Learning Differential Invariants of Planar Curves
This work addresses the challenge of computing geometric measures for planar curves in computer vision or geometry, offering an alternative to traditional methods, but it appears incremental as it applies existing DNN capabilities to a specific domain.
The authors tackled the problem of numerically approximating differential invariants of planar curves by proposing a learning paradigm using deep neural networks, which overcomes instabilities and sampling artifacts to produce consistent signatures under transformations, and they compared it to state-of-the-art axiomatic methods with qualitative and quantitative evaluations.
We propose a learning paradigm for the 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 consistent 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 differential invariants. We evaluate our models qualitatively and quantitatively and propose a benchmark dataset to evaluate approximation models of differential invariants of planar curves.