MAPPING SEALED SURFACES FROM CHRIS

MAPPING SEALED SURFACES FROM CHRIS/PROBA DATA: A MULTIPLE ENDMEMBER UNMIXING APPROACH Luca Demarchi, Frank Canters, Jonathan Cheung-Wai Chan, Tim Van de Voorde Cartography and GIS Research Group, Department of Geography, Vrije Universiteit Brussel ABSTRACT Previous work on spectral unmixing of medium-resolution multispectral data for mapping of sealed surfaces has pointed out the limitations of the approach, which are mostly related to the confusion between sealed surface materials and spectrally similar non-artificial land-cover types. Use of hyperspectral data may improve the accuracy of sealed surface mapping in urbanized areas. In this paper the potential of multiple endmember unmixing for sealed surface mapping from hyperspectral CHRIS/Proba data is examined using a modeling scenario based on endmembers for four major classes: grey sealed surfaces, red sealed surfaces, bare soil and vegetation. A reference database was developed for validating the sub-pixel fractions using 25 cm resolution aerial photographs. The average proportional error for sealed surfaces, vegetation and bare soil is around 15%. Defining a model selection criterion that favors the use of models with few endmembers leads to a substantial improvement of the accuracy of the unmixing. Index Terms — sealed surfaces, CHRIS/Proba imagery, multiple endmember unmixing 1. INTRODUCTION In recent years many studies have focused on mapping of sealed surfaces from medium-resolution multispectral satellite data. Various sub-pixel regression and sub-pixel classification methods have been proposed to obtain the proportion of sealed surfaces at sub-pixel level, including methods based on regression analysis, linear spectral unmixing, artificial neural networks and decision trees. One of the problems in these studies is the spectral heterogeneity of sealed surfaces, which is caused by the use of different building materials, and by the spectral similarity between some types of sealed surfaces and other land-cover types, such as bare soil or dark vegetated areas. Both phenomena explain the strong spatial variability of the error that is often observed in maps of sealed surface proportions. The launch of space-born hyperspectral sensors like Hyperion and CHRIS/Proba has opened up new opportunities for mediumresolution mapping at the sub-pixel scale. Indeed, the increased spectral resolution of the data obtained from hyperspectral sensors may reduce the confusion between

sealed surface materials and spectrally similar land-cover types when applying standard unmixing approaches on these data and, as such, improve the performance of the unmixing [1]. The higher dimensionality of hyperspectral data also offers better opportunities to spectrally characterize various types of sealed surfaces and take account of the spectral heterogeneity of sealed surface types in the process of unmixing. An unmixing approach that has been reported as very effective in dealing with spectral heterogeneity within classes is Multiple Endmember Spectral Mixture Analysis (MESMA) [2]. In MESMA, each class to be unmixed can be represented by a set of endmembers describing different appearances of that class. For each pixel to be unmixed MESMA evaluates the performance of different unmixing models, each model corresponding to a different combination of endmembers belonging to the various classes. Different criteria are used to select the best model for unmixing the pixel. The objective of this research was to examine the potential of multiple endmember unmixing for sealed surface mapping using hyperspectral CHRIS/Proba imagery. The best model for unmixing individual pixels was selected based on an RMSE criterion favoring models with few endmembers above models with more endmembers. The approach was tested in a mixed urban-rural area covering the southern part of the city of Leuven, Belgium. To assess the results of the unmixing, a validation at sub-pixel level was performed, based on reference proportions derived from 25cm aerial photography. 2. STUDY AREA, DATA AND PREPROCESSING The test area for this study is located in the urban fringe of Leuven, a small regional town in Flanders, Belgium, and is characterized by a complex mixture of urban materials and non-urban land-cover types. A CHRIS/Proba image covering the area was acquired in MODE 3 on May 20, 2008, including 18 spectral bands scanned at 18 meter pixel resolution. A subset of 5km by 12km, with a northeast/south-west orientation was extracted from the original image, in order to obtain a completely cloud free scene. Drop-outs and vertical striping generated during the image formation process were removed and at-sensor radiance data were converted into surface reflectance using the BEAM Toolbox software [3]. The image was georeferenced in the

Belgian Lambert coordinate system using aerial orthophotos at 0.25 m resolution as a reference. To correct for brightness differences and reduce the spectral heterogeneity within classes, the brightness normalization method proposed by Wu [4] was applied. By applying this method emphasis is put on the shape information of each spectrum, while differences in absolute reflectance values are minimized. 3. METHODOLOGY 3.1. Multiple-endmember unmixing Linear spectral mixture analysis assumes that the reflectance of a pixel is the sum of the reflectance of each material that occurs within the sensor’s field of view, weighted by its respective fractional cover. N

'

ρλ =

 f *ρ λ + ε λ i

i

(1)

i =1

where: ρiλ is the reflectance of endmember i for a specific band (), f i is the fraction of endmember i, N is the number of endmembers, ε λ is the residual.

While linear spectral mixture analysis is a useful approach that has been proven to be able to generate reliable fractions of land-cover types at sub-pixel level, it underutilizes the potential of remote sensing data for discriminating between different types of materials. Because endmembers are the same for each pixel, it does not fully account for differences in land-cover composition at pixel level, nor does it account for spectral variations observed for the same type of land cover. Multiple endmember unmixing allows endmembers to vary on a per-pixel basis [2]. Various models using different combinations of endmembers are tested, and the ‘best-fit’ model for each pixel is used for unmixing the pixel. However, using lowest RMSE (root-mean-square of the residual error term in equation (1) over all spectral bands) as a criterion for selecting the best model for unmixing will often lead to the selection of models with more EMs than actually present within a pixel. If more endmembers are used than are required for modeling the spectrum of a pixel, the RMSE values may indeed be smaller, yet the fractional error will be higher. To deal with this, in our study we calculate the relative increase in RMSE obtained by reducing the number of endmembers by one. For each pixel, 4-, 3- and 2-endmember models with the lowest RMSE are compared. The relative increase in RMSE by going from a 4- to a 3-endmember model and from a 3- to a 2-endmember model is calculated as follows:

INCRrel =

RMSE( n _ EM ) − RMSE( n +1_ EM ) RMSE( n +1_ EM )

*100

(2)

where RMSE(n_EM) is the lowest RMSE value of all nendmember models and RMSE(n+1_EM) is the lowest RMSE value of all n+1-endmember models. If the relative increase in RMSE (INCRrel) is less than a predefined threshold, the model with less endmembers is selected as the ‘best-fit-model’ and is used to unmix the corresponding pixel. Tests were performed with different threshold values (from 0 to 100) to find out for which value the best results in terms of fractional error are obtained. 3.2. Collecting and selecting EMs In order to take full advantage of the multiple unmixing technique the choice of suitable endmembers for unmixing is essential. Spectra that occupy an extreme position in feature space and that correspond to pure pixels are considered good candidate endmembers. In this study, candidate endmembers were collected from the image using a supervised approach. Spatially homogeneous polygons were delineated in the 0.25 m ortho-photoseries corresponding to different types of land cover that could be distinguished in the area and fully including one or more CHRIS/Proba pixels. For sealed surfaces it was impossible to identify a sufficient number of CHRIS/Proba pixels that were fully covered by one type of material (concrete, cobblestone, gravel, bitumen,…). Therefore at the level of endmember collection sealed surface materials were grouped into three classes: grey roof materials, grey road materials and red clay. The latter class was included because of the prominent occurrence of red roof-tiles in the area, with clearly distinct spectral characteristics compared to other types of sealed surfaces. For each level-3 land-cover type in table 1 polygons were delineated. To verify that the polygons selected for each level-3 class occupy extreme and well-defined positions in feature space, a Minimum Noise Fraction (MNF) transformation was applied. Spectra of CHRIS/Proba pixels located within the selected polygons were visualized in scatter plots, based on the first three MNF components. A set of 1213 candidate endmembers was retained. Endmembers were grouped into thematic classes that define the separate land-cover components to be used in the unmixing. Level 1 in table 1 corresponds to the major landcover classes for which we want to derive class fractions; level 2 indicates the different land-cover components that were used to define the unmixing models. Level 3 represents the so-called endmember classes from which the most representative endmembers for unmixing were selected. Different methods have been proposed to select optimal endmembers for each class from a spectral library. In this

3.3. Validation of land-cover fractions To evaluate the results of the unmixing, a validation at subpixel level is required. Reference class proportions were derived from the same 0.25 m resolution orthophotos that were used for georeferencing the CHRIS/Proba data and for defining candidate endmember locations. A stratified random sampling approach was applied. Three sets of 30 “pure” CHRIS/Proba pixels were selected, each set corresponding to pixels that were fully covered by sealed surfaces, vegetation and bare soil respectively. Sets of 30 pixels were also collected for each two-class combination and for the combination of the three classes, resulting in a total of 210 validation pixels. Class fractions obtained by unmixing were compared to the reference fractions: perclass fractional error and per-class absolute fractional error were calculated (in %) and averaged over all validation pixels, yielding a per-class mean error (MEc) and a per-class mean absolute error (MAEc). Summing the MAEc values over all classes produces the total mean absolute error (TMAE). Level 1 Sealed surfaces

Level 2 Grey surfaces Red surfaces

Vegetation

Vegetation

Bare soil

Bare soil

Level 3 Grey road materials Grey roof materials Red roof materials Deciduous forest Coniferous forest Herbaceous Bare soil 1 Bare soil 2

Tab.1. Definition of land-cover classes(level 1), land-cover components for unmixing(level 2) and endmember classes(level 3).

4. RESULTS AND DISCUSSION In multiple endmember unmixing the number of possible models that may be used for unmixing each pixel depends on the number of land-cover components that is defined as well as on the number of endmembers used for each component. In this study unmixing was done with 4 landcover components described by 8 endmembers, respectively corresponding to level 2 and level 3 in table 1. Each unmixing model combines endmembers belonging to different land-cover components (2, 3 or 4 components).

Endmembers representing the same component are never used as part of the same model. The use of 4 land-cover components and 8 endmembers in this study leads to 63 possible unmixing models. As explained above, the best model for unmixing a pixel was determined by comparing the RMSE values obtained with each model and identifying the 2-, 3- and 4-endmember model with the lowest RMSE. If the relative increase in RMSE when choosing for a 4- instead of a 3-endmember model, and subsequently for a 3- instead of a 2-endmember model was smaller than a predefined threshold, then the model with the lower number of endmembers was selected. This approach for model selection was applied for different threshold values, ranging from 0 to 100%. As shown in figure 1, increasing the threshold value for the selection of models with less endmembers strongly improves the unmixing results in terms of total mean absolute error (TMAE). If no threshold is used, all pixels will be unmixed with models that use the maximum number of endmembers (4 in this case), while the use of a threshold value allows models with less endmembers to be selected. A substantial improvement in model performance is observed by increasing the threshold value from 0% and 40%, corresponding to a lowering of the TMAE from 51.44 to 44.97. For higher threshold values the TMAE seems to stabilize around a value of 45%.

TMAE

paper the Minimum Average Spectral Angle (MASA) method [5] was used, which is implemented in ‘VIPERtools’ (www.vipertools.org). The method calculates the average spectral angle between a candidate endmember and all other endmembers belonging to the same class and selects the spectrum that produces the lowest value.

52 51 50 49 48 47 46 45 44 0

20

40

60

80 100 Threshold value (%)

Fig.1. TMAE for different RMSE criterion threshold values.

Table 2 shows the mean absolute fractional error (MAE) and the mean fractional error (ME) (in %) for sealed surfaces, vegetation and bare soil for different RMSE threshold values. The magnitude of the per-classs fractional error, indicated by the MAE values proves to be similar for the three major land-cover classes (close to 15%). Mean fractional error values (ME) point at an overall tendency for overestimation of sealed surface fractions and underestimation of the vegetation fraction of around 5% for RMSE threshold values of 30% and more. For bare soil the systematic error becomes very small for RMSE threshold values above 40%.

threshold

MAE sealed

MAE veget.

MAE bare

TMAE

ME sealed

ME veget.

ME bare

0 20 40 60 80

17.76 15.27 13.67 14.15 14.50

14.56 14.86 14.81 14.47 14.40

19.12 17.80 16.48 15.95 15.88

51.44 47.93 44.97 44.56 44.78

1.84 3.43 5.74 4.58 4.58

5.58 -5.78 -5.78 -5.79 -5.75

4.74 -4.16 -3.32 -0.37 0.29

100

14.47

14.45

15.55

44.47

4.55

-5.72

0.82

Tab.2. Per-class mean absolute error (MAE), total mean absolute error (TMAE) and per-class mean error (ME) for different RMSE criterion threshold values.

Fig.2. Sub-pixel proportion maps for grey surfaces, red surfaces, vegetation and bare soil for a scenario with a RMSE criterion threshold value of 60%.

Fig. 2 shows fractional component values for grey surfaces, red surfaces, vegetation and bare soil for part of the study area for an unmixing scenario based on an RMSE threshold value of 60%. The spatial distribution of impervious surfaces in the scene clearly reveals the urban structure of the city of Leuven and indicates a good distinction between urban and non-urban surface types. Yet some confusion remains, mostly between bare soil and sealed surface materials with similar spectral properties.

aerial photographs of the test area. The accuracy of the unmixing was also shown to be very sensitive to the way the criterion for selecting the optimal model for unmixing each pixel is defined. Adapting the selection criterion so that models with fewer endmembers are more frequently selected proves to substantially increase the accuracy of the unmixing, even if these fewer-endmember models have clearly higher RMSE values than models with more endmembers.

5. CONCLUSIONS

6. REFERENCES

In this paper a multiple endmember unmixing approach was tested on CHRIS/Proba data for mapping sealed surfaces in a mixed rural-urban area. Unmixing was done with 63 models corresponding with 2-, 3- and 4-endmember combinations of four major land-cover classes (grey surfaces, red surfaces, vegetation and bare soil). “Best-fit” models were selected based on an RMSE criterion favoring the use of models with few endmembers. The study demonstrated that sealed surfaces can be mapped with reasonable accuracy from CHRIS/Proba data. An average proportional error of around 15% was obtained. While some confusion remains, mostly between sealed surfaces and bare soil, the spatial distribution of sealed surface proportions proved to correspond well with the pattern of urban structures observed on high resolution

[1] Q. Weng, X. Hu and D. Lu, “Extracting impervious surfaces from medium spatial resolution multispectral and hyperspectral imagery: a comparison”, Int. J. of R. S., 29, pp.3209-3232, 2008. [2] D.A. Roberts, M. Gardner, R. Church, S. Ustin, G. Scheer and R.O. Green, “Mapping chaparral in the Santa Monica Mountains using multiple endmember spectral mixture models”, Rem. Sens. of Env., 65, pp.267-279, 1998. [3] L. Guanter, R. Richter, J. Moreno, “Spectral calibration of hyperspectral imagery using atmospheric absorption features”, Applied Optics IP, 45, (10), pp.2360-2370, 1996. [4] C. Wu, “Normalized spectral mixture analysis for monitoring urban composition using ETM+ imagery”, Rem. Sens. of Env., 93, pp.480-492, 2003. [5] P.E. Dennison, K. Halligan and D.A. Roberts, “A comparison of error metrics and constrains for Multiple Endmember Spectral Mixture Analysis and Spectral Angle Mapper”, Rem. Sens. of Env., 93, pp.359-367, 2004.