Learning Invariant Representations Of Planar Curves
This work addresses the need for robust invariant representations in computer vision and geometry processing, offering incremental improvements over existing axiomatic approaches.
The authors tackled the problem of constructing invariant geometric functions for planar curves under Euclidean and similarity transformations by proposing a metric learning framework using convolutional neural networks, achieving invariants with improved numerical qualities such as robustness to noise and adaptability to occlusion compared to axiomatic methods.
We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural networks to compute these geometric quantities. In comparison with axiomatic constructions, we show that the invariants approximated by the learning architectures have better numerical qualities such as robustness to noise, resiliency to sampling, as well as the ability to adapt to occlusion and partiality. Finally, we develop a novel multi-scale representation in a similarity metric learning paradigm.