Rotation Differential Invariants of Images Generated by Two Fundamental Differential Operators

TL;DR

This paper introduces two new differential operators to derive rotation-invariant image features expressed as homogeneous polynomials, enabling high-order invariants for improved image analysis tasks.

Contribution

The paper presents a novel method for generating explicit high-order rotation differential invariants using two fundamental differential operators, expanding the set of available image features.

Findings

High-order rotation invariants improve texture classification accuracy.

The invariants outperform some traditional features in certain image verification tasks.

Explicit forms of many high-order invariants are provided for the first time.

Abstract

In this paper, we design two fundamental differential operators for the derivation of rotation differential invariants of images. Each differential invariant obtained by using the new method can be expressed as a homogeneous polynomial of image partial derivatives, which preserve their values when the image is rotated by arbitrary angles. We produce all possible instances of homogeneous invariants up to the given order and degree, and discuss the independence of them in detail. As far as we know, no previous papers have published so many explicit forms of high-order rotation differential invariants of images. In the experimental part, texture classification and image patch verification are carried out on popular real databases. These rotation differential invariants are used as image feature vector. We mainly evaluate the effects of various factors on the performance of them. The experimental results also validate that they have better performance than some commonly used image features in some cases.