Self-dual inclusion filters for grayscale imagery

Using the structure of an adjacency-tree for binary-valued images, we define inclusion filters, a class of connected operators. Inclusion filters modify the image by filling or retaining the holes of the connected components of foreground and those of the background of a binary image depending on application-specific criteria, which are increasing in the set theoretic sense. We demonstrate a straightforward method to achieve self-duality (gray level inversion invariance) of inclusion filters on the discrete Cartesian domain by considering only 8-adjacency. Inclusion filters are extended to the grayscale images by the threshold decomposition principle. As an application, inclusion filters are shown to improve the performance of snake-based tracking of leukocytes observed in intravital microscopic video imagery. In this set of experiments the mean position error is reduced by a factor of 2.5 using the inclusion filter.