A method for affine invariant curve smoothing

Takahiro Nishida; Takashi Toriu

doi:10.1117/12.2050235

10 January 2014 A method for affine invariant curve smoothing

Takahiro Nishida, Takashi Toriu

Proceedings Volume 9069, Fifth International Conference on Graphic and Image Processing (ICGIP 2013); 90690S (2014) https://doi.org/10.1117/12.2050235
Event: Fifth International Conference on Graphic and Image Processing, 2013, Hong Kong, China

Abstract

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.

Citation Download Citation

Takahiro Nishida and Takashi Toriu "A method for affine invariant curve smoothing", Proc. SPIE 9069, Fifth International Conference on Graphic and Image Processing (ICGIP 2013), 90690S (10 January 2014); https://doi.org/10.1117/12.2050235

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