9i,SrSSKrSSKrSSKrSrSrg)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. NcURnURSS- nURnUR[R SS9n[R "U5nUS:dUS;a [S5eUnUS:XGaUS US - nUS US - nUS US 'US:a0US XeS -- US 'US XeS -- US 'USXuS -- US'US:aUSSU-US -- XuS -- US-US --Xv-US --US'USSU-US -- XeS-- SU-U-US --US'USSU-US -- SUS--US --US'USSU-US-- SUS--US --US'GOFUSUS- nUSUS- nUSUS- nUSUS'US:alU*US-US-US'U*US-US-US'U*US-US-US'U*US-US-US'U*US-US-US'U*US-US-US'US:GaSUS--US-SU-US-- US-US'U*US-SU-XuS-US- --US-US'US-US-SU-US-- XUS-US- --US -US 'SUS--US-SU-US-- US!-US!'U*US-SU-XeS-US- --US"-US"'U*US-XvUS-US- --XUS-US- --US#-US#'U*US-SU-U*US-US--- US$-US$'US-US-SU-US-- XUS-US- --US%-US%'US-US-SU-US-- XvUS-US- --US&-US&'SUS--US-SU-US-- US'-US''URUSS9$)(a#Analytical 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 c/var/www/html/land-doc-ocr/venv/lib/python3.13/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*)<  #s * # G C (FsH )__doc__r$r"numpyrrr6rrr:s! m;`,r