Abstract
A basic and rather longstanding (e.g., [1]) question in the morphology community is the following: given a 1-D digital signal or a 2-D digital image, find another such signal or image that is both open and closed with respect to a given structural element and optimally “close” to the original signal or image. For binary 1-D signals, and a window of length M as structural element, this problem is a special instance of the following problem: given a finite-alphabet sequence of finite extent, \( y = \{ y(n)\}_{n = 0}^{N - 1} \), find a finite-alphabet sequence, \( \mathop X\limits^\wedge = \{ \mathop x\limits^\wedge (n)\}_{n = 0}^{N - 1} \), which minimizes \( d\left( {x,y} \right) = \sum\nolimits_{n = o}^{N - 1} {{d_n}(y(n),x(n))} \) subject to: X is piecewise constant of plateau run-length ≥ M. We show how a suitable reformulation of the problem naturally leads to a Viterbi-type solution. We call the resulting nonlinear I/O operator the Viterbi Optimal Runlength-Constrained Approximation (VORCA) filter. The VORCA is optimal, computationally efficient, and can be designed to be idempotent, and self-dual. The most intriguing observation is that the VORCA is not increasing, and, therefore, not a morphological filter.
N.D. Sidiropoulos can be reached (301) 405-6591, or via e-mail at nikos@Glue.umd.edu
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© 1996 Kluwer Academic Publishers
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Sidiropoulos, N.D. (1996). The Viterbi Optimal Runlength-Constrained Approximation Nonlinear Filter. In: Maragos, P., Schafer, R.W., Butt, M.A. (eds) Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0469-2_23
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DOI: https://doi.org/10.1007/978-1-4613-0469-2_23
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