Affine Differential Invariants for Invariant Feature Point Detection

TL;DR

This paper introduces a 2D affine-invariant feature point detector based on differential invariants, extending the concept to 3D image volumes, addressing the limitations of Euclidean-only invariance in traditional detectors.

Contribution

It presents a novel affine-invariant detector using differential invariants derived via the equivariant method of moving frames, applicable to both 2D and 3D images.

Findings

Demonstrates the effectiveness of the affine-invariant detector on 2D images.

Computes fundamental equi-affine invariants for 3D image volumes.

Addresses limitations of Euclidean-invariant detectors.

Abstract

Image feature points are detected as pixels which locally maximize a detector function, two commonly used examples of which are the (Euclidean) image gradient and the Harris-Stephens corner detector. A major limitation of these feature detectors are that they are only Euclidean-invariant. In this work we demonstrate the application of a 2D affine-invariant image feature point detector based on differential invariants as derived through the equivariant method of moving frames. The fundamental equi-affine differential invariants for 3D image volumes are also computed.