Optimal mean-absolute-error filtering of gray-scale signals by the morphological hit-or-miss transform Academic Article uri icon

abstract

  • The binary hit-or-miss transform is applied to filter digital gray-scale signals. This is accomplished by applying a union of hit-or-miss transforms to an observed signal's umbra and then taking the surface of the filtered umbra as the estimate of the ideal signal. The hit-or-miss union is constructed to provide the optimal mean-absolute-error filter for both the ideal signal and its umbra. The method is developed in detail for thinning hit-or-miss filters and applies at once to the dual thickening filters. It requires the output of the umbra filter to be an umbra, which in general is not true. A key aspect of the paper is the complete characterization of umbra-preserving union-of-hit-or-miss thinning and thickening filters. Taken together, the mean-absolute-error theory and the umbra-preservation characterization provide a full characterization of binary hit-or-miss filtering as applied to digital gray-scale signals. The theory is at once applicable to hit-or-miss filtering of digital gray-scale images through the three-dimensional (3-D) binary hit-or-miss transform. 1994 Kluwer Academic Publishers.

published proceedings

  • Journal of Mathematical Imaging and Vision

author list (cited authors)

  • Dougherty, E. R.

citation count

  • 10

complete list of authors

  • Dougherty, Edward R

publication date

  • July 1994