The Blake-Zisserman model for digital surface models segmentation

The Blake-Zisserman functional is a second-order variational model for data segmentation. The model is build up of several terms, the nature and the interaction of them allow to obtain a smooth approximation of the data that preserves the constant-gradient areas morphology, which are explicitly detected by partitioning the data with the graph of two special functions: the edge-detector function, which detects discontinuities of the datum, and the edge/crease-detector function, which also detects discontinuities of the gradient. First, the main features of the model are presented to justify the sense of the application of the model to DSMs. It is stressed the fact that the model can yield an almost piecewise-linear approximation of the data. This result is certainly of some interest for the specific application of the model to urban DSMs. Then, an example of its application is presented and the results are discussed to highlight how the features of the model affect the model outputs. The smooth approximation of the data produced by the model is thought to be a better candidate for further processing. In this sense, the application of the Blake-Zisserman model can be seen as a useful preprocessing step in the chain of DSMs processing. Eventually, some perspectives are presented to show some promising applications and developments of the Blake-Zisserman model.