3D Non-separable Moment Invariants and Their Use in Neural Networks

Recognition of 3D objects is an important task in many bio-medical and industrial applications. The recognition algorithms should work regardless of a particular orientation of the object in the space. In this paper, we introduce new 3D rotation moment invariants, which are composed of non-separable Appell moments. We show that non-separable moments may outperform the separable ones in terms of recognition power and robustness thanks to a better distribution of their zero surfaces over the image space. We test the numerical properties and discrimination power of the proposed invariants on three real datasets—MRI images of human brain, 3D scans of statues, and confocal microscope images of worms. We show the robustness to resampling errors improved more than twice and the recognition rate increased by 2–10 % comparing to most common descriptors. In the last section, we show how these invariants can be used in state-of-the-art neural networks for image recognition. The proposed H-NeXtA architecture improved the recognition rate by 2–5 % over the current networks.