Learning Invariant Representations Of Planar Curves

TL;DR

This paper introduces a neural network-based framework for learning invariant geometric functions of planar curves, improving robustness and adaptability over traditional axiomatic methods, with a novel multi-scale similarity metric approach.

Contribution

It presents a new deep learning method for constructing invariant geometric functions of planar curves, outperforming axiomatic approaches in robustness and adaptability.

Findings

Learned invariants show improved noise robustness.

Method adapts well to occlusion and partial data.

Introduces a multi-scale similarity metric learning approach.

Abstract

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.