Abstract
A parameterized τ-opening is a filter defined as a union of openings by a collection of compact, convex structuring elements, each scalar multiplied by the parameter. For a reconstructive τ-opening, the filter is modified by fully passing any connected component not completely eliminated. Applied to the signal-union-noise model, in which the reconstructive filter is designed to sieve out clutter while passing the signal, the optimization problem is to find a parameter value that minimizes the MAE between the filtered and ideal image processes. The present study introduces an adaptation procedure for the design of reconstructive τ-openings. The adaptive filter fits into the framework of Markov processes, the adaptive parameter being the state of the process. There exists a stationary distribution governing the parameter in the steady state and convergence is characterized via the steady-state distribution. Key filter properties such as parameter mean, parameter variance, and expected error in the steady state are characterized via the stationary distribution. The Chapman-Kolmogorov equations are developed for various scanning modes and transient behavior is examined.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 266-282 |
| Number of pages | 17 |
| Journal | Journal of Electronic Imaging |
| Volume | 5 |
| Issue number | 3 |
| State | Published - 1996 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Atomic and Molecular Physics, and Optics
- Computer Vision and Pattern Recognition
Cite this
Adaptive reconstructive τ-openings : Convergence and the steady-state distribution. / Chen, Yidong; Dougherty, Edward R.
In: Journal of Electronic Imaging, Vol. 5, No. 3, 1996, p. 266-282.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Adaptive reconstructive τ-openings
T2 - Convergence and the steady-state distribution
AU - Chen, Yidong
AU - Dougherty, Edward R.
PY - 1996
Y1 - 1996
N2 - A parameterized τ-opening is a filter defined as a union of openings by a collection of compact, convex structuring elements, each scalar multiplied by the parameter. For a reconstructive τ-opening, the filter is modified by fully passing any connected component not completely eliminated. Applied to the signal-union-noise model, in which the reconstructive filter is designed to sieve out clutter while passing the signal, the optimization problem is to find a parameter value that minimizes the MAE between the filtered and ideal image processes. The present study introduces an adaptation procedure for the design of reconstructive τ-openings. The adaptive filter fits into the framework of Markov processes, the adaptive parameter being the state of the process. There exists a stationary distribution governing the parameter in the steady state and convergence is characterized via the steady-state distribution. Key filter properties such as parameter mean, parameter variance, and expected error in the steady state are characterized via the stationary distribution. The Chapman-Kolmogorov equations are developed for various scanning modes and transient behavior is examined.
AB - A parameterized τ-opening is a filter defined as a union of openings by a collection of compact, convex structuring elements, each scalar multiplied by the parameter. For a reconstructive τ-opening, the filter is modified by fully passing any connected component not completely eliminated. Applied to the signal-union-noise model, in which the reconstructive filter is designed to sieve out clutter while passing the signal, the optimization problem is to find a parameter value that minimizes the MAE between the filtered and ideal image processes. The present study introduces an adaptation procedure for the design of reconstructive τ-openings. The adaptive filter fits into the framework of Markov processes, the adaptive parameter being the state of the process. There exists a stationary distribution governing the parameter in the steady state and convergence is characterized via the steady-state distribution. Key filter properties such as parameter mean, parameter variance, and expected error in the steady state are characterized via the stationary distribution. The Chapman-Kolmogorov equations are developed for various scanning modes and transient behavior is examined.
UR - http://www.scopus.com/inward/record.url?scp=0002163039&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0002163039&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0002163039
VL - 5
SP - 266
EP - 282
JO - Journal of Electronic Imaging
JF - Journal of Electronic Imaging
SN - 1017-9909
IS - 3
ER -