| 1. |
- Berthilsson, Rikard
(author)
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A Statistical Theory of Shape
- 1998
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In: Advances in Pattern Recognition. Joint IAPR International Workshops SSPR'98 and SPR'98. Proceedings. - 3 540 64858 5 ; , s. 677-686
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Conference paper (other academic/artistic)abstract
- We study the statistical theory of shape for ordered finite point configurations, or otherwise stated, the uncertainty of geometric invariants. A general approach for defining shape and finding its density, expressed in the densities for the individual points, is developed. Some examples that can be computed analytically are given, including both affine and positive similarity shape. Projective shape and projective invariants are important topics in computer vision and are also discussed
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| 2. |
- Berthilsson, Rikard
(author)
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Affine Correlations
- 1998
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In: [Host publication title missing]. ; 2, s. 1458-1460
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Conference paper (other academic/artistic)abstract
- We propose a method for maximising the affine correlation between images. The method is more global in its search than for example steepest descent based methods. In a first approximation, there is no need to compute any derivatives and it is shown that the results are very good. The method is based on certain changes of coordinates in the images and extensive use of the fast Fourier transformation (FFT). This makes the method very fast, when implemented on a computer
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| 3. |
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| 4. |
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| 5. |
- Berthilsson, Rikard, et al.
(author)
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Extension of Affine Shape
- 1999
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In: Journal of Mathematical Imaging and Vision. - 0924-9907. ; 11:2, s. 119-136
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Journal article (peer-reviewed)
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| 6. |
- Berthilsson, Rikard
(author)
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Extensions and Applications of Affine Shape
- 1999
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Doctoral thesis (other academic/artistic)abstract
- A central problem in computer vision is to reconstruct the three-dimensional structure of a scene from a set of two-dimensional images. Traditionally this is done by extracting a set of characteristic points in the scene and to compute a reconstruction of these points. In this thesis we propose a novel method that allows reconstruction of a wider class of objects, including curves and surfaces. As always when dealing with measured data, the handling of noise is crucial. In this thesis we analyze the impact of uncertainty in measurements on feature parameters, and how these can be estimated in maximum likelihood sense. The thesis consists of an introduction and six separate papers. The introduction gives an overview and motivation for the contents of the thesis. Paper I presents an extension of the so called affine shape of finite point configuration to affine shape of for example curves and surfaces. An algorithm for reconstructing curves is also presented. In paper II it is shown how the extension of affine shape can be used to recognize curves and in particular how it can be used to interpret handwriting. Paper III presents an extension to surfaces of the method for reconstructing curves in paper I based on affine shape. The paper also uses results from paper IV, where it is shown how images can be matched by allowing for deformations and using correlation. The matching is done by an iterative algorithm, where the fast Fourier transformation is used in each iteration to speed up computations. Papers V and VI consider statistical issues in computer vision. In paper V we discuss how uncertainties in measurements of point configurations are influencing the shape. More precisely, it is shown how the probability measure of shape can be computed from the probability measure of the point configurations. In paper VI we discuss how the characteristic function can be used to compute maximum likelihood estimates of matching constraints and how to obtain densities of estimated parameters. In particular, we present a novel method for estimating the fundamental matrix.
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| 7. |
- Berthilsson, Rikard, et al.
(author)
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Projective Reconstruction of 3D-curves from its 2D-images using Error Models and Bundle Adjustments
- 1997
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In: Proceedings of the 10th Scandinavian Conference on Image Analysis. - 9517641451 ; , s. 581-588
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Conference paper (other academic/artistic)abstract
- In this paper, an algorithm for projective reconstruction of general 3D-curves from a number of its 2D-images taken by uncalibrated cameras is proposed. No point correspondences between the images are assumed. The curve and the view points are uniquely reconstructed, modulo projective transformations. The algorithm is divided into two separate algorithms, where the output of the first is used as input to the second. The first algorithm is independent of the choice of coordinates in the images and is based on orthogonal projections and aligning subspaces. The ideas behind the algorithm are based on an extension of aOEne shape of finite point configurations to curves. The second algorithm uses the well-known technique of bundle adjustments, where an error function is minimised with respect to all free parameters. The errors in the detection of the curve in the images are used in the error function. These errors are obtained from a proposed model of image acquisition and scale space smoothing, making it possible to analyse the errors in a simple edge detection algorithm. Finally, experiments using real images, have been carried out and it is shown that the results are superior to previous approaches.
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| 8. |
- Berthilsson, Rikard, et al.
(author)
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Recognition of Planar Point Configurations using the Density of Affine Shape
- 1998
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In: [Host publication title missing]. - 3 540 64569 1 ; 1, s. 72-88
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Conference paper (other academic/artistic)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 first-order 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
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| 9. |
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| 10. |
- Berthilsson, Rikard, et al.
(author)
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Reconstruction of 3D-Curves from 2D-Images Using Affine Shape Methods for Curves
- 1997
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In: [Host publication title missing]. - 1063-6919. ; , s. 476-481
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Conference paper (other academic/artistic)abstract
- In this paper, we propose an algorithm for doing reconstruction of general 3D-curves from a number of 2D-images taken by uncalibrated cameras. No point correspondences between the images are assumed. The curve and the view points are uniquely reconstructed, modulo common projective transformations and the point correspondence problem is solved. Furthermore, the algorithm is independent of the choice of coordinates, as it is based on orthogonal projections and aligning subspaces. The algorithm is based on an extension of affine shape of finite point configurations to more general objects.
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