Affine Moment Invariants in 2D and 3D
Jan Flusser, Tomáš Suk, Barbara Zitová · 2016
This chapter focuses on the affine moment invariants (AMIs), which play a very important role in moment-based theories and in invariant object recognition. It begins with an explanation of the projective imaging and the relationship between projective and affine transforms. The chapter presents four different methods that allow a systematic design of the AMIs of any order, the graph method, the normalization method, the method based on the Caley-Aronhold equation, and the transvectant method. It discusses the differences between them and illustrates the numerical properties of the AMIs. The chapter introduces affine invariants of color images and vector fields, 3D AMIs, and the idea of moment matching. The AMIs play an important role in view-independent object recognition and have been widely used not only in tasks where image deformation is intrinsically affine but also commonly substitute projective invariants.