Minimal-memory bit-vector architecture for computational mathematical morphology using subspace projections

Computational mathematical morphology (CMM) is a nonlinear filter representation particularly amenable to real-time image processing. A windowed, translation-invariant filter is represented by a set of less-than-or-equal decisions that are executed by a parallel arrangement of comparators. In the state-of-the-art implementation, each pixel value of a windowed observation is indexed into separate lookup tables to retrieve a set of bit vectors which are "anded" together to produce a bit vector with a unique nonzero bit. The position of that bit is used to look up a filter value in a table. The number of stored bit vectors is proportional to the number of image gray levels. An architecture for CMM is presented that uses a minimal number of bit vectors so that required memory is less sensitive to the number of gray levels. The number of pixels in the observation window is the dimension of the image space. In the proposed architecture, basis elements are projected to subspaces of the image space and only bit vectors unique to each subspace are stored. Each projection corresponds to a subspace partition. Filter memory is greatly reduced by using intermediate lookup tables to map observations to unique bit vectors. We investigate two possible projection strategies: A fixed, singleton architecture, in which each subspace is one dimension, and a minimal architecture, in which a large number of subspace projections are searched for, one with minimal memory. Insensitivity to the number of gray levels is demonstrated through simulated, random-image space tessellations. We also present memory savings in a digital photocopier application.