As common features for graphics and images, differential invariants and integral invariants represented by moment invariants play significant roles in such fields as computer vision, pattern recognition, and computer graphics. In the past two decades, based on fundamental generating functions, our research group have constructed moment invariants of various data types of graphics and images, including grayscale images, color images, vector fields, point clouds, curves, and mesh surfaces, under the conditions of geometric transforms, color transforms, image blurring, and total transforms. The research proved the existence of the isomorphism between geometric moment invariants and differential invariants under affine transform, proposed a simple method for the generation of affine differential invariants by means of this property, and further derived differential invariants of graphics and images under projective transform and Möbius transform. In order to enhance the invariance of deep neural networks for the commonly used graphic/image transform models, the exploration was conducted on how to combine certain invariants of graphics or images with deep neural network models. This paper reviewed and summarized our previous work. In addition, a brief introduction was presented on how to utilize fundamental generating functions to generate geometric moment invariants and differential invariants of graphics and images under affine transform. Analyses were also undertaken on typical applications, advantages, and disadvantages of graphic and image invariants, with future research plan proposed.
