  Affine transformation is one of the most common transformations in nature,
which is an important issue in the field of computer vision and shape analysis.
And affine transformations often occur in both shape and color space
simultaneously, which can be termed as Dual-Affine Transformation (DAT). In
general, we should derive invariants of different data formats separately, such
as 2D color images, 3D color objects, or even higher-dimensional data. To the
best of our knowledge, there is no general framework to derive invariants for
all of these data formats. In this paper, we propose a general framework to
derive moment invariants under DAT for objects in M-dimensional space with N
channels, which can be called dual-affine moment invariants (DAMI). Following
this framework, we present the generating formula of DAMI under DAT for 3D
color objects. Then, we instantiated a complete set of DAMI for 3D color
objects with orders and degrees no greater than 4. Finally, we analyze the
characteristic of these DAMI and conduct classification experiments to evaluate
the stability and discriminability of them. The results prove that DAMI is
robust for DAT. Our derivation framework can be applied to data in any
dimension with any number of channels.
