On the Circular Area Signature for Graphs
On the Circular Area Signature for Graphs
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关于图的圆面积签名
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Esedoglu
中科院分区：
文献类型：
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作者：
J. Calder;S. Esedoglu
曲线的积分不变特征表示是形状识别和分类的重要步骤。积分不变量比它们的微分不变量更受欢迎，因为它们对噪声具有稳健性。然而，与曲线的微分不变量相比，目前尚不清楚积分签名是否提供了曲线的唯一表示。本文证明了圆区域签名唯一性的一些结果。特别地，我们研究了周期函数图的情况。我们证明了，如果以$x$轴为参数，则圆形区域签名是唯一的。此外，我们还证明了真圆面积签名(由弧长参数表示)在常值函数邻域中是唯一的。最后，我们在感兴趣的函数在宽度为$2R$的区间上一致的特殊情况下证明了唯一性。
The representation of curves by integral invariant signatures is an important step in shape recognition and classification. Integral invariants are preferred over their differential counterparts due to their robustness with respect to noise. However, in contrast to differential invariants of curves, it is currently unknown whether integral signatures offer unique representations of curves. In this article, we prove some results on the uniqueness of the circular area signature. In particular, we study the case for graphs of periodic functions. We show that the circular area signature is unique if taken with respect to parametrization by the $x$-axis. Furthermore, we prove that the true circular area signature (parametrized by arclength) is unique in a neighborhood of constant functions. Finally, we show uniqueness in the special case that the functions of interest agree on an interval of width $2r$.