Recognition of Planar Point Configurations using the Density of Affine Shape
(1998) Computer Vision  ECCV'98 5th European Conference on Computer Vision 1. p.7288 Abstract
 We study the statistical theory of shape for ordered finite point configurations, or otherwise stated, the uncertainty of geometric invariants. Such studies have been made for affine invariants, where a bound on errors is used instead of errors described by density functions, and a firstorder approximation gives an ellipsis as uncertainty region. Here, a general approach for defining shape and finding its density, expressed in the densities for the individual points, is developed. No approximations are made, resulting in an exact expression of the uncertainty region. Similar results have been obtained for the special case of the density of the cross ratio. In particular, we concentrate on the affine shape, where often analytical... (More)
 We study the statistical theory of shape for ordered finite point configurations, or otherwise stated, the uncertainty of geometric invariants. Such studies have been made for affine invariants, where a bound on errors is used instead of errors described by density functions, and a firstorder approximation gives an ellipsis as uncertainty region. Here, a general approach for defining shape and finding its density, expressed in the densities for the individual points, is developed. No approximations are made, resulting in an exact expression of the uncertainty region. Similar results have been obtained for the special case of the density of the cross ratio. In particular, we concentrate on the affine shape, where often analytical computations are possible. In this case confidence intervals for invariants can be obtained from a priori assumptions on the densities of the detected points in the images. However, the theory is completely general and can be used to compute the density of any invariant (Euclidean, similarity, projective etc.) from arbitrary densities of the individual points. These confidence intervals can be used in such applications as geometrical hashing, recognition of ordered point configurations and error analysis of reconstruction algorithms. Finally, an example is given, illustrating an application of the theory for the problem of recognising planar point configurations from images taken by an affine camera. This case is of particular importance in applications where details on a conveyor belt are captured by a camera, with image plane parallel to the conveyor belt and extracted feature points from the images are used to sort the objects (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/787214
 author
 Berthilsson, Rikard ^{LU} and Heyden, Anders ^{LU}
 organization
 publishing date
 1998
 type
 Chapter in Book/Report/Conference proceeding
 publication status
 published
 subject
 keywords
 computational geometry, computer vision, error analysis, feature extraction, image recognition, image reconstruction, statistical analysis
 host publication
 [Host publication title missing]
 volume
 1
 pages
 72  88
 publisher
 Springer
 conference name
 Computer Vision  ECCV'98 5th European Conference on Computer Vision
 conference location
 Freiburg, Germany
 conference dates
 19980602  19980606
 external identifiers

 scopus:84957632590
 ISBN
 3 540 64569 1
 language
 English
 LU publication?
 yes
 id
 123476257e2a4d26a8290be14e99f824 (old id 787214)
 date added to LUP
 20160404 10:57:50
 date last changed
 20220129 21:09:16
@inproceedings{123476257e2a4d26a8290be14e99f824, abstract = {{We study the statistical theory of shape for ordered finite point configurations, or otherwise stated, the uncertainty of geometric invariants. Such studies have been made for affine invariants, where a bound on errors is used instead of errors described by density functions, and a firstorder approximation gives an ellipsis as uncertainty region. Here, a general approach for defining shape and finding its density, expressed in the densities for the individual points, is developed. No approximations are made, resulting in an exact expression of the uncertainty region. Similar results have been obtained for the special case of the density of the cross ratio. In particular, we concentrate on the affine shape, where often analytical computations are possible. In this case confidence intervals for invariants can be obtained from a priori assumptions on the densities of the detected points in the images. However, the theory is completely general and can be used to compute the density of any invariant (Euclidean, similarity, projective etc.) from arbitrary densities of the individual points. These confidence intervals can be used in such applications as geometrical hashing, recognition of ordered point configurations and error analysis of reconstruction algorithms. Finally, an example is given, illustrating an application of the theory for the problem of recognising planar point configurations from images taken by an affine camera. This case is of particular importance in applications where details on a conveyor belt are captured by a camera, with image plane parallel to the conveyor belt and extracted feature points from the images are used to sort the objects}}, author = {{Berthilsson, Rikard and Heyden, Anders}}, booktitle = {{[Host publication title missing]}}, isbn = {{3 540 64569 1}}, keywords = {{computational geometry; computer vision; error analysis; feature extraction; image recognition; image reconstruction; statistical analysis}}, language = {{eng}}, pages = {{7288}}, publisher = {{Springer}}, title = {{Recognition of Planar Point Configurations using the Density of Affine Shape}}, volume = {{1}}, year = {{1998}}, }