Projective Areainvariants as an extension of the CrossRatio
(1991) In Graphical Models 54(1). p.145159 Abstract
 Projective invariants provide a framework for computer vision where the image of an object is described by its intrinsic properties, independently of the particular view. It is advantageous if these intrinsic properties are defined in terms of computationally simple features. An areameasurement provides a good candidate that is easy to reliably compute from a particular image of the object. The main contributions of this paper are the definition and justification of areainvariants in projective geometry and the indication of its relevance in image analysis. A framework that covers onedimensional intervals and twodimensional figures has been developed. In the linear case, the invariants are linear only in two cases. The first case is... (More)
 Projective invariants provide a framework for computer vision where the image of an object is described by its intrinsic properties, independently of the particular view. It is advantageous if these intrinsic properties are defined in terms of computationally simple features. An areameasurement provides a good candidate that is easy to reliably compute from a particular image of the object. The main contributions of this paper are the definition and justification of areainvariants in projective geometry and the indication of its relevance in image analysis. A framework that covers onedimensional intervals and twodimensional figures has been developed. In the linear case, the invariants are linear only in two cases. The first case is the well known crossratio, and the second case is called the polar case. The generalization to the plane can be done in different directions. One can use either points (on the line or in the plane) or the geometric figures (intervals, triangles, circles) as the basic entities involved. The first view was adopted already by Möbius, who generalized the crossratio in various directions. The second view used here leads to another generalization of the crossratio, where the invariants are relations between the areas of a class of geometric figures, related to each other in a certain manner. Remarkably enough, these invariants turn out to be linear if the figures involved are related in a pole/ polar configuration (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/788248
 author
 Nielsen, Lars and Sparr, Gunnar ^{LU}
 organization
 publishing date
 1991
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Graphical Models
 volume
 54
 issue
 1
 pages
 145  159
 publisher
 Elsevier
 external identifiers

 scopus:0026358093
 ISSN
 15240703
 DOI
 10.1016/10499660(91)900795
 language
 English
 LU publication?
 yes
 id
 f64fa2ea1295407b81a62823c89b73d7 (old id 788248)
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 http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WDD4DX42XNP1&_cdi=6764&_user=745831&_orig=search&_coverDate=07%2F31%2F1991&_sk=999459998&view=c&wchp=dGLbVtbzSkWA&md5=f0316ea4abbb5288c2db5b125aefd38c&ie=/sdarticle.pdf
 date added to LUP
 20160401 11:42:33
 date last changed
 20210103 03:55:28
@article{f64fa2ea1295407b81a62823c89b73d7, abstract = {{Projective invariants provide a framework for computer vision where the image of an object is described by its intrinsic properties, independently of the particular view. It is advantageous if these intrinsic properties are defined in terms of computationally simple features. An areameasurement provides a good candidate that is easy to reliably compute from a particular image of the object. The main contributions of this paper are the definition and justification of areainvariants in projective geometry and the indication of its relevance in image analysis. A framework that covers onedimensional intervals and twodimensional figures has been developed. In the linear case, the invariants are linear only in two cases. The first case is the well known crossratio, and the second case is called the polar case. The generalization to the plane can be done in different directions. One can use either points (on the line or in the plane) or the geometric figures (intervals, triangles, circles) as the basic entities involved. The first view was adopted already by Möbius, who generalized the crossratio in various directions. The second view used here leads to another generalization of the crossratio, where the invariants are relations between the areas of a class of geometric figures, related to each other in a certain manner. Remarkably enough, these invariants turn out to be linear if the figures involved are related in a pole/ polar configuration}}, author = {{Nielsen, Lars and Sparr, Gunnar}}, issn = {{15240703}}, language = {{eng}}, number = {{1}}, pages = {{145159}}, publisher = {{Elsevier}}, series = {{Graphical Models}}, title = {{Projective Areainvariants as an extension of the CrossRatio}}, url = {{http://dx.doi.org/10.1016/10499660(91)900795}}, doi = {{10.1016/10499660(91)900795}}, volume = {{54}}, year = {{1991}}, }