  We proposed a kind of naturally combined shape-color affine moment invariants
(SCAMI), which consider both shape and color affine transformations
simultaneously in one single system. In the real scene, color and shape
deformations always exist in images simultaneously. Simple shape invariants or
color invariants can not be qualified for this situation. The conventional
method is just to make a simple linear combination of the two factors.
Meanwhile, the manual selection of weights is a complex issue. Our construction
method is based on the multiple integration framework. The integral kernel is
assigned as the continued product of the shape and color invariant cores. It is
the first time to directly derive an invariant to dual affine transformations
of shape and color. The manual selection of weights is no longer necessary, and
both the shape and color transformations are extended to affine transformation
group. With the various of invariant cores, a set of lower-order invariants are
constructed and the completeness and independence are discussed detailedly. A
set of SCAMIs, which called SCAMI24, are recommended, and the effectiveness and
robustness have been evaluated on both synthetic and real datasets.
