A Method to Improve the Accuracy of Remote Sensing Data Classification by Exploiting the Multi-Scale Properties in the Scene

Similar documents
Impacts of sensor noise on land cover classifications: sensitivity analysis using simulated noise

Urban remote sensing: from local to global and back

Deriving Uncertainty of Area Estimates from Satellite Imagery using Fuzzy Land-cover Classification

Joint International Mechanical, Electronic and Information Technology Conference (JIMET 2015)

Digital Change Detection Using Remotely Sensed Data for Monitoring Green Space Destruction in Tabriz

EFFECT OF ANCILLARY DATA ON THE PERFORMANCE OF LAND COVER CLASSIFICATION USING A NEURAL NETWORK MODEL. Duong Dang KHOI.

Classification of High Spatial Resolution Remote Sensing Images Based on Decision Fusion

Comparison of MLC and FCM Techniques with Satellite Imagery in A Part of Narmada River Basin of Madhya Pradesh, India

IMPROVING REMOTE SENSING-DERIVED LAND USE/LAND COVER CLASSIFICATION WITH THE AID OF SPATIAL INFORMATION

Land cover/land use mapping and cha Mongolian plateau using remote sens. Title. Author(s) Bagan, Hasi; Yamagata, Yoshiki. Citation Japan.

ASSESSING THEMATIC MAP USING SAMPLING TECHNIQUE

The Self-adaptive Adjustment Method of Clustering Center in Multi-spectral Remote Sensing Image Classification of Land Use

KNOWLEDGE-BASED CLASSIFICATION OF LAND COVER FOR THE QUALITY ASSESSEMENT OF GIS DATABASE. Israel -

1. Introduction. S.S. Patil 1, Sachidananda 1, U.B. Angadi 2, and D.K. Prabhuraj 3

An Automated Object-Oriented Satellite Image Classification Method Integrating the FAO Land Cover Classification System (LCCS).

Use of Corona, Landsat TM, Spot 5 images to assess 40 years of land use/cover changes in Cavusbasi

Data Fusion and Multi-Resolution Data

DEVELOPMENT OF DIGITAL CARTOGRAPHIC DATABASE FOR MANAGING THE ENVIRONMENT AND NATURAL RESOURCES IN THE REPUBLIC OF SERBIA

A DATA FIELD METHOD FOR URBAN REMOTELY SENSED IMAGERY CLASSIFICATION CONSIDERING SPATIAL CORRELATION

This is trial version

1. Introduction. Chaithanya, V.V. 1, Binoy, B.V. 2, Vinod, T.R. 2. Publication Date: 8 April DOI: /cloud.ijarsg.

Land Cover Classification Over Penang Island, Malaysia Using SPOT Data

A COMPARISON BETWEEN DIFFERENT PIXEL-BASED CLASSIFICATION METHODS OVER URBAN AREA USING VERY HIGH RESOLUTION DATA INTRODUCTION

Vegetation Change Detection of Central part of Nepal using Landsat TM

Cell-based Model For GIS Generalization

GeoComputation 2011 Session 4: Posters Accuracy assessment for Fuzzy classification in Tripoli, Libya Abdulhakim khmag, Alexis Comber, Peter Fisher ¹D

CHAPTER 1 THE UNITED STATES 2001 NATIONAL LAND COVER DATABASE

2 Dr.M.Senthil Murugan

IMAGE CLASSIFICATION TOOL FOR LAND USE / LAND COVER ANALYSIS: A COMPARATIVE STUDY OF MAXIMUM LIKELIHOOD AND MINIMUM DISTANCE METHOD

Object-based Vegetation Type Mapping from an Orthorectified Multispectral IKONOS Image using Ancillary Information

M.C.PALIWAL. Department of Civil Engineering NATIONAL INSTITUTE OF TECHNICAL TEACHERS TRAINING & RESEARCH, BHOPAL (M.P.), INDIA

LAND USE MAPPING AND MONITORING IN THE NETHERLANDS (LGN5)

Landuse and Landcover change analysis in Selaiyur village, Tambaram taluk, Chennai

LAND COVER AND LAND USE CHANGE DETECTION AND ANALYSES IN PLOVDIV, BULGARIA, BETWEEN 1986 AND 2000

Spatial Process VS. Non-spatial Process. Landscape Process

LANDSCAPE PATTERN AND PER-PIXEL CLASSIFICATION PROBABILITIES. Scott W. Mitchell,

GLOBAL/CONTINENTAL LAND COVER MAPPING AND MONITORING

Object-based land use/cover extraction from QuickBird image using Decision tree

Techniques for Estimating the Positional and Thematic Accuracy of Remotely Sensed Products. Carlos Antonio Oliveira Vieira 1 Paul M.

LARGE AREA LAND COVER CLASSIFICATION WITH LANDSAT ETM+ IMAGES BASED ON DECISION TREE

West meets East: Monitoring and modeling urbanization in China Land Cover-Land Use Change Program Science Team Meeting April 3, 2012

A SURVEY OF REMOTE SENSING IMAGE CLASSIFICATION APPROACHES

International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July ISSN

INTERNATIONAL JOURNAL OF GEOMATICS AND GEOSCIENCES Volume 4, No 1, 2013

Land Features Extraction from Landsat TM Image Using Decision Tree Method

Classification of Agricultural Crops and Quality Assessment Using Multispectral and Multitemporal Images

Investigation of the Effect of Transportation Network on Urban Growth by Using Satellite Images and Geographic Information Systems

CHANGE DETECTION USING REMOTE SENSING- LAND COVER CHANGE ANALYSIS OF THE TEBA CATCHMENT IN SPAIN (A CASE STUDY)

SYNERGISTIC USE OF FIA PLOT DATA AND LANDSAT 7 ETM+ IMAGES FOR LARGE AREA FOREST MAPPING

VISUALIZATION URBAN SPATIAL GROWTH OF DESERT CITIES FROM SATELLITE IMAGERY: A PRELIMINARY STUDY

Land Surface Processes and Land Use Change. Lex Comber

Hyperspectral image classification using Support Vector Machine

CLASSIFICATION OF MULTI-SPECTRAL DATA BY JOINT SUPERVISED-UNSUPERVISED LEARNING

The Redwood National and State Parks Vegetation Classification and Mapping Project Map Data Sets Completed and Delivered! 1

Community Identification Based on Multispectral Image Classification for Local Electric Power Distribution Systems

International Journal of Remote Sensing, in press, 2006.

Comparison between Land Surface Temperature Retrieval Using Classification Based Emissivity and NDVI Based Emissivity

Application of ZY-3 remote sensing image in the research of Huashan experimental watershed

The Application of Extreme Learning Machine based on Gaussian Kernel in Image Classification

AN INVESTIGATION OF AUTOMATIC CHANGE DETECTION FOR TOPOGRAPHIC MAP UPDATING

URBAN CHANGE DETECTION OF LAHORE (PAKISTAN) USING A TIME SERIES OF SATELLITE IMAGES SINCE 1972

Object-based classification of residential land use within Accra, Ghana based on QuickBird satellite data

ANALYSIS AND VALIDATION OF A METHODOLOGY TO EVALUATE LAND COVER CHANGE IN THE MEDITERRANEAN BASIN USING MULTITEMPORAL MODIS DATA

ASSESSMENT OF NDVI FOR DIFFERENT LAND COVERS BEFORE AND AFTER ATMOSPHERIC CORRECTIONS

RVM-based multi-class classification of remotely sensed data

REMOTE SENSING ACTIVITIES. Caiti Steele

SATELLITE REMOTE SENSING

GIS GIS.

Preparation of LULC map from GE images for GIS based Urban Hydrological Modeling

USE OF RADIOMETRICS IN SOIL SURVEY

NR402 GIS Applications in Natural Resources. Lesson 9: Scale and Accuracy

Progress and Land-Use Characteristics of Urban Sprawl in Busan Metropolitan City using Remote sensing and GIS

7.1 INTRODUCTION 7.2 OBJECTIVE

Quick Response Report #126 Hurricane Floyd Flood Mapping Integrating Landsat 7 TM Satellite Imagery and DEM Data

Accuracy Assessment of Per-Field Classification Integrating Very Fine Spatial Resolution Satellite Imagery with Topographic Data

Identifying Audit, Evidence Methodology and Audit Design Matrix (ADM)

USING GIS CARTOGRAPHIC MODELING TO ANALYSIS SPATIAL DISTRIBUTION OF LANDSLIDE SENSITIVE AREAS IN YANGMINGSHAN NATIONAL PARK, TAIWAN

AssessmentofUrbanHeatIslandUHIusingRemoteSensingandGIS

URBAN LAND COVER AND LAND USE CLASSIFICATION USING HIGH SPATIAL RESOLUTION IMAGES AND SPATIAL METRICS

Land Use and Land Cover Detection by Different Classification Systems using Remotely Sensed Data of Kuala Tiga, Tanah Merah Kelantan, Malaysia

Using Cellular Automaton to Simulate Urban Expansion in Changchun, China

Simulation of Wetlands Evolution Based on Markov-CA Model

CORRELATION BETWEEN URBAN HEAT ISLAND EFFECT AND THE THERMAL INERTIA USING ASTER DATA IN BEIJING, CHINA

Land Use/Land Cover Mapping in and around South Chennai Using Remote Sensing and GIS Techniques ABSTRACT

COMPARISON OF PIXEL-BASED AND OBJECT-BASED CLASSIFICATION METHODS FOR SEPARATION OF CROP PATTERNS

Scientific registration n : 2180 Symposium n : 35 Presentation : poster MULDERS M.A.

STUDY ON FOREST VEGETATION CLASSIFICATION BASED ON MULTI- TEMPORAL REMOTE SENSING IMAGES

MAPPING LAND USE/ LAND COVER OF WEST GODAVARI DISTRICT USING NDVI TECHNIQUES AND GIS Anusha. B 1, Sridhar. P 2

Object-based feature extraction of Google Earth Imagery for mapping termite mounds in Bahia, Brazil

FINDING SPATIAL UNITS FOR LAND USE CLASSIFICATION BASED ON HIERARCHICAL IMAGE OBJECTS

DIGITAL EARTH: QUANTIFYING URBAN LANDSCAPE CHANGES FOR IMPACT ANALYSIS

DEPENDENCE OF URBAN TEMPERATURE ELEVATION ON LAND COVER TYPES. Ping CHEN, Soo Chin LIEW and Leong Keong KWOH

Spectral and Spatial Methods for the Classification of Urban Remote Sensing Data

An Internet-based Agricultural Land Use Trends Visualization System (AgLuT)

Modeling urban growth pattern for sustainable archaeological sites: A case study in Siem Reap, Cambodia

STUDY OF NORMALIZED DIFFERENCE BUILT-UP (NDBI) INDEX IN AUTOMATICALLY MAPPING URBAN AREAS FROM LANDSAT TM IMAGERY

INTERNATIONAL JOURNAL OF GEOMATICS AND GEOSCIENCES Volume 2, No 1, 2011

Landsat-based Global Urban Area Map

UNCERTAINTY AND ERRORS IN GIS

Crops Planting Information Retrieval at Farmland Plot Scale Using Multi-Sources Satellite Data

Transcription:

Proceedings of the 8th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences Shanghai, P. R. China, June 25-27, 2008, pp. 183-188 A Method to Improve the Accuracy of Remote Sensing Data Classification by Exploiting the Multi-Scale Properties in the Scene Yanchen Bo 1, 2 + 1. State Key Laboratory of Remote Sensing Science, Jointly Sponsored by Beijing Normal University and Institute of Remote Sensing Applications, CAS, Bejing, China 2. Research Center for Remote Sensing and GIS, School of Geography, Beijing Key Laboratory for Remote Sensing of Environment and Digital Cities, Beijing Normal University, Beijing, 100875, China Abstract. Land use mapping is one of the major applications of remote sensing. While most studies focus on the advanced remote sensing thematic classification algorithms for land use mapping, the scale factor in remote sensing data classification was less recognized. Previous studies showed that while the multi-scale characteristics exist in the remotely sensed data for land use classification, some classes are mostly accurately classified at a finer resolution, and others at coarser ones. Thus, it is helpful to improve the overall classification accuracy by mapping different land use classes at different scales. In this paper, a framework for improving the land use classification accuracy by exploiting the multi-scale properties of remotely sensed data is presented. Firstly, the remotely sensed data at original fine resolution was up-scaled to different coarser resolutions; Secondly, the up-scaled data were classified by independently trained Maximum Likelihood Classifier at every resolution, and the corresponding a Posteriori Probability of MLC classification was saved; Thirdly, the classification results at different resolutions were integrated by comparing the a Posteriori Probability of classification at every resolution. The final class of pixel was labeled as the class that has the maximum a Posteriori Probability. A case study on the land use mapping using Landsat TM data using this framework was conducted in the Dianchi Watershed in Yunnan Province of China. The land use was categorized into 6 classes. The classification accuracy was assessed using the Confusion Matrix. Comparison between the classification accuracy at multi-scale and that at original resolution showed an improvement of overall classification accuracy by about 10%. The study showed that by exploiting the multi-scale properties in the remotely sensed data, the accuracy the land use mapping can be improved significantly. Keywords: remote sensing, classification, multi-scale characteristics, uncertainty, land use 1. Introduction Land use mapping is one of the major applications in remote sensing. How to accurately acquire the land use information by classifying remotely sensed data have been extensively studied in the past decades of time. While most of the studies in land use classification focused on developing new classification algorithm such as artificial neural network and Support Vector Machine (SVM), some others focused on incorporating ancillary data into the classification feature space so that the classes can be more easily discriminated. While many features such as textures, NDVI et al., have been used for land use mapping, the multi-scale feature is attracting more and more interests. Present satellite data are able to provide remotely sensed data with spatial resolution ranges from less than 1m to nearly 100 kilometres. When users try to use these remotely sensed data, it is natural that one has to choose the data with optimal spatial resolution so that the thematic information extracted from it contains the least uncertainty. Among the factors such as spectral resolution, training strategies and classification + Corresponding author. Tel.: +86-10-58802062; fax: +86-10-58805274 E-mail address: boyc@bnu.edu.cn ISBN: 1-84626-170-8, ISBN13: 978-1-84626-170-1

algorithm, the scale factor is one of the most important factors that influence the uncertainty of thematic information derived from remotely sensed data. In remote sensing, the spatial scale refers to the spatial resolution of remotely sensed data. The effect of spatial scale in remotely sensed data classification has been recognized since 1980 s. Woodcock et al. (1987) analyzed the scale effect of remote sensing data classification by using the local variance analysis. It showed that the local variance reaches its maximum while the size the object is almost equal to the pixel size. Arbia et al.(1996) pointed out that the scale effect in remote sensing is a special case of the Modifiable Areal Unit Problem (MAUP) in scale research. He studied the scale effect in the Maximum Likelihood Classification of remote sensing data using the simulated imagery. The results showed that the classification error increase while the spatial resolution of remote sensing data become coarser. The scale effect is most significant in the boundaries between thematic classes. No single optimal spatial resolution exists for all classes in complex landscape classification (Marceau et al., 1994a; 1994b). Bo et al. (2003) explored the scale effect in remote sensing data classification by using the statistical separability of features and pointed out that, the scale effect of separabilities between classes were highly related to the spatial patterns of classes in the scene. Finer spatial resolution does not definitely lead to higher classification accuracy. Due to the scale effect in remote sensing data classification, for the complex landscape, classification accuracy of some classes is high at high resolution, and some others at low resolution. Integrating multi-scale remote sensing data for classification is a natural way to improve the accuracy in land use mapping. Chen (2003) presented a strategy to integrating multispectral remote sensing data with different spatial resolution to improve the land use classification accuracy. However, acquiring remote sensing data with different spatial resolution increase the cost of land use mapping. In addition, because the satellite data with different spatial resolution also have different spectral band configuration and spectral resolution, the improvement of integrating multi-scale remote sensing data is hard to be rigorously evaluated. In this paper, an approach to integrating multi-scale properties in remote sensing data for land use mapping is presented. Instead of using remote sensing data from different sensors, the multiple resolution remote sensing data was acquired by aggregating the high spatial resolution data to different spatial resolution, so that the spectral band configuration and spectral resolution of the data at different scale were preserved. The paper was arranged in 4 sections. Section 2 describes the method and data for integrating multi-scale remote sensing data for land use classification. Section 3 gives a comprehensive interpretation of the results. Section 4 concludes the whole paper and discusses the related problems. 2. Principles and Methods 2.1 Acquisition of Multi-scale remote sensing data Instead of using multispectral remote sensing data with different spatial resolution acquired from different sensors, the multi-scale remote sensing data were acquired by re-sampling the high spatial resolution data to different spatial resolution. The benefit of the method is that the spectral band configuration and spectral resolution of original high spatial resolution data is preserved. The resampling method used in this paper is the cubic convolution resampling. 2.2 Method of integrating multi-scale data for classification The method of integrating multi-scale remote sensing data for classification has two basic steps. Firstly, the multi-scale remote sensing data obtained using resampling were independently trained and classified. Secondly, the classified results from multi-scale remote sensing data were integrated using an optimal decision method. To integrate the results from multi-scale data classification, an integration criterion should be premeditated. In this paper, the posteriori probability in the classification of every scale data was chosen as the integration criterion. The posteriori probability was obtained in the process of the Maximum Likelihood Classification (MLC) of remote sensing data. The pixel to be classified is labeled as the class that has the maximum posteriori probability. The integration method based on the posteriori probability is illustrated in Figure 1. 184

Fig.1. The illustration of the multi-scale classification integration based on the posteriori probability in classification 2.3 Integration strategy in multi-scale data for classification To integrate the classification results of remote sensing data at multi-scale based on the posteriori probability, a bottom-to-top integration strategy was used. In this strategy, for a pixel to be classified, if the posteriori probability of the classification highest spatial resolution is equals to the maximum posteriori probability at all resolutions, the pixel was labeled using the label classified at the highest spatial resolution data. If the posteriori probability of the classification highest spatial resolution is less than the maximum posteriori probability at all resolutions, then the posteriori probability at the coarser resolution is compared to the maximum posteriori probability at all resolutions. The comparison process was repeated until find the scale at which the posteriori probability equals to the maximum posteriori probability at all resolutions, and the pixel was labeled using the label classified at the scale at which it has the maximum posteriori probability. Assume the original multispectral remote sensing data was resampled to N resolutions. The spatial resolution was ranked from high to coarse as: R 1, R 2,,R n. The classified results and the corresponding posteriori probability were noted as C 1, C 2,,C n and P 1, P 2,,P n respectively. Let Pmax=Max(P 1,P 2,,P n ), where the Max prefer to the Maximum of (P 1,P 2,,P n ). The integration strategy can be described as follow: 3. Data and Results If P 1 =P max C=C 1 Else if P 2 =P max C=C 2. Else if P i =P max C=C i.. Else if P n-1 = P max C=C n-1 Else C=C n... To examine the effectiveness of the multi-scale remote sensing data classification in improving accuracy of land use mapping, the Lansat-5 Thematic Mapper data in Dianchi watershed, Yunnan Province, China was used to conduct the multi-scale classification. The data was acquired in 1990. the original data with 30m spatial resolution was resampled to the spatial resolution of 60m, 90m, 120m, 180m, 270m and 360m respectively by the cubic resampling technique. The multi-scale TM data was independently trained and classified using the Maximum Likelihood Classifier. besides the classification results, their corresponding posteriori probability were saved. The classification results were assessed by using the Error Matrix method. 185

The reference data in accuracy assessment is from the China Land Use Database. Because the classification were conducted at different scale, to compare the classification results and their posteriori probability, the classification results and posteriori probability have to be transformed to the original resolution. To preserve the value of the classification results and posteriori probability at different scale, the data were transformed to original resolution by splitting one pixel into N pixel without changing any pixel value. The transformation process was illustrated in Figure 2. Fig.2. Illustration of the information transformation from coarse resolution to fine resolution Fig. 3. The classified results of the data with different spatial resolution Table 1. The accuracy of the classification at different spatial resolution Spatial Resolution 30m 60m 90m 120m 180m 270m 360m Kappa Statistics 0.4712 0.4402 0.4158 0.4349 0.4662 0.4154 0.4150 Overall Accuracy 0.5593 0.5311 0.5113 0.5282 0.5537 0.5113 0.5113 The classification results of the TM data at multi-scale were presented in Figure 3. the accuracy of the classification at every spatial resolution was shown in Table 1. Table 1 showed that the classification accuracy changes while the spatial resolution of the data changes, but high spatial resolution does not definitely lead to high classification accuracy. 186

The multi-scale classification integration experiments were conducted by integrating the classification at original TM spatial resolution with different number of coarser spatial resolution. The results and their accuracy were presented in Figure 4 and Table 2 respectively. Fig.4. The classification results by integrating different spatial resolution data Table 2. The accuracy of classification in integration of multi-scale remote sensing Experiment No. The spatial resolution of the data Kappa Statistics Overall Accuracy 1 30m, 60m 0.5097 0.5932 2 30m, 60m, 90m 0.5299 0.6102 3 30m, 60m, 90m,120m 0.5603 0.6360 4 30m, 60m, 90m,120m,180m 0.6021 0.6695 5 30m, 60m, 90m,120m,180m, 270m 0.5513 0.6271 6 30m, 60m, 90m,120m,180m, 270m, 360m 0.5430 0.6186 Compare the Table 2 to the Table 1 shows that all the experiments of multi-scale remote sensing data classification integration can improve the classification accuracy. The overall accuracy and the Kappa Statistics can be improved by 4-11% and 3-13% respectively. Meanwhile, it was showed that more scale of data being integrated does not mean higher accuracy. When the number of scale of data is small, the classification accuracy increases with the number of scale of data increase. However, when the number of scale of data is larger than a threshold, the classification accuracy decrease with the number of scale continuously increases. This phenomenon is reasonable in theory. When the spatial resolution of data become coarser, the within class variance decreases so that the separability between classes increase and the 187

posteriori probability of the classification increase, thus the classification accuracy increase. However, when the spatial resolution of data become coarser than a threshold, some objects in the imagery will aggregated with adjacent pixels and could be classified as other classes with high posteriori probability, which makes the accuracy of final classification that integrated very coarse spatial resolution data decrease. For a given landscape, there exists a threshold scale. In this experiment, the maximum classification accuracy appears in the integration of data with spatial resolution from 30m to 180m. When data with spatial resolution coarser than 180m was integrated, the final classification accuracy decreased. 4. Conclusions and Discussions Because of the multi-scale properties of natural landscape, integrate multi-scale remote sensing data for is a promising way to improving the classification accuracy land use. In this paper, a bottom to top method was presented to integrate the multi-scale remote sensing data classification to improve the land use mapping accuracy. This method assume that when the posteriori probability of the classification at two resolution equals, the results at finer resolution is more reliable. the multi-scale remote sensing data was acquired by resampling the Landsat TM data to different coarser resolutions. The performances of integrating different number of resolution data were evaluated. It can be conclude that integrating the classification of multi-scale remote sensing data is a effective way to improve the land use mapping accuracy. However, integrating larger number of spatial resolution data does not definitely lead to higher land use mapping accuracy. There is a threshold spatial resolution exists. It was also testified that need not any other ancillary data, just scaling the remote sensing data to different scale and integrate the classification results at these scale could improve the final classification accuracy significantly. 5. Acknowledgement This research were supported by, National Basic Research Program of China (Project No.2007CB714402-10), State Key Lab. of Remote Sensing Science, the grants from NSFC (No.40301033), and the Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT, No.IRT0409) 6. References [1] Arbia G., R.Benedeiti and G. Espa, Effect of the MAUP on image classification, Geographical System, 1996, 3: 123-141. [2] Bo Y. and Wang J., Uncertainty in Remote Sensing: Classification and Scale Effect Modelling. Geological Press, Beijing 2003 [3] Chen D.M., Strategies eor integrating information from multiple spatial resolutions into Land-Use/Land-Cover Classification Routines, Photogrammetric Engineering and Remote Sensing. 2003, 69(11): 1279-1287. [4] Marceau D.J., P.M.Howarth and D.J. Gratton, Remote sensing and the measurement of geographical entities in a forested Environment, Part 1: The scale and spatial aggregation problem, Remote Sensing of Environment, 1994a, 49: 93-104. [5] Marceau D. J., D.J. Gratton, R. Foumier, and J.P. Fortin, Remote sensing and the measurement of geographical entities in a forested environment, Part 2: The optimal spatial resolution, Remote Sensing of Environment, 1994b, 49: 105-117. [6] Markham B.L. and Townshend J.R.G., Landcover classification accuracy as a function of sensor spatial resolution. Proc. 15th International Symposium of Remote Sensing of Environment. Ann Arbor, 1981: 1075. [7] Woodcock C. E. and A.H. Strahler, The factor of scale in remote sensing, Remote Sensing of Environment, 1987, 21: 311-332. 188