Statistical morphology and Bayesian reconstruction
Abstract The aim of this paper is to show that basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum-variance estimators of probabilit...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yuille, Alan [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
1992 |
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| Anmerkung: |
© Kluwer Academic Publishers 1992 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of mathematical imaging and vision - Kluwer Academic Publishers, 1992, 1(1992), 3 vom: Sept., Seite 223-238 |
|---|---|
| Übergeordnetes Werk: |
volume:1 ; year:1992 ; number:3 ; month:09 ; pages:223-238 |
| Links: |
|---|
| DOI / URN: |
10.1007/BF00129877 |
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OLC2070019543 |
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| 520 | |a Abstract The aim of this paper is to show that basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum-variance estimators of probability distributions. It enables us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β=1/T. They become purely morphological as β goes to infinity and become purely linear averages as β goes to zero. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimum-variance estimators. Finally, we describe simulations comparing statistical morphology and Bayesian methods for image smoothing, edge detection, and noise reduction. | ||
| 700 | 1 | |a Vincent, Luc |4 aut | |
| 700 | 1 | |a Geiger, Davi |4 aut | |
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10.1007/BF00129877 doi (DE-627)OLC2070019543 (DE-He213)BF00129877-p DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl 54.00 bkl Yuille, Alan verfasserin aut Statistical morphology and Bayesian reconstruction 1992 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1992 Abstract The aim of this paper is to show that basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum-variance estimators of probability distributions. It enables us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β=1/T. They become purely morphological as β goes to infinity and become purely linear averages as β goes to zero. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimum-variance estimators. Finally, we describe simulations comparing statistical morphology and Bayesian methods for image smoothing, edge detection, and noise reduction. Vincent, Luc aut Geiger, Davi aut Enthalten in Journal of mathematical imaging and vision Kluwer Academic Publishers, 1992 1(1992), 3 vom: Sept., Seite 223-238 (DE-627)13114278X (DE-600)1127403-7 (DE-576)038688964 0924-9907 nnns volume:1 year:1992 number:3 month:09 pages:223-238 https://doi.org/10.1007/BF00129877 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2244 31.00 VZ 54.00 VZ AR 1 1992 3 09 223-238 |
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10.1007/BF00129877 doi (DE-627)OLC2070019543 (DE-He213)BF00129877-p DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl 54.00 bkl Yuille, Alan verfasserin aut Statistical morphology and Bayesian reconstruction 1992 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1992 Abstract The aim of this paper is to show that basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum-variance estimators of probability distributions. It enables us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β=1/T. They become purely morphological as β goes to infinity and become purely linear averages as β goes to zero. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimum-variance estimators. Finally, we describe simulations comparing statistical morphology and Bayesian methods for image smoothing, edge detection, and noise reduction. Vincent, Luc aut Geiger, Davi aut Enthalten in Journal of mathematical imaging and vision Kluwer Academic Publishers, 1992 1(1992), 3 vom: Sept., Seite 223-238 (DE-627)13114278X (DE-600)1127403-7 (DE-576)038688964 0924-9907 nnns volume:1 year:1992 number:3 month:09 pages:223-238 https://doi.org/10.1007/BF00129877 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2244 31.00 VZ 54.00 VZ AR 1 1992 3 09 223-238 |
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10.1007/BF00129877 doi (DE-627)OLC2070019543 (DE-He213)BF00129877-p DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl 54.00 bkl Yuille, Alan verfasserin aut Statistical morphology and Bayesian reconstruction 1992 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1992 Abstract The aim of this paper is to show that basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum-variance estimators of probability distributions. It enables us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β=1/T. They become purely morphological as β goes to infinity and become purely linear averages as β goes to zero. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimum-variance estimators. Finally, we describe simulations comparing statistical morphology and Bayesian methods for image smoothing, edge detection, and noise reduction. Vincent, Luc aut Geiger, Davi aut Enthalten in Journal of mathematical imaging and vision Kluwer Academic Publishers, 1992 1(1992), 3 vom: Sept., Seite 223-238 (DE-627)13114278X (DE-600)1127403-7 (DE-576)038688964 0924-9907 nnns volume:1 year:1992 number:3 month:09 pages:223-238 https://doi.org/10.1007/BF00129877 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2244 31.00 VZ 54.00 VZ AR 1 1992 3 09 223-238 |
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10.1007/BF00129877 doi (DE-627)OLC2070019543 (DE-He213)BF00129877-p DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl 54.00 bkl Yuille, Alan verfasserin aut Statistical morphology and Bayesian reconstruction 1992 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1992 Abstract The aim of this paper is to show that basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum-variance estimators of probability distributions. It enables us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β=1/T. They become purely morphological as β goes to infinity and become purely linear averages as β goes to zero. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimum-variance estimators. Finally, we describe simulations comparing statistical morphology and Bayesian methods for image smoothing, edge detection, and noise reduction. Vincent, Luc aut Geiger, Davi aut Enthalten in Journal of mathematical imaging and vision Kluwer Academic Publishers, 1992 1(1992), 3 vom: Sept., Seite 223-238 (DE-627)13114278X (DE-600)1127403-7 (DE-576)038688964 0924-9907 nnns volume:1 year:1992 number:3 month:09 pages:223-238 https://doi.org/10.1007/BF00129877 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2244 31.00 VZ 54.00 VZ AR 1 1992 3 09 223-238 |
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10.1007/BF00129877 doi (DE-627)OLC2070019543 (DE-He213)BF00129877-p DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl 54.00 bkl Yuille, Alan verfasserin aut Statistical morphology and Bayesian reconstruction 1992 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1992 Abstract The aim of this paper is to show that basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum-variance estimators of probability distributions. It enables us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β=1/T. They become purely morphological as β goes to infinity and become purely linear averages as β goes to zero. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimum-variance estimators. Finally, we describe simulations comparing statistical morphology and Bayesian methods for image smoothing, edge detection, and noise reduction. Vincent, Luc aut Geiger, Davi aut Enthalten in Journal of mathematical imaging and vision Kluwer Academic Publishers, 1992 1(1992), 3 vom: Sept., Seite 223-238 (DE-627)13114278X (DE-600)1127403-7 (DE-576)038688964 0924-9907 nnns volume:1 year:1992 number:3 month:09 pages:223-238 https://doi.org/10.1007/BF00129877 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2244 31.00 VZ 54.00 VZ AR 1 1992 3 09 223-238 |
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Abstract The aim of this paper is to show that basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum-variance estimators of probability distributions. It enables us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β=1/T. They become purely morphological as β goes to infinity and become purely linear averages as β goes to zero. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimum-variance estimators. Finally, we describe simulations comparing statistical morphology and Bayesian methods for image smoothing, edge detection, and noise reduction. © Kluwer Academic Publishers 1992 |
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Abstract The aim of this paper is to show that basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum-variance estimators of probability distributions. It enables us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β=1/T. They become purely morphological as β goes to infinity and become purely linear averages as β goes to zero. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimum-variance estimators. Finally, we describe simulations comparing statistical morphology and Bayesian methods for image smoothing, edge detection, and noise reduction. © Kluwer Academic Publishers 1992 |
| abstract_unstemmed |
Abstract The aim of this paper is to show that basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum-variance estimators of probability distributions. It enables us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β=1/T. They become purely morphological as β goes to infinity and become purely linear averages as β goes to zero. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimum-variance estimators. Finally, we describe simulations comparing statistical morphology and Bayesian methods for image smoothing, edge detection, and noise reduction. © Kluwer Academic Publishers 1992 |
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10.1007/BF00129877 |
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2024-07-03T23:59:30.303Z |
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These operations can then be expressed in terms of finding minimum-variance estimators of probability distributions. It enables us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β=1/T. They become purely morphological as β goes to infinity and become purely linear averages as β goes to zero. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimum-variance estimators. 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