Fast efficient algorithms for 3x3 ranked filters using finite-state machines

Frederick M. Waltz, Ralf Hack, Bruce G. Batchelor, Bruce G. Batchelor, John W. V. Miller, Susan S. Solomon
1998 Machine Vision Systems for Inspection and Metrology VII  
Median filters and ranked filters of ranks other than median have often been proposed or used to remove image noise as well as for other reasons. These are nonlinear operations, and often have relative long execution times, making them unsatisfactory for many speed-critical industrial applications. This paper builds on the earlier work of Mahmoodi and Waltz 1 to provide efficient implementations of 3x3 ranked filters of ranks 1 (minimum), 2, 3, 4, 5 (median), 6, 7, 8, and 9 (maximum). These
more » ... maximum). These implementations are based on a partial realization of the SKIPSM (S Separated-K Kernel I Image P Processing using finite-S State M Machines) paradigm. A full SKIPSM realization is not possible because, except for the filters of ranks 1 and 9, these operations are not separable. This paper shows that, in spite of this lack of separability, the finite-state machine aspect of SKIPSM can be used to advantage. The emphasis is on software implementations, but implementations in pipelined hardware have also been demonstrated. In addition, a fast "full-SKIPSM" implementation of a slightly different ranked filter, sometimes called the "separable median" filter, is presented. This filter guarantees that the output pixels are of rank 4, 5, or 6. For typical noise-reduction applications, it is difficult to find a convincing argument that this filter is inferior in any meaningful way to the true median filter.
doi:10.1117/12.326970 fatcat:hjh6th2fkfa2rh32amnkpisykm