Shrinking Binary Images

The general problem of shrinking binary images is addressed with emphasis on the problem of shrinking to a residue. Past work in this area is reviewed, fundamental limits are discussed and open questions are identified. Emphasis is given to techniques which can be used to verify correct performance of shrinking algorithms, including successful algorithm termination and connectivity preservation. New connectivity preservation tests are developed for parallel 2D reductive-augmentative algorithms and the application of these tests is demonstrated for a variety of shrinking algorithms. A new 2D completely parallel single-operator shrinking algorithm is developed using connectivity preservation requirements to guide the design process. Issues in 3D shrinking are also reviewed.