Multiscale Landscape Representation Derived from Remote Sensing Images Using Spatial Subpixel Models and Combinatorial Maps

Landscapes can be modelled as sets of homogeneous objects (landscape elements) forming areas of characteristic patterns (landscape units). The common way to represent landscapes is by vector GIS data structures which do not provide a mechanism for storing the spatial relationships between the objects in explicit form. Also, they do not account for a multi-scale representation. Graphs can be used for describing the topology of a set of objects and the dual graph approach allows for a representation of its embedding into the Euclidean plane. The combinatorial map concept is eligible for the simultaneous representation of dual graphs in one single data structure by orientation and splitting of edges into so-called half-edges or darts. Combinatorial maps also allow for a dual graph representation of a landscape at different scales by creating a map for each hierarchy level and linking them together. The task of obtaining a landscape representation from remote sensing images can be accomplished by deriving an adequate combinatorial map representation from the image data. This is done by segmentation of the image. Adverse effects by mixed pixels on the segmentation result can be reduced by spatial subpixel analysis. This method is based on the geometric description of object boundaries that intersect pixels and thus lead to mixed pixels. Its applicability depends on the relationship between the size of the remotely sensed objects and the pixel size of the sensor. Since the distribution of grey values in the neighbourhood of any mixed pixel not only depends on the parameters of the geometric model of land cover boundaries but also on the spatial response of the sensor, knowledge about the sensors point spread function can be used to enhance performance of spatial subpixel analysis. The result of applying spatial subpixel analysis to the remote sensing image is a vector representation of edges in the image which can be transformed into the combinatorial map structure. Then segmentation can be performed by manipulation of the permutations defining the combinatorial map. This leads to a new combinatorial map which can be regarded as a representation of the landscape at a certain scale. This step can be applied repeatedly for obtaining a hierarchy of combinatorial maps each of which defining the landscape at a different abstraction level. In this work we show how spatial subpixel models and the representation of remote sensing images by combinatorial maps can be combined to retrieve a multi-scale description of landscapes with subpixel accuracy from satellite images.