  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.
