U ?h@s0dZddlZddlZddlZddZddZdS)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 Cs |j}|jdd}|j}|jtjdd}t|}|dksD|dkrLtd|}|dkr|d |d }|d |d }|d |d <|dkr|d ||d |d <|d ||d |d <|d||d |d<|dkr|dd||d ||d |d|d |||d |d<|dd||d ||dd|||d |d<|dd||d d|d|d |d<|dd||dd|d|d |d<n6|d|d}|d|d}|d|d}|d|d<|dkr| |d|d|d<| |d|d|d<| |d|d|d<| |d|d|d<| |d|d|d<| |d|d|d<|dkrd|d|dd||d|d|d<| |dd|||d|d|d|d<|d|dd||d|||d|d|d |d <d|d|dd||d|d!|d!<| |dd|||d|d|d"|d"<| |d|||d|d|||d|d|d#|d#<| |dd|| |d|d|d$|d$<|d|dd||d|||d|d|d%|d%<|d|dd||d|||d|d|d&|d&<d|d|dd||d|d'|d'<|j|ddS)(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)rrr)rr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)ndimshapedtypeZastypenpZfloat64 zeros_like ValueError) moments_rawrorderZ float_dtypemoments_centralmZcxcyczrU/var/www/html/venv/lib/python3.8/site-packages/skimage/measure/_moments_analytical.py_moments_raw_to_central_fasts    ""04       rc Cs|j}|jdd}|dkr,|dkr,t|St|}|}t|ttj|td|d|}|dkr,t|dD]}t|dD]}|||krqt|dD]~}t ||} | |d ||9} t|dD]J} t || } | |d || 9} |||f| | ||| f7<qqqqv|St j t|df|D]} t | |krZqDt j dd | DD]Z} || }t| || D].\}}}|t ||9}|| ||9}q|| |7<qnqD|S) Nrrrr)r )rrcSsg|]}t|dqS)r)range).0orrr sz*moments_raw_to_central..)rr rr r tupleeyeintrmathcomb itertoolsproductsumzip)rrrrrZcenterspqiZterm1jZterm2ZordersZidxsvalZi_ordercidxrrrmoments_raw_to_centralqs< &    ,r+)__doc__r rnumpyr rr+rrrrs c