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G.H.: Optimal orientation detection of linear symmetry (1987)
| Venue: | In: Proceedings of the IEEE First International Conference on Computer Vision, London, Great Britain |
| Citations: | 182 - 27 self |
BibTeX
@INPROCEEDINGS{Bigun87g.h.:optimal,
author = {Josef Bigun},
title = {G.H.: Optimal orientation detection of linear symmetry},
booktitle = {In: Proceedings of the IEEE First International Conference on Computer Vision, London, Great Britain},
year = {1987},
pages = {433--438}
}
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Abstract
The problem of optimal detection of orientation in arbitrary neighborhoods is solved in the least squares sense. It is shown that this corresponds to fitting an axis in the Fourier domain of the n-dimensional neighborhood, the solution of which is a well known solution of a matrix eigenvalue problem. The eigenvalues are the variance or inertia with respect to the axes given by their respective eigen vectors. The orientation is taken as the axis given by the least eigenvaJ~e~ Moreover it is shown that the necessary computations can be pursued in the spatial domain without doing a Fourier transformation. An implementation for 2-D is presented. Two certainty measures are given corresponding to the orientation estimate. These are the relative or the absolute distances between the two eigenvalues, revealing whether the fitted axis is much better than an axis orthogonal to it. The result of the implementation is verified by experiments which confirm an accurate orientation estimation and reliable certainty measure in the presence of additive noise at high level as well as low levels.
Keyphrases
optimal orientation detection linear symmetry arbitrary neighborhood fourier transformation certainty measure accurate orientation estimation axis orthogonal fitted axis respective eigen vector optimal detection reliable certainty measure fourier domain square sense high level additive noise absolute distance spatial domain low level matrix eigenvalue problem necessary computation n-dimensional neighborhood orientation estimate
