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1 June 1992 Height distributions in opened finite signals
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Morphological opening operations are useful in discriminating between lengths of sequences of non-zero signal amid a zero-valued background in a signal. In order to study simple one-dimensional detection algorithms involving openings, we would like to know how a finite-extent stochastic signal changes when it is opened with a convex, zero-height structuring element. Because the opening operation is nonlinear and the model signal has some spatial structure due to its finite extent, the opened model signal is not spatially stationary. This nonstationarity is dealt with by introducing the concept of the translation class1 of signal elements to distinguish the different distributions of those elements in the opened signal. The signal height distribution for a given translation class of an opened signal is derived using an extension of the method given by Stevenson and Arce in [2] to evaluate morphological operations on infinite-length sequences.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Wendy Swan Costa and Robert M. Haralick "Height distributions in opened finite signals", Proc. SPIE 1769, Image Algebra and Morphological Image Processing III, (1 June 1992);

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