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The equivalence of ...
The equivalence of two definitions of compatible homography matrices
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- Chojnacki, W. (author)
- University of Adelaide,The University of Adelaide, Australia,Australian Institute for Machine Learning
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- Szpak, Z. L. (author)
- University of Adelaide,The University of Adelaide, Australia,Australian Institute for Machine Learning
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- Wadenbäck, Mårten, 1987 (author)
- Linköpings universitet,Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, Tillämpad matematik och statistik,Department of Mathematical Sciences, Applied Mathematics and Statistics,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg,Datorseende,Tekniska fakulteten,University of Gothenburg, Gothenburg, Sweden
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(creator_code:org_t)
- Elsevier BV, 2020
- 2020
- English.
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In: Pattern Recognition Letters. - : Elsevier BV. - 0167-8655 .- 1872-7344. ; 135, s. 38-43
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Abstract
Subject headings
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- In many computer vision applications, one acquires images of planar surfaces from two different vantage points. One can use a projective transformation to map pixel coordinates associated with a particular planar surface from one image to another. The transformation, called a homography, can be represented by a unique, to within a scale factor, 3 × 3 matrix. One requires a different homography matrix, scale differences apart, for each planar surface whose two images one wants to relate. However, a collection of homography matrices forms a valid set only if the matrices satisfy consistency constraints implied by the rigidity of the motion and the scene. We explore what it means for a set of homography matrices to be compatible and show that two seemingly disparate definitions are in fact equivalent. Our insight lays the theoretical foundations upon which the derivation of various sets of homography consistency constraints can proceed. © 2020 Elsevier B.V.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datorseende och robotik (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Vision and Robotics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
Keyword
- Fundamental matrix
- Homography matrix
- Latent variable
- Multiple homographies
- Pattern recognition
- Software engineering
- Computer vision applications
- Consistency constraints
- Homographies
- Homography matrices
- Planar surface
- Projective transformation
- Scale Factor
- Theoretical foundations
- Linear transformations
Publication and Content Type
- ref (subject category)
- art (subject category)
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