Deep Signatures -- Learning Invariants of Planar Curves
This work addresses the problem of computing stable geometric invariants for planar curves, which is important for applications in computer vision and shape analysis, though it appears incremental as it applies existing deep learning techniques to a specific domain.
The authors tackled the problem of numerically approximating differential invariants of planar curves by proposing a deep learning paradigm that uses neural networks to estimate geometric measures, showing it can overcome instabilities and sampling artifacts to produce stable signatures under transformations. They demonstrated this as a preferable alternative to existing axiomatic constructions, comparing favorably to state-of-the-art methods.
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.