Rotation Differential Invariants of Images Generated by Two Fundamental Differential Operators
This work addresses the problem of rotation-invariant image feature extraction for computer vision applications, but it appears incremental as it builds on existing differential invariant methods.
The paper introduces two fundamental differential operators to derive rotation differential invariants for images, which are expressed as homogeneous polynomials of image partial derivatives and remain unchanged under arbitrary rotations. Experimental results on texture classification and image patch verification show these invariants outperform some commonly used image features in certain cases.
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.