Mathematical Nonlinear Image Processing pp 59-75 | Cite as

# Root-Signal Sets of Morphological Filters and their Use in Variable-Length BTC Image Coding

## Abstract

The characterization of the root-signal set of a nonlinear operator has proved to be a crucial step in understanding the utility and usefulness of the operator. The set of root signals constitutes the passband of the nonlinear operator, and the complement of this set represents the stopband of the operator. Knowledge of these two sets for all operators determines which one must be used for any particular task. In this paper we investigate the root signals of the basic morphological filters, we study the properties of these signals, and we derive a system of equations to compute the number of binary-root signals for these morphological filters with structuring element of width *k* and signals of length *ri.* The derivation is based on the state description for these root signals. Simple recursive equations are derived for counting the number of root signals of opening, closing, open-closing, and clos-opening. An application example in which these root signals are used in block truncation coding for image compression is discussed.

## Keywords

Median Filter State Diagram Mathematical Morphology Mean Absolute Error Signal Length## Preview

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