Gaussian-Hermite Moment Invariants of General Multi-Channel Functions

With the development of data acquisition technology, large amounts of multi-channel data are collected and widely used in many fields. Most of them, such as RGB images and vector fields, can be expressed as different types of multi-channel functions. Feature extraction of multi-channel data for identifying interest patterns is a critical but challenging task. This paper focuses on constructing moment-based features of general multi-channel functions. Specifically, we define two transform models, rotation-affine transform and total rotation transform, to describe real deformations of multi-channel data. Then, we design a structural framework to generate Gaussian-Hermite moment invariants for these two transform models systematically. It is the first time that a unified framework has been proposed in the literature to construct orthogonal moment invariants of general multi-channel functions. Given a specific type of multi-channel data, we demonstrate how to utilize the new method to derive all possible invariants and eliminate dependences among them. We obtain independent sets of invariants with low orders and low degrees for RGB images, 2D vector fields and color volume data. Based on synthetic and real multi-channel data, we conduct extensive experiments to evaluate the stability and discriminability of these invariants and their robustness to noise. The results show that new moment invariants significantly outperform previous moment invariants of multi-channel data in RGB image classification and vortex detection in 2D vector fields.