Image below are:

Original image
Gray from Photoshop's grayscale mode
New gray matching same dynamic range as original luminance channel
New gray + chrominance
New gray using full dynamic range (in L* [0,100])
New gray(full) + chrominance

A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original A_Original

B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray B_OldGray

C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray C_NewGray

D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor D_NewColor

E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray E_FullGray

F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor F_FullColor

Short summary of Color2Grey Algorithm using Poisson Solver

Convert images to CIELAB
   but don't normalize L*A*B*  (L in [0,100], A in [-500,500], B in [-200,200])

Calculate Gradients with respect to X and Y in CIELAB, call them G_L(X), G_A(X), G_B(X), etc.



Update Luminance Graident with Info from Chrominance Gradient
  In each direction (X and Y)
     For each pixel i
        //blend from G_L[i] = 0 (isoluminant) to major contribution by tempGradient[i]
        //Do a sort of gaussian blend 
      w = .5;  //width of gaussian
      C = sign(LumGrad[i])*sqrt((G_A[i]*G_A[i])+(G_B[i]*G_B[i]));
      NewGradient[i] = ((exp(-w*G_L[i]*G_L[i])*C)+Grad_L[i])

SolvePoisson with NewGradient_X() and NewGradient_Y()

Scale Result to fit in dynamic range
  //Need to fix this in the future
   Let org_min = min_grey_value of original
       org_max = max grey value of original
   if org_min & org_max are approximately equal
       Scale image to range 0 to 1
   else
      Scale image to range org_min to org_max