(eng): Invariants to image scaling composed of Gaussian–Hermite moments are introduced in this paper for the first time. To achieve the invariance, we propose to modulate the Gaussian–Hermite polynomial basis using variable parameter σ, the value of which depends on the input image. The scaling invariance property can be coupled with the rotation invariance presented earlier. This approach is applicable in 2D as well as in 3D and provides very good numerical stability, as demonstrated by several experiments on real data.