Normalized cross correlation (NCC) based template matching is insensitive to intensity changes and it has many
applications in image processing, object detection, video tracking and pattern recognition. However, normalized
cross correlation implementation is computationally expensive since it involves both correlation computation and
normalization implementation. In this paper, we propose Legendre moment approach for fast normalized cross
correlation implementation and show that the computational cost of this proposed approach is independent of
template mask sizes which is significantly faster than traditional mask size dependent approaches, especially for
large mask templates. Legendre polynomials have been widely used in solving Laplace equation in electrodynamics
in spherical coordinate systems, and solving Schrodinger equation in quantum mechanics. In this paper, we extend
Legendre polynomials from physics to computer vision and pattern recognition fields, and demonstrate that
Legendre polynomials can help to reduce the computational cost of NCC based template matching significantly.
Bing C. Li, "Fast Legendre moment computation for template matching," Proc. SPIE 10202, Automatic Target Recognition XXVII, 102020J (Presented at SPIE Defense + Security: April 11, 2017; Published: 1 May 2017); https://doi.org/10.1117/12.2262783.
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