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code at https://github.com/howardyclo/clcc-cvpr21/blob/master/util/raw2raw.py#L92
M_AC = (1 - w[:,None,None]) * I + w[:,None,None] * M_AB
M_BC = (1 - w[:,None,None]) * I + w[:,None,None] * M_BA
if Ill_c be defined by M_AC ,then M_BC should be M_BC = (1 - w[:,None,None]) * M_BA + w[:,None,None] *I
prove as below:
M_BC = M_BA @ M_AC = M_BA @ ( (1 - w[:,None,None]) * I + w[:,None,None] * M_AB )
## ==>
M_BC = ( (1 - w[:,None,None]) * M_BA + w[:,None,None] * M_BA @M_AB )
## M_BA @M_AB closed to I theoretically.
M_BC = (1 - w[:,None,None]) * M_BA + w[:,None,None] *I
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