Development of an Advanced Uncertainty Measure for Classified Remotely Sensed Scenes

Classified remotely sensed data serves as the basis for various types of city models. Since the requirements concerning the correctness of these models are rapidly growing, the demands for a significant assurance of their quality increase as well. Standard methods for the a posteriori evaluation of classified data have successfully been applied but they do not fully meet the requirements resulting from recent developments, primarily the higher geometric and thematic accuracies of modern sensor systems. One consequence is that the uncertainties inherent in all kinds of data cannot be ignored anymore – not even those in the so-called ground truth data which is used as reference in the quality assessment process. Hence, we propose an integrated approach that considers uncertainties in both the classification and the reference data. The phenomenon of indeterminate boundaries – another effect of more accurate remote sensing data – is treated using a border model based on fuzzy logic. This paper describes the overall concept (section 1) as well as its key steps, the generation of transition zones including the fuzzification process (section 2) and the derivation of the advanced uncertainty measure (section 3). In section 4 we present an example application of the concept dealing with the evaluation of a classified orthophoto scene. 1. CONCEPTUAL OVERVIEW Basically, the conventional evaluation procedures for classified remote sensing data (especially in connection with a comparison between classification result and reference) take the reference data to be error-free (ground truth). This assumption is certainly acceptable for lower resolution remote sensing data due to a larger probability of the existence of reference data of higher order. But for high resolution data uncertainties in the reference data should not be neglected because of the worse ‘relative resolution’ between reference and sensor data. Consequently, we propose an integrated evaluation method which considers uncertainties in the reference data as well. Due to the higher spatial resolution the effect of indeterminate boundaries between certain object classes is increased in terms of the absolute number of pixels of the respective transition zones. Although adapted methods (like fuzzy logic approaches) have been developed for the actual thematic classification, analogous fuzzy logic methods for evaluation purposes are hardly applied. We propose an integrated fuzzy approach which deals with the issue of indeterminate boundaries by the definition of buffer zones around the object boundaries. This allows for the computation of the class-specific fuzzy certainty measure (CFCM) which implicates uncertainty information. Figure 1 outlines the resulting overall process whose key procedures, i.e. the generation of transition zones and the derivation of an integrated uncertainty measure, will be treated in detail in the next sections. Figure 1. Overall workflow for the derivation of the advanced uncertainty measure CFCM 2. GENERATION OF TRANSITION ZONES 2.1 Idea and previous work During an interpretation process rules for the allocation of an image object to a given (topographic) class normally assume determinate, discrete boundaries between these objects. However, in high resolution remotely sensed data larger regions (i.e. a larger number of pixels) evolve between classes (e.g. along the boundary of a forest) which make a unique allocation impossible or at least very subjective. Such indeterminate transition zones originate from limited positional accuracies or insufficient semantic definition of objects and their boundaries. Using modern sensors this fuzziness effect is even more severe due to the smaller ground pixel sizes. The spectral variance within regions representing a single topographical object increases and this leads to a larger number of mixed elements (e.g. forest consists of trees, bare ground, etc.). For modeling indeterminate regions within a classification process the application of (ε-) bands (refer to Chrisman, 1992) and the fuzzy logic theory have been proposed. With respect to the latter the concept of varying memberships to a class (from ‘no membership at all’ to ‘perfect membership’) along with its application for classification tasks, have been demonstrated by Fisher (2000). Also Wang (1990) warrants the application and proposes the derivation of a fuzzy partition matrix which summarizes the membership values of a feature to every possible class as defined in the object catalogue. Edwards & Lowell (1996) define a membership function for the description of spatial uncertainties. Here for all pairs of objects classes (so-called twains) fuzzy widths are introduced based on the mean deviations derived from repeatedly digitizing boundaries from aerial photos. 2.2 Geometric aspects The transition zones serve as a model of the boundary area between two classified geographical objects. Their geometry is constructed depending on the kind of object pair. Basically it is assumed that the transition areas are symmetric, i.e. two adjacent objects share the same transition zone geometry. In order to create the geometries for these zones the boundaries are buffered on both sides (figure 2). The boundary width depends on the classes of the respective objects and is determined in advance on the basis of semantic aspects for each occurring pair of object classes (see section 2.3). Inside of the transition zone a fuzzy membership function is defined perpendicular to the object's boundary. The result is a function that provides a value of 1.0 (full membership to an object class) on the inner boundary of the transition zone and a value of 0.0 (no membership) on the outer boundary. Currently, the concept is limited to linear fuzzy functions but future research will consider non-linear membership functions as well. It appears reasonable to apply different kinds of fuzzy functions in order to consider the shape of different transitions between certain objects. In the case of an object with multiple neighbouring objects, its boundary is being split up and the partial boundaries are buffered separately. After this, all single zones along each boundary are aggregated to an overall zone using a standard union operation (see the example application in chapter 4). Figure 2. Generation of transition zones and fuzzification per class 2.3 Semantic aspects As already pointed out, the thematic membership of the neighbouring objects have a significant influence on the fuzziness of the boundary and the width of the transition zone (Edwards & Lowell, 1996). A generally accepted specification for the width of border regions in terms of absolute numbers is virtually not possible due to a couple of factors like different ground sampling distances, seasonal influences or up-todateness. Alternatively, a qualitative approach for the definition of the width of boundary regions can be transferred from ecology. Jalas (1955) and Sukopp (1972) developed a system that describes the intensity of human influences, distinguishing between ‘natural habitats’ and ‘artificial habitats’. Based on that, regions under consideration are classified on a scale from ahemerob (natural) to polyhemerob (artificial) – which is a measure for the influence of mankind on landscape. First approaches for the combination of the degree of naturalness with remote sensing data have been developed in the Austrian SINUS-project (refer to Wrbka et al. 2003). In this project a statistical correlation has been determined between landscape metrices calculated from remote sensing data and the degree of naturalness. Based on these results and our own test series we have started with a qualitative definition of boundary region widths. The result is a ranking that includes typical object class pairs and their boundary width in relation to each other (on a scale from ‘0’ to ‘+++++’). This guideline helps us to assign absolute, quantitative zone widths to the object classes of a specific classification dataset. This must be done with respect to the characteristics of the classification data and the used object class catalogue (minimum mapping unit, quality of data sources etc.). Obviously, expert knowledge is needed for this initial step of the process so our aim is to build up a collection of parameters for common landcover / landuse catalogues (e.g. CORINE Landcover) being transferable to different datasets of the same classification product. 3. DERIVATION OF THE CHARACTERISTIC VALUE