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 shaperepresentation - the LBP scale space - is defined as a filtration based on the varia-tion of an LBP parameter. A relation between the LBP scale space and a variationof thresholds used in the segmentation of a graylevel image is discussed. Usingthe LBP scale space a characterization of (parts of) shapes is demonstrated basedon simple shape primitives, the observations may also be generalized for smoothcurves. The LBP scale space is augmented by associating it with polar coordi-nates (with the origin located at the LBP center). In this way a procedure of shapereconstruction based on the LBP scale space is defined and its reconstruction ac-curacy is demonstrated in an experiment. Furthermore, this augmented LBP scalespace representation is invariant to translation and rotation of the shape.