Topological class models of composite classes

A key strategy in object-based image analysis is multi-scale representation of the entire scene content. When generating image objects in a nested hierarchy, higher-level composite objects are usually more complex than lower-level ones. While simple, elementary objects (building blocks) are characterized by spectral homogeneity, complex objects bear ‘functional homogeneity’, which is more difficult to grasp and harmonize across expert opinions.  Higher image resolutions increase the level of details along the geographical scaling ladder but the principle of (homogenous) building blocks and (heterogeneous) composites remains the same. On the other hand, the scaling ladder is not infinite as the human scale domain seems to have natural limits, comprising by finer and coarser scales the basic level(s) of geographical ontology/ies.

The internal heterogeneity of complex target classes can be captured by statistical pattern measures, while the actual spatial arrangement is a topological-relational property, rather than a statistical. Class modeling can be utilized to topologically describe such ‘body plans of spatial constellations employing relational features. This PhD topic will combine topological class descriptions with pattern indices forming an ‘envelope’ for complex composite classes also considering the issue of scale specificity. The topic will be guided by the following research questions:

1.    How can we operationalize topological descriptors for composite objects and object-relational class models, irrespective of absolute size or position?
2.    How can these be combined with classical, pixel-based entropy measures (e.g. Moran’s I, Geary’s C or the Contagion Index)?
3.    Is there a way to establish an absolute or universal hierarchy of geographic objects in human-scale GEOBIA where different sensor resolution levels cover certain portions?

There are strong interdisciplinary links foreseen in clarifying whether OBIA hierarchical object representations can be linked to the theory of typicality and category hierarchies in cognitive science.