i,dZddlZddlZddlZdZdZy)a)Analytical transformations from raw image moments to central moments. The expressions for the 2D central moments of order <=2 are often given in textbooks. Expressions for higher orders and dimensions were generated in SymPy using ``tools/precompute/moments_sympy.py`` in the GitHub repository. Nc|j}|jddz }|j}|jtj d}t j |}|dk\s|dvr td|}|dk(r|d |d z }|d |d z }|d |d <|dkDr3|d ||d zz |d <|d ||d zz |d <|d||d zz |d<|dkDr|dd|z|d zz ||d zz |dz|d zz||z|d zz|d<|dd|z|d zz ||dzz d|z|z|d zz|d<|dd|z|d zz d|dzz|d zz|d<|dd|z|dzz d|dzz|d zz|d<nK|d|dz }|d|dz }|d|dz }|d|d<|dkDrl| |dz|dz|d<| |dz|dz|d<| |dz|dz|d<| |dz|dz|d<| |dz|dz|d<| |dz|dz|d<|dkDrd|dzz|dzd|z|dzz |dz|d<| |dzd|z||dz|dz zz|dz|d<|dz|dzd|z|dzz |||dz|dz zz|d z|d <d|dzz|dzd|z|dzz |d!z|d!<| |dzd|z||dz|dz zz|d"z|d"<| |dz|||dz|dz zz|||dz|dz zz|d#z|d#<| |dzd|z| |dz|dzzz |d$z|d$<|dz|dzd|z|dzz |||dz|dz zz|d%z|d%<|dz|dzd|z|dzz |||dz|dz zz|d&z|d&<d|dzz|dzd|z|dzz |d'z|d'<|j|dS)(aOAnalytical formulae for 2D and 3D central moments of order < 4. `moments_raw_to_central` will automatically call this function when ndim < 4 and order < 4. Parameters ---------- moments_raw : ndarray The raw moments. Returns ------- moments_central : ndarray The central moments. rF)copyz:This function only supports 2D or 3D moments of order < 4.r)rr)rr)rr)rr)rr)rr)rr)rr)r rr )rr )rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr )rrr)rrr)rr r)rrr)rrr)rrr)rrr)rrr)r rr)ndimshapedtypeastypenpfloat64 zeros_like ValueError) moments_rawr order float_dtypemoments_centralmcxcyczs /var/www/ITT-ServiceAPI-Services/ITT-Document-Scan/mrzscanner/mrzenv/lib/python3.12/site-packages/skimage/measure/_moments_analytical.py_moments_raw_to_central_fastrs>   D   a 1 $E##K$$RZZe$$>RUQtWAT$TOD !$%dGa"fqw.>$>RUQtWAT$TOD !wZ!G* $ wZ!G* $ wZ!G* $#$W: 19(*sQwZ'7!G*'DOG $(*sQwZ'7!G*'DOG $(*sQwZ'7!G*'DOG $(*sQwZ'7!G*'DOG $(*sQwZ'7!G*'DOG $(*sQwZ'7!G*'DOG $ 19BE AgJ&R!G*)<r:s! m;`,r