论文标题
深度签名 - 平面曲线不变的学习
Deep Signatures -- Learning Invariants of Planar Curves
论文作者
论文摘要
我们提出了一种学习范式，用于平面曲线的差异不变剂的数值近似。深度神经网络（DNNS）通用近似特性用于估计几何措施。所提出的框架被证明是公理构造的最佳选择。具体而言，我们表明DNN可以学会克服不稳定性和采样伪像，并为受平面中给定的转换群体的曲线产生数值稳定的签名。我们将所提出的方案与组不变长度和曲率的替代性最新公理构建体进行了比较。
We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is shown to be a preferable alternative to axiomatic constructions. Specifically, we show that DNNs can learn to overcome instabilities and sampling artifacts and produce numerically-stable signatures for curves subject to a given group of transformations in the plane. We compare the proposed schemes to alternative state-of-the-art axiomatic constructions of group invariant arc-lengths and curvatures.
