Representing Directions for Hough Transforms
Many algorithms in computer vision operate with directions, i. e. with representations of 3D-points by ignoring their distance to the origin. Even though minimal parametrizations of directions may contain singularities, they can enhance convergence in optimization algorithms and are required e. g. for accumulator spaces in Hough transforms. There are numerous possibilities for parameterizing directions. However, many do not account for numerical stability when dealing with noisy data. This paper gives an overview of different parametrizations and shows their sensitivity with respect to noise. In addition to standard approaches in the field of computer vision, representations originating from the field of cartography are introduced. Experiments demonstrate their superior performance in computer vision applications in the presence of noise as they are suitable for Gaussian filtering.
KeywordsParametrization vanishing points direction unit sphere Hough transform
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