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Takahiro Nishida

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Proceedings Article | 10 January 2014 Paper

A method for affine invariant curve smoothing

Takahiro Nishida, Takashi Toriu

Proceedings Volume 9069, 90690S (2014) https://doi.org/10.1117/12.2050235

KEYWORDS: Atrial fibrillation, Gaussian filters, Shape analysis, Nonlinear filtering, Machine vision, Computer vision technology, Distortion, Error analysis, Object recognition, Visualization

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This paper proposes a new curve smoothing method invariant to affine transformation. Curve smoothing is one of the important challenges in computer vision as a procedure for noise suppression in shape analysis such as Curvature Scale Space (CSS). Currently, Gaussian filtering is widely used among a lot of smoothing methods. However Gaussian filtering is not affine invariant. This paper proposes a new method for curve smoothing that is invariant under affine transformation such that area of any region in the image does not change. Specifically, we introduce an affine invariant evaluate function with a metric tensor. The original curve is smoothed by minimizing the evaluation function. We mathematically prove that this method is affine invariant. Further, experimental results show that the proposed method is almost never affected by affine transformation different from usual Gaussian filtering. In the proposed method, processing results are expected to be not affected much by variation of the viewpoint.

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