The computing method for orthogonal Fourier–Mellin moments in a polar coordinate system is presented in detail. The image expressed in a Cartesian system has to be transformed into a polar coordinate system first when we calculate the orthogonal Fourier–Mellin moments of the image in a polar coordinate system, which will increase both computational complexity and error. To solve the problem, a new direct computing method for orthogonal Fourier–Mellin moments in a Cartesian coordinate system is proposed, which can avoid the image transformation between two coordinate systems and eliminate the rounding error in coordinate transformation and decrease the computational complexity.
© 2009 Optical Society of America
Original Manuscript: December 18, 2008
Revised Manuscript: February 16, 2009
Manuscript Accepted: February 21, 2009
Published: April 1, 2009
Hai-tao Hu and Ping Zi-liang, "Computation of orthogonal Fourier-Mellin moments in two coordinate systems," J. Opt. Soc. Am. A 26, 1080-1084 (2009)