### Reconstruction and Prediction from Three Images of Uncalibrated Cameras

(1995) Proceedings of 9th Conference on Theory and Applications of Image Analysis II p.113-126- Abstract
- This paper deals with the problem of reconstructing the locations of a number of points in space from three different images taken by uncalibrated cameras. It is assumed that the correspondences between the points in the different images are known. In the case of six points this paper shows that there are in general three solutions to the problem of determining the shape of the object, but some of them may be complex and some may not be physically realisable (e.g. points behind the camera). The solutions are given by a third degree polynomial with coefficients depending on the coordinates of the points in the image. It is also shown how a priori information of the object, such as planarity of subsets of the points, can be used to make... (More)
- This paper deals with the problem of reconstructing the locations of a number of points in space from three different images taken by uncalibrated cameras. It is assumed that the correspondences between the points in the different images are known. In the case of six points this paper shows that there are in general three solutions to the problem of determining the shape of the object, but some of them may be complex and some may not be physically realisable (e.g. points behind the camera). The solutions are given by a third degree polynomial with coefficients depending on the coordinates of the points in the image. It is also shown how a priori information of the object, such as planarity of subsets of the points, can be used to make reconstruction. In this case the reconstruction is unique and it is obtained by a linear method. Furthermore it is shown how additional points in the first two images can be used to predict the location of the corresponding point in the third image, without calculating the epipoles. Finally, a linear method for the reconstruction in the case of at least seven point matches are given (Less)

Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/787277

- author
- Heyden, Anders
^{LU} - organization
- publishing date
- 1995
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- computer vision, image reconstruction, matrix algebra, stereo image processing
- host publication
- [Host publication title missing]
- editor
- Borgefors, G.
- pages
- 113 - 126
- publisher
- World Scientific Publishing
- conference name
- Proceedings of 9th Conference on Theory and Applications of Image Analysis II
- conference location
- Uppsala, Sweden
- conference dates
- 0001-01-02
- ISBN
- 981 02 2448 6
- language
- English
- LU publication?
- yes
- id
- c4a6650f-6396-4869-9238-2a0d88d46102 (old id 787277)
- date added to LUP
- 2016-04-04 11:34:07
- date last changed
- 2021-01-25 10:54:24

@inproceedings{c4a6650f-6396-4869-9238-2a0d88d46102, abstract = {{This paper deals with the problem of reconstructing the locations of a number of points in space from three different images taken by uncalibrated cameras. It is assumed that the correspondences between the points in the different images are known. In the case of six points this paper shows that there are in general three solutions to the problem of determining the shape of the object, but some of them may be complex and some may not be physically realisable (e.g. points behind the camera). The solutions are given by a third degree polynomial with coefficients depending on the coordinates of the points in the image. It is also shown how a priori information of the object, such as planarity of subsets of the points, can be used to make reconstruction. In this case the reconstruction is unique and it is obtained by a linear method. Furthermore it is shown how additional points in the first two images can be used to predict the location of the corresponding point in the third image, without calculating the epipoles. Finally, a linear method for the reconstruction in the case of at least seven point matches are given}}, author = {{Heyden, Anders}}, booktitle = {{[Host publication title missing]}}, editor = {{Borgefors, G.}}, isbn = {{981 02 2448 6}}, keywords = {{computer vision; image reconstruction; matrix algebra; stereo image processing}}, language = {{eng}}, pages = {{113--126}}, publisher = {{World Scientific Publishing}}, title = {{Reconstruction and Prediction from Three Images of Uncalibrated Cameras}}, year = {{1995}}, }