591 (53.5%) samples were found within one pixel distance to the unchanged area (see locations of these sample points in figure 4). 5. Discussion 5.1. Overall accuracy of the five-time multi-temporal land cover classification The overall accuracy of the five-time rationality evaluation is shown in table 7 by compiling the results from the above change trajectory tests. From table 7, the overall test for classification accuracy shows that 86.9% of samples were correctly

1046 H. Liu and Q. Zhou Figure 4. Urban expansion of Chaoyang District of Beijing. Note most samples where land cover type shifting was greater than two were one pixel distant from the unchanged area. Table 5. Change trajectory test: stage 1 results. Pixel number Percentage Total samples 3171 100 Correct (total) 2066 65.2 Correct (Rule I) 1362 43.0 Correct (Rule II) 704 22.2 Uncertain 1105 34.8 classified, 5.5% were incorrectly classified, and 7.6% were in the fuzzy states. It is therefore concluded that the overall accuracy of the multi-temporal land cover classification was at least 86.9%, assuming the worst scenario (i.e. all fuzzy samples are errors).

Accuracy analysis of remote sensing change detection 1047 Table 6. Change trajectory test: stage 2 results. Pixel number Percentage of test samples Total uncertain samples 1105 100 Rule III 43 3.9 Rule IV 100 9.0 Rule V 242 21.8 Rule VI True 591 53.5 False 130 11.8 Table 7. Overall rule-based rationality evaluation results. Rules Pixel numbers % Correct Rule I 1362 43.0 Rule II 704 22.2 Rule IV 100 3.2 Rule VI: True 591 18.6 Total 2757 86.9 Incorrect Rule III 43 1.4 Rule VI: False 130 4.1 Total 173 5.5 Fuzzy Rule V 242 7.6 Total 3171 100 5.2. Rules Rules applied in this study are based on the characteristics of land use change in the urban fringe area of Chaoyang District in Beijing, and the focus of this study (i.e. urban expansion). In the urban fringe area, urban growth is the most significant spatio-temporal change in land use, which shows some predictable change trajectories (e.g. other land use types to built-up area). The evaluation of accuracy rationality is based on these trajectories. It is argued that the land use trajectories can be various in different study areas and thus the rules for this study may not apply. On the other hand, this approach can be useful to other applications of change detection such as deforestation detection and monitoring, where land cover change trajectories are well known (Mertens and Lambin 2000). 5.3. Influence of image registration accuracy In this study, image geometric rectification was undertaken before classification and rationality evaluation. The multi-temporal image-to-image registration was controlled in an allowable range (average rms~0.56 with the maximum of 0.8). There was still potential registration error as it was hard to keep the geometric correction error below half a pixel for the entire image, although some registration noise reduction methods may be applied (Gong et al. 1992). This potential registration error, therefore, was considered with Rule VI, discussed above, which identified more than 18% of the total samples located in one pixel distance to the unchanged area mask and classified them into correctly classified cases. Although it is recognized that the spatial registration error is unavoidable and the accuracy shown in this study is quite acceptable, whether the marginal samples show the

1048 H. Liu and Q. Zhou true land use change or the false cases caused by image registration inaccuracy obviously represents an uncertainty. 5.4. Overall evaluation of the method In this study the change trajectory test revealed an overall accuracy of 86.9% with an uncertainty of 7.6% (see 5.1). Given the 20.4% classification error found by the one-time accuracy assessment on the classification of the 1991 image against the reference data, and 5.5% error found through the trajectory test, it is estimated that the overall propagated error of the overall change detection study should be within the range of 21.1% (fuzzy cases as correct ) to 22.5% (fuzzy cases as incorrect ). This estimation would be significantly different from that obtained using the method proposed by Lunetta and Elvidge (1999), by which the overall change detection accuracy is approximated by multiplying the accuracies of individual classifications. We believe, however, the trajectory test will provide a more realistic scenario since the one-time classification error may be cancelled out by other multitemporal image classifications, provided that there are sufficient observation dates to ensure the confidence of the test. 6. Conclusion In this study, 3171 samples were selected to evaluate the accuracy of change detection using the rule-based rationality evaluation. Six rules based on the recognized land use change trajectory in the urban fringe area of Chaoyang District in Beijing were established and applied to the results of post-classification comparison of multi-temporal TM images. Using the change trajectory test, samples showing locally recognized land use change trend (e.g. change from other land use to built-up area) could be identified and classified as true change cases. The results also showed that more than half of the uncertain samples were caused by the slight image registration errors that were within the allowable range. The trajectory test showed that the overall change detection accuracy was 86.9%, with 5.5% error and 7.6% in fuzzy states. This gives an overall error assessment of 22.5% or less, given the 20.4% one-time classification error. Ideally the error assessment for change detection using the post-classification comparison method should follow the traditional error assessment method, i.e. assessing errors using simultaneous reference data for each image classification, and then evaluating the overall accuracy using an error propagation model. However, since in reality it is almost impossible to obtain simultaneous reference data for long-term change detection in most application cases, an alternative approach has to be engaged. This study demonstrates a promising method employing a rule-based change trajectory test to the error assessment. Our approach is in some way close to that of consistency checking proposed by Gong and Mu (2000), but in the context of consistency checking in time instead of in space. Although there are still questions to be answered such as whether the rules have sufficient coverage of all possible scenarios or if they are applicable to other cases, this approach has nevertheless been shown to be a realistic and practical method for error assessment with confidence.

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