This paper considers the problem of estimating the length of digitized straight lines in three dimensions. Two methods are proposed here for the measurement purpose. In the first method 2D estimators are used in an in...
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This paper considers the problem of estimating the length of digitized straight lines in three dimensions. Two methods are proposed here for the measurement purpose. In the first method 2D estimators are used in an indirect way, whereas in the second method estimation is carried out directly. The estimators used in both the methods are tested and evaluated with different sets of randomly generated lines in 3D. A comparative assessment among the estimators is also made.
If a continuous straight line segment is digitized on a regular grid, obviously a loss of information occurs. As a result, the discrete representation obtained (e.g., a chaincode string) can be coded more conveniently...
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If a continuous straight line segment is digitized on a regular grid, obviously a loss of information occurs. As a result, the discrete representation obtained (e.g., a chaincode string) can be coded more conveniently than the continuous line segment, but measurements of properties (such as line length) performed on the representation have an intrinsic inaccuracy due to the digitization process. In this paper, two fundamental properties of the quantization of straight line segments are treated. 1) It is proved that every ``straight"" chaincode string can be represented by a set of four unique integer parameters. Definitions of these parameters are given. 2) A mathematical expression is derived for the set of all continuous line segments which could have generated a given chaincode string. The relation with the chord property is briefly discussed.","doi":"10.1109/TPAMI.1984.4767550","publicationTitle":"IEEE Transactions on Pattern Analysis and Machine Intelligence","startPage":"450","endPage":"463","rightsLink":"http://***/AppDispatchServlet?publisherName=ieee&publication=0162-8828&title=Discrete+Representation+of+Straight+Lines&isbn=&publicationDate=July+1984&author=Leo+Dorst&ContentID=10.1109/TPAMI.1984.4767550&orderBeanReset=true&startPage=450&endPage=463&volumeNum=PAMI-6&issueNum=4","displayPublicationTitle":"IEEE Transactions on Pattern Analysis and Machine Intelligence","pdfPath":"/iel5/34/4767540/***","keywords":[{"type":"IEEE Keywords","kwd":["Quantization","Low earth orbit satellites","Length measurement","Performance evaluation","Disruption tolerant networking","Laboratories","Physics","Pathology","Biomedical informatics","Encoding"]},{"type":"Author Keywords ","kwd":["quantization error","chaincode string","chord property","coding efficiency","digitized straight lines"]}],"allowComments":false,"pubLink":"/xpl/***?punumber=34","issueLink":"/xpl/***?isnumber=4767540","standardTitle":"Discrete Representation of St
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