Persistence Based on LBP Scale Space

This paper discusses the connection between the texture operator LBP (local binary pattern) and an application of LBPs to persistent homology. A shape representation the LBP scale space is defined as a filtration based on the variation of an LBP parameter. A relation between the LBP scale space and a variation of thresholds used in the segmentation of a graylevel image is discussed. Using the LBP scale space a characterization of (parts of) shapes is demonstrated based on simple shape primitives, the observations may also be generalized for smooth curves. The LBP scale space is augmented by associating it with polar coordinates (with the origin located at the LBP center). In this way a procedure of shape reconstruction based on the LBP scale space is defined and its reconstruction accuracy is demonstrated in an experiment. Furthermore, this augmented LBP scale space representation is invariant to translation and rotation of the shape.