On the Statistical Analysis of Dirty Pictures
A continuous two-dimensional region is partitioned into a fine rectangular array of sites or "pixels", each pixel having a particular "colour" belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly mu...
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| Veröffentlicht in: | Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1986-07, Vol.48 (3), p.259-302 |
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| container_title | Journal of the Royal Statistical Society. Series B, Methodological |
| container_volume | 48 |
| creator | Besag, Julian |
| description | A continuous two-dimensional region is partitioned into a fine rectangular array of sites or "pixels", each pixel having a particular "colour" belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a non-degenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable large-scale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does not depend on these large-scale characteristics. The method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field. Some complications, including parameter estimation, are discussed. Potential applications are mentioned briefly. |
| doi_str_mv | 10.1111/j.2517-6161.1986.tb01412.x |
| format | Article |
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Series B, Methodological</title><description>A continuous two-dimensional region is partitioned into a fine rectangular array of sites or "pixels", each pixel having a particular "colour" belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a non-degenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable large-scale properties of the random field. 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Potential applications are mentioned briefly.</description><subject>Applied sciences</subject><subject>Artificial intelligence</subject><subject>Artificial satellites</subject><subject>auto‐normal models</subject><subject>classification</subject><subject>Computer science; control theory; systems</subject><subject>Data smoothing</subject><subject>Error rates</subject><subject>Exact sciences and technology</subject><subject>gibbs sampler</subject><subject>grey‐level scenes</subject><subject>Image analysis</subject><subject>Image processing</subject><subject>Image reconstruction</subject><subject>image restoration</subject><subject>iterated conditional modes</subject><subject>Markov models</subject><subject>markov random fields</subject><subject>maximum a posteriori estimation</subject><subject>pairwise interactions</subject><subject>pattern recognition</subject><subject>Pattern recognition. Digital image processing. Computational geometry</subject><subject>Pixels</subject><subject>pseudo‐likelihood estimation</subject><subject>remote sensing</subject><subject>segmentation</subject><subject>Simulated annealing</subject><subject>Statistics</subject><issn>0035-9246</issn><issn>1369-7412</issn><issn>2517-6161</issn><issn>1467-9868</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1986</creationdate><recordtype>article</recordtype><sourceid>K30</sourceid><recordid>eNqVkF1PwyAUhonRxDn9B1406m0rB1pavJvzM1ky4_SaMAqRZq4KLK7_XmqX3cvNIZyX58CD0AXgDOK6bjJSQJkyYJABr1gWlhhyINn2AI32rUM0wpgWKSc5O0Yn3jcYY6A5HaF0vk7Ch04WQQbrg1VylUzWctV565PWJHfWhS55sSpsnPan6MjIlddnuzpG7w_3b9OndDZ_fJ5OZqmivCBpacoSam4YlsC4ZsZoo7AuOM5NPK24wlXFJGP1knFMKwlLostCKU7KGnhNx-hy4H659nujfRBNu3HxWV4AxYRzwATH1M2QUq713mkjvpz9lK4TgEWvRzSidyB6B6LXI3Z6xDZevtqNkD5-2ji5VtbvCRWpcsogxiZD7MeudPePAeJ1sbj920fG-cBofGjdnkFoXuSE0V8TEoGv</recordid><startdate>198607</startdate><enddate>198607</enddate><creator>Besag, Julian</creator><general>Royal Statistical Society</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>HGTKA</scope><scope>JILTI</scope><scope>K30</scope><scope>PAAUG</scope><scope>PAWHS</scope><scope>PAWZZ</scope><scope>PAXOH</scope><scope>PBHAV</scope><scope>PBQSW</scope><scope>PBYQZ</scope><scope>PCIWU</scope><scope>PCMID</scope><scope>PCZJX</scope><scope>PDGRG</scope><scope>PDWWI</scope><scope>PETMR</scope><scope>PFVGT</scope><scope>PGXDX</scope><scope>PIHIL</scope><scope>PISVA</scope><scope>PJCTQ</scope><scope>PJTMS</scope><scope>PLCHJ</scope><scope>PMHAD</scope><scope>PNQDJ</scope><scope>POUND</scope><scope>PPLAD</scope><scope>PQAPC</scope><scope>PQCAN</scope><scope>PQCMW</scope><scope>PQEME</scope><scope>PQHKH</scope><scope>PQMID</scope><scope>PQNCT</scope><scope>PQNET</scope><scope>PQSCT</scope><scope>PQSET</scope><scope>PSVJG</scope><scope>PVMQY</scope><scope>PZGFC</scope></search><sort><creationdate>198607</creationdate><title>On the Statistical Analysis of Dirty Pictures</title><author>Besag, Julian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3952-7f771d9f60a169e6ffefc0e5904f9f689c0886a66db69038a1b2e75cc927d19d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1986</creationdate><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Artificial satellites</topic><topic>auto‐normal models</topic><topic>classification</topic><topic>Computer science; control theory; systems</topic><topic>Data smoothing</topic><topic>Error rates</topic><topic>Exact sciences and technology</topic><topic>gibbs sampler</topic><topic>grey‐level scenes</topic><topic>Image analysis</topic><topic>Image processing</topic><topic>Image reconstruction</topic><topic>image restoration</topic><topic>iterated conditional modes</topic><topic>Markov models</topic><topic>markov random fields</topic><topic>maximum a posteriori estimation</topic><topic>pairwise interactions</topic><topic>pattern recognition</topic><topic>Pattern recognition. Digital image processing. Computational geometry</topic><topic>Pixels</topic><topic>pseudo‐likelihood estimation</topic><topic>remote sensing</topic><topic>segmentation</topic><topic>Simulated annealing</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Besag, Julian</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Periodicals Index Online Segment 18</collection><collection>Periodicals Index Online Segment 32</collection><collection>Periodicals Index Online</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - West</collection><collection>Primary Sources Access (Plan D) - International</collection><collection>Primary Sources Access & Build (Plan A) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Midwest</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Northeast</collection><collection>Primary Sources Access (Plan D) - Southeast</collection><collection>Primary Sources Access (Plan D) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Southeast</collection><collection>Primary Sources Access (Plan D) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - UK / I</collection><collection>Primary Sources Access (Plan D) - Canada</collection><collection>Primary Sources Access (Plan D) - EMEALA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - International</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - International</collection><collection>Primary Sources Access (Plan D) - West</collection><collection>Periodicals Index Online Segments 1-50</collection><collection>Primary Sources Access (Plan D) - APAC</collection><collection>Primary Sources Access (Plan D) - Midwest</collection><collection>Primary Sources Access (Plan D) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Canada</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - EMEALA</collection><collection>Primary Sources Access & Build (Plan A) - APAC</collection><collection>Primary Sources Access & Build (Plan A) - Canada</collection><collection>Primary Sources Access & Build (Plan A) - West</collection><collection>Primary Sources Access & Build (Plan A) - EMEALA</collection><collection>Primary Sources Access (Plan D) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - Midwest</collection><collection>Primary Sources Access & Build (Plan A) - North Central</collection><collection>Primary Sources Access & Build (Plan A) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - Southeast</collection><collection>Primary Sources Access (Plan D) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - APAC</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - MEA</collection><jtitle>Journal of the Royal Statistical Society. Series B, Methodological</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Besag, Julian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Statistical Analysis of Dirty Pictures</atitle><jtitle>Journal of the Royal Statistical Society. Series B, Methodological</jtitle><date>1986-07</date><risdate>1986</risdate><volume>48</volume><issue>3</issue><spage>259</spage><epage>302</epage><pages>259-302</pages><issn>0035-9246</issn><issn>1369-7412</issn><eissn>2517-6161</eissn><eissn>1467-9868</eissn><coden>JSTBAJ</coden><abstract>A continuous two-dimensional region is partitioned into a fine rectangular array of sites or "pixels", each pixel having a particular "colour" belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a non-degenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable large-scale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does not depend on these large-scale characteristics. 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| identifier | ISSN: 0035-9246 |
| ispartof | Journal of the Royal Statistical Society. Series B, Methodological, 1986-07, Vol.48 (3), p.259-302 |
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| language | eng |
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| source | Periodicals Index Online; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | Applied sciences Artificial intelligence Artificial satellites auto‐normal models classification Computer science control theory systems Data smoothing Error rates Exact sciences and technology gibbs sampler grey‐level scenes Image analysis Image processing Image reconstruction image restoration iterated conditional modes Markov models markov random fields maximum a posteriori estimation pairwise interactions pattern recognition Pattern recognition. Digital image processing. Computational geometry Pixels pseudo‐likelihood estimation remote sensing segmentation Simulated annealing Statistics |
| title | On the Statistical Analysis of Dirty Pictures |
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