Fast Algorithm for Zernike Moments Invariants in Scene Matching

Zernike moments are well-suited for unmanned aerial vehicle scene matching because of their rotation invariance and robustness to noise. However, their high computational complexity poses challenges for meeting the real-time requirements of navigation systems. To address this issue and enhance the real-time performance of scene matching navigation, this study proposed a hybrid matching strategy. This strategy, based on Wee&#x2019;s high-precision &#x201C;GMs-to-ZMs&#x201D; Zernike moment calculation method, combines offline and online computational phases to reduce online matching time during flight. In the offline phase, we precompute all the required multi-order cumulative geometric moment tables and a binomial coefficients table. In the online phase, these precomputed lookup tables reduce the computational complexity of the Zernike moments for each reference sub-image from <inline-formula> <tex-math notation="LaTeX">${\mathrm { O}}(n^{2})$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">${\mathrm { O}}(1)$ </tex-math></inline-formula>. Furthermore, the introduction of normalized moments enhances the adaptability of the algorithm to scale variations. Experimental results demonstrate that the proposed method significantly improves real-time performance while maintaining matching accuracy, offering an effective solution for the practical application of Zernike moments in unmanned aerial vehicle navigation.