MODELLING UNCERTAINTY IN THEMATIC MAPS DERIVED FROM REMOTE SENSING DATA

Abstract

In recent years, there has been a growing concern on the use and acceptance of thematic maps derived from remote sensing image classification. During the process of digital image classification, thematic and positional errors may creep in, which affect the quality of these maps. Generally, the quality of remotely sensed derived thematic maps is expressed in terms of accuracy measures. However, these measures may not be able to reveal complete information on the quality of thematic maps. Moreover, the existing accuracy measures are global indicators of quality on map basis or individual class basis and hence have inability to convey spatial distribution of quality. Further, to evaluate the quality of thematic maps using accuracy measures, error free reference data is required, which sometimes may not be available, or difficult to collect. In such situations, additional indicators of quality may be useful. Uncertainty may be used to supplement the statements of accuracy in providing information on quality. Corresponding to both thematic and positional errors, uncertainty modelling can be performed. Positional uncertainty relates to the modelling of errors in the location of pixel (i.e., row-column coordinates), whereas thematic uncertainty relates to the error in attribute (e.g., land cover type) of the pixel. During the last decade, uncertainty as a quality assessment tool has become a key subject in remote sensing studies and has attracted attention of many researchers (e.g., Canters 1997, Kiiveri 1997, Foody 2002, Lucieer and Kraak 2004, Ibrahim et Modelling Uncertainty in ThematicMaps Derivedfrom Remote Sensing Data al. 2005, Cayuela et al. 2006). A review of literature indicates that a number of uncertainty models have been postulated based on several mathematical theories, viz., probability theory, theory of evidence, fuzzy set, possibility and rough set theories. This has led to many remote sensing studies on uncertainty determination via different measures. A number of measures such as entropy (Maselli et al. 1994, Legleiter and Goodchild 2005, Hamid and Hassan, 2006), quadratic score (Glasziou and Hilden 1989, Fatemi et al. 2004), ignorance and exaggeration uncertainty (AXing Zhu 1997), non-specificity and U-uncertainty (Ricotta 2005), confusion index (Burrough et al. 1997, Kyriakidis and Dungan 2001) and index of fuzziness (Binaghi et al. 1999, Ibrahim et al. 2005) have been suggested to quantify pixel level thematic uncertainty. However, a proper analysis is needed to group these measures on the basis of their similarities and the type of uncertainty they intend to represent. Moreover, since different uncertainty measures may portray varied characteristics of errors, there is a need to combine different measures of thematic uncertainty. Further, positional quality of thematic maps depends on the quality of geometric registration performed on the remotely sensed images. A standard and common method of assessing the positional quality is based on comparison of deviations between locations of ground control points (GCPs) on the reference map/image and the geometrically corrected image. Based on this comparison, Root Mean Squared Error (RMSE) of control points can be estimated and used to depict the positional quality. The RMSE is a global measure and represents the quality of whole image as single value. Therefore, a methodology needs to be framed to model positional uncertainty at pixel level instead of accepting the quality based on a single value ofRMSE. Abstract The work presented in this thesis is therefore, aimed to significantly advance the research on modelling thematic and positional uncertainties in remotely sensed derived maps. The major objectives of this research can be summarised as, comparative study, evaluation and categorisation of some of thematic uncertainty measures, modelling combined thematic uncertainty to represent different forms of uncertainty that may arise for a pixel during class allocation and to model pixel level positional uncertainty to indicate positional quality. Two data sets, synthetic data and remote sensing data, have been used in this study to achieve the research objectives. Synthetic images mimicking a Landsat ETM+ image in six spectral bands have been generated and have been used to evaluate various thematic uncertainty measures. Remote sensing data consists of images acquired from ETM+ sensor on-board Landsat satellite and is used to gauge the applicability of thematic and positional uncertainty models in a wider spectrum. Fuzzy c-means (FCM) classification derived class membership values of pixels become the input to a number of thematic uncertainty measures such as entropy, relative entropy, ignorance uncertainty, non-specificity, U-uncertainty, exaggeration uncertainty, confusion index in two forms, index of fuzziness and a measure of classification uncertainty provided in IDRISI image processing software. The results show that some of the measures of thematic uncertainty are similar in conveying uncertainty information. It has been observed that entropy, relative entropy, quadratic score and ignorance uncertainty are similar. Relative entropy and ignorance uncertainty are the normalized versions of entropy. Nonspecificity and U-uncertainty which are based on possibility theory also appear Modelling Uncertainty in ThematicMaps Derivedfrom Remote Sensing Data similar. Exaggeration uncertainty and a measure of classification uncertainty provided in IDRISI software have also been found to be similar. The two forms of confusion index have exhibited some disparity in conveying uncertainty information. Some of the relationships between these measures have also been proved mathematically. Based on the theoretical background, type of uncertainty and the experimental results, the measures of thematic uncertainty considered in this study have been categorized into different groups. Accordingly, ambiguity due to imprecision, which is one of the forms of uncertainty, can be represented by entropy, relative entropy and ignorance uncertainty within the probabilistic framework. In contrast, non-specificity and U-uncertainty represent ambiguity due to imprecision within possibilistic framework. Ambiguity due to conflict or overlap between two classes can be represented by two forms of confusion index, while ambiguity due to inaccuracy may be represented by exaggeration uncertainty. Other form of uncertainty, i.e., fuzziness can be quantified using index of fuzziness. Based on the comparative analysis, a taxonomy of uncertainty measures for remote sensing image classification has been suggested and the suitability of these measures has been evaluated using a measure of Goodness of Fit. The taxonomy assist the users in selection of a measure of thematic uncertainty keeping in view the following factors viz., quantity of mixed pixels present in the image to be classified, the type of uncertainty to be represented and the theoretical framework of uncertainty measure. IV * Abstract However, each group is intended to represent a particular type of uncertainty and hence, is capable of representing only one facet of uncertainty. For example, entropy indicates the uncertainty due to heterogeneity of class membership values in a pixel whereas the measures of confusion index indicate conflict due to overlapping of two most probable classes in a pixel. Occurrence of different types of thematic uncertainty in a pixel due to different reasons can thus, not be ruled out. For example, three components of thematic uncertainty may be assumed to be associated with a pixel during class allocation. These three components correspond to three different stages of decision making process of allocating a pixel to a class. The class membership vector of a pixel derived from fuzzy classification exhibits ambiguity due to imprecision, which may be quantified using entropy (in the probabilistic frame work) or non-specificity (in fuzzy/ possibilistic frame work). Secondly, ambiguity in making a decision on the belongingness of a pixel to one of the two classes can be estimated using measures of confusion such as confusion index. Finally, it is also a common practice to assign the pixel to that class to which it has the highest membership. In doing so, even if the maximum class membership is marginally higher than the second highest class membership, the pixel is allocated to the class having maximum membership. This leads to an error in class assignment and introduces uncertainty due to a state of inaccuracy. This type of uncertainty may be quantified by exaggeration uncertainty. Therefore, the above three components of thematic uncertainty conveying different types of uncertainty have been integrated in the form of a combined thematic uncertainty model. The model aggregates these measures using fuzzy Modelling Uncertainty in Thematic Maps Derivedfrom RemoteSensing Data algebraic sum operator. In addition, the use of Dempster's orthogonal sum for aggregating individual measures of uncertainty has also been explored. The performance of the combined uncertainty model has been evaluated by considering the percentage of misclassifications vis a vis uncertainty values. The results from the application of combined uncertainty model indicate that the percentage of misclassification increases with the increase in the magnitude of combined thematic uncertainty; an outcome, which could not be achieved through assessment of individual uncertainty measure. A methodology to estimate positional uncertainty at pixel level has also been proposed and implemented on experimental data. The proposed methodology utilises the x and y residual errors for the GCPs to estimate corresponding errors at pixel level using kriging interpolation. Random error fields have been simulated and added to the interpolated errors to generate multiple realizations of residual errors. The multiple values of x and y residual errors for each pixel have been further used to estimate the parameters of standard error ellipse and 95% confidence ellipse. The positional uncertainty of each pixel has been expressed as the length of semi major axis of 95% confidence ellipse. The major advantage of the proposed methodology lies in spatial representation of positional quality. A total uncertainty model which integrates thematic uncertainty and positional uncertainty quantified using the methodology proposed in this research has also been implemented. Two experiments, one combining non-specificity with the positional uncertainty and the other which combines both positional and combined thematic uncertainty have been conducted. The results from the experiments indicate VI * Abstract that the total uncertainty model is able to depict uncertainty in various portions of the image in a realistic way. In summary, it may be concluded that i. The proposed taxonomy of various thematic uncertainty measures based on their similarities, differences and relationships amongst them may help in the selection of an appropriate measure in a justifiable manner. ii. Better understanding of the spatial distribution of positional errors may also possible with the help of the proposed positional uncertainty model. iii. The proposed combined thematic uncertainty model may assist in quantifying different facets of uncertainty that may arise during class allocation, in a single model. The outcome of this research may help users in creating awareness about the presence of uncertainty in thematic maps. No doubt, fixing some standards and guidelines for the acceptability and usability of thematic maps derived from remote sensing data based on uncertainty may be beneficial both to the producers and users of thematic maps in many different ways. Vll