  Classification of remotely sensed images into land cover or land use is
highly dependent on geographical information at least at two levels. First,
land cover classes are observed in a spatially smooth domain separated by sharp
region boundaries. Second, land classes and observation scale are also tightly
intertwined: they tend to be consistent within areas of homogeneous appearance,
or regions, in the sense that all pixels within a roof should be classified as
roof, independently on the spatial support used for the classification. In this
paper, we follow these two observations and encode them as priors in an energy
minimization framework based on conditional random fields (CRFs), where
classification results obtained at pixel and region levels are
probabilistically fused. The aim is to enforce the final maps to be consistent
not only in their own spatial supports (pixel and region) but also across
supports, i.e., by getting the predictions on the pixel lattice and on the set
of regions to agree. To this end, we define an energy function with three
terms: 1) a data term for the individual elements in each support
(support-specific nodes); 2) spatial regularization terms in a neighborhood for
each of the supports (support-specific edges); and 3) a regularization term
between individual pixels and the region containing each of them (intersupports
edges). We utilize these priors in a unified energy minimization problem that
can be optimized by standard solvers. The proposed 2LCRF model consists of a
CRF defined over a bipartite graph, i.e., two interconnected layers within a
single graph accounting for interlattice connections.
