## 3 Image Segmentation and the Scale of Analysis  
Image segmentation clusters the original image pixels into segments, based on one or more criteria of similarity in one or more dimensions of a feature space, and is a preliminary and crucial step in object-based image analysis [1]. An efficient graph-based image segmentation algorithm, which has been originally developed by [PERSON] and [PERSON] [26], is used within this study. The algorithm measures the evidence for a boundary between two segments by comparing the feature vectors across the boundary with those between neighboring pixels within each segment. The brightness values of the image pixels in all spectral bands of the satellite image are used to define the input feature space for segmentation, and the L2 Euclidean distance is used to measure the dissimilarity. A threshold function with runtime parameters \(k\) (scale parameter) and \(m\) (minimum allowable segment size) allow to effectively set a spatial scale of analysis, since larger values for \(k\) and \(m\) favor larger segments.  
Ideal segments are considered as singular entities outlining objects of homogeneous appearance without over- or under-segmenting them. To define the scale of analysis, segmentation parameters must be adjusted and quantitative evaluation of the segmentation quality becomes important. In this study, segmentation parameters for the VHR images have been adjusted based on a comparison of the segmentation results with reference objects by using supervised segmentation quality measures [28]. In a set of segmentations, the parameter values that produced the best area-fit to the reference objects with the least number of segments where selected.  
Compared to VHR images where analysis scales can be defined by comparing the segmentations with reference objects, the delineation of reference objects in MR images is problematic due to their large GSD. Given a GSD in a range of 15-60 m for Landsat imagery, individual buildings cannot be detected. However, larger morphological units that are composed of a mixture of buildings, streets and open-space can be distinguished from this image type. Such units cannot be delineated solely based on geometrical properties, but are mainly defined by spectral and textural image properties. This makes the manual delineation of reference objects difficult and potentially strongly biased from an operator's point of view. It emphasizes that segmentation quality needs to be assessed in an unsupervised way using image statistics. A generally accepted segmentation quality measure is based on the comparison of intra-segment homogeneity and inter-segment heterogeneity [29]. In a set of segmentations, the segmentation that minimizes intra-segment variability and maximizes inter-segment separability is defined as being optimal in terms of providing the most appropriate analysis scale for a given image scene. A global Moran's I has been utilized to quantify inter-segment heterogeneity. The standard deviation of the brightness values of the input image bands, weighted by each segment's size and summed over all the segments in the image scene, has been used for assessing intra-segment homogeneity [30]. Parameter values resulting in the segmentation with largest inter-segment heterogeneity and intra-segment homogeneity have been selected.