DCTL for Root Polynomial Degree 4?

[LucasGodzilla]

Hello Ethan,

For about half a week now on and off, I have been trying to piece together custom DCTL plugins to apply the matrices generator by your Camera Match library directly inside of Da Vinci Resolve to avoid the use of a LUT.

While I have been successful in implementing a Degree 3 DCTL, I have been stuck at trying to create a Degree 4 DCTL for some reason.

The code itself should be fairly simple going off the Finlayson 2015 documentation I could find from Colour Science, and from my testing, the math should be correct—though I had to manually define my inputs as Constants instead of UI Sliders as DCTL only supported 64 of them.

[[-261346.9106751648 -280938.7950292614 17042.3295917317
  13764445.2638926059 -1314065.8834489791 269142.2770083626
  -14398071.1334277075 1252353.1562157504 -297589.2138827664
  -13474283.1793841682 1419049.9173040469 -239783.8256689388
  -98493.0047027412 6973398.6725546997 113847.0118633829 7701599.0578824533
  -776860.2946374351 158394.1921955326 -644658.1150428661 36050.0813998114
  41174.3347936619 39595.1608919792]

 [-199203.7713849060 -210242.9778685250 3671.1088273078 10204496.3039917685
  -460314.3124146534 131620.9336613363 -10553485.0740822535
  398373.5091930552 -141393.2366282719 -10102808.8260098975
  544158.3457493571 -117884.6268541000 -81224.1256896322 5257524.6216813214
  54390.1047581435 5612822.9510746449 -312224.5900445678 72365.8816136498
  -196912.6681236209 30694.8553637392 33018.7768176074 32557.8780022507]

 [-46950.7510616470 -71661.2046957209 -9804.4149705661 2500437.6548817428
  586857.3693750774 -48938.6547746651 -2606066.7397758248
  -563759.5604125325 47867.1319108658 -2459754.2824597401
  -628580.0843041310 48978.5954363124 17273.9318953632 1277626.8390139220
  -24812.7878715092 1393670.0243389183 341857.5346836292 -23887.3208098403
  290126.7520122456 -6304.5730566768 -7760.0067832336 -6414.3194653750]]

__DEVICE__ float mypowf (float base, float exp)
{
    return _copysignf(_powf(_fabs(base), exp), base);
}

__DEVICE__ float3 transform(int p_Width, int p_Height, int p_X, int p_Y, float p_R, float p_G, float p_B)
{

    //////
    //  Degree 4 Matrix has too many UI Parameters and must be defined in-code as variables

    ////    Red
    //  1
    const float red_r =         -261346.8614695633      ;
    const float red_g =         -280938.7547033542      ;
    const float red_b =         17042.3139221903        ;
    //  2
    const float red_rt_rg =     13764442.7055367529     ;
    const float red_rt_gb =     -1314065.1009736201     ;
    const float red_rt_rb =     269142.2990315667       ;
    //  3
    const float red_rt_rg2 =    -14398068.4827105850    ;
    const float red_rt_gb2 =    1252352.3805370491      ;
    const float red_rt_rb2 =    -297589.2366363414      ;
    const float red_rt_gr2 =    -13474280.6483757198    ;
    const float red_rt_bg2 =    1419049.1114064993      ;
    const float red_rt_br2 =    -239783.8468399671      ;
    const float red_rt_rgb =    -98492.9954246925       ;
    //  4
    const float red_rt_r3g =    6973397.3557095863      ;
    const float red_rt_r3b =    113847.0223287557       ;
    const float red_rt_g3r =    7701597.6460746182      ;
    const float red_rt_g3b =    -776859.8675437035      ;
    const float red_rt_b3r =    158394.2052652900       ;
    const float red_rt_b3g =    -644657.7096753955      ;
    const float red_rt_r2gb =   36050.0773770861        ;
    const float red_rt_g2rb =   41174.3303323984        ;
    const float red_rt_b2rg =   39595.1565379622        ;

    ////    Green
    //  1
    const float grn_r =         -199203.7582843798      ;
    const float grn_g =         -210242.9650707165      ;
    const float grn_b =         3671.1056783151         ;
    //  2
    const float grn_rt_rg =     10204495.5799025185     ;
    const float grn_rt_gb =     -460314.1208756918      ;
    const float grn_rt_rb =     131620.9456886460       ;
    //  3
    const float grn_rt_rg2 =    -10553484.3228744976    ;
    const float grn_rt_gb2 =    398373.3193960916       ;
    const float grn_rt_rb2 =    -141393.2476468480      ;
    const float grn_rt_gr2 =    -10102808.1077691447    ;
    const float grn_rt_bg2 =    544158.1494033572       ;
    const float grn_rt_br2 =    -117884.6378000051      ;
    const float grn_rt_rgb =    -81224.1245409784       ;
    //  4
    const float grn_rt_r3g =    5257524.2481600670      ;
    const float grn_rt_r3b =    54390.1104690309        ;
    const float grn_rt_g3r =    5612822.5512599843      ;
    const float grn_rt_g3b =    -312224.4872269094      ;
    const float grn_rt_b3r =    72365.8876717333        ;
    const float grn_rt_b3g =    -196912.5696254597      ;
    const float grn_rt_r2gb =   30694.8540255078        ;
    const float grn_rt_g2rb =   33018.7751607543        ;
    const float grn_rt_b2rg =   32557.8765079035        ;

    ////    Blue
    //  1
    const float blu_r =         -46950.6952389541       ;
    const float blu_g =         -71661.1609506553       ;
    const float blu_b =         -9804.4337590240        ;
    //  2
    const float blu_rt_rg =     2500434.7481498034      ;
    const float blu_rt_gb =     586858.3166443132       ;
    const float blu_rt_rb =     -48938.6417227647       ;
    //  3
    const float blu_rt_rg2 =    -2606063.7277709227     ;
    const float blu_rt_gb2 =    -563760.5014380891      ;
    const float blu_rt_rb2 =    47867.1171433433        ;
    const float blu_rt_gr2 =    -2459751.4104897310     ;
    const float blu_rt_bg2 =    -628581.0614164971      ;
    const float blu_rt_br2 =    48978.5827169900        ;
    const float blu_rt_rgb =    17273.9444326147        ;
    //  4
    const float blu_rt_r3g =    1277625.3456099702      ;
    const float blu_rt_r3b =    -24812.7806100923       ;
    const float blu_rt_g3r =    1393668.4202844591      ;
    const float blu_rt_g3b =    341858.0545124854       ;
    const float blu_rt_b3r =    -23887.3120578217       ;
    const float blu_rt_b3g =    290127.2433076900       ;
    const float blu_rt_r2gb =   -6304.5777155657        ;
    const float blu_rt_g2rb =   -7760.0119717876        ;
    const float blu_rt_b2rg =   -6414.3245199491        ;

    //////

    float rFinal =  //  1
                    (p_R * red_r) +
                    (p_G * red_g) +
                    (p_B * red_b) +
                    //  2
                    (mypowf((p_R * p_G), 0.5) * red_rt_rg) +
                    (mypowf((p_G * p_B), 0.5) * red_rt_gb) +
                    (mypowf((p_R * p_B), 0.5) * red_rt_rb) +
                    //  3
                    (mypowf((p_R * p_G * p_G), _frecip(3)) * red_rt_rg2) +
                    (mypowf((p_G * p_B * p_B), _frecip(3)) * red_rt_gb2) +
                    (mypowf((p_R * p_B * p_B), _frecip(3)) * red_rt_rb2) +
                    (mypowf((p_G * p_R * p_R), _frecip(3)) * red_rt_gr2) +
                    (mypowf((p_B * p_G * p_G), _frecip(3)) * red_rt_bg2) +
                    (mypowf((p_B * p_R * p_R), _frecip(3)) * red_rt_br2) +
                    (mypowf((p_R * p_G * p_B), _frecip(3)) * red_rt_rgb) +
                    //  4
                    (mypowf((p_R * p_R * p_R * p_G), 0.25) * red_rt_r3g) +
                    (mypowf((p_R * p_R * p_R * p_B), 0.25) * red_rt_r3b) +
                    (mypowf((p_G * p_G * p_G * p_R), 0.25) * red_rt_g3r) +
                    (mypowf((p_G * p_G * p_G * p_B), 0.25) * red_rt_g3b) +
                    (mypowf((p_B * p_B * p_B * p_R), 0.25) * red_rt_b3r) +
                    (mypowf((p_B * p_B * p_B * p_G), 0.25) * red_rt_b3g) +
                    (mypowf((p_R * p_R * p_G * p_B), 0.25) * red_rt_r2gb) +
                    (mypowf((p_G * p_G * p_R * p_B), 0.25) * red_rt_g2rb) +
                    (mypowf((p_B * p_B * p_R * p_G), 0.25) * red_rt_b2rg);

    float gFinal =  //  1
                    (p_R * grn_r) +
                    (p_G * grn_g) +
                    (p_B * grn_b) +
                    //  2
                    (mypowf((p_R * p_G), 0.5) * grn_rt_rg) +
                    (mypowf((p_G * p_B), 0.5) * grn_rt_gb) +
                    (mypowf((p_R * p_B), 0.5) * grn_rt_rb) +
                    //  3
                    (mypowf((p_R * p_G * p_G), _frecip(3)) * grn_rt_rg2) +
                    (mypowf((p_G * p_B * p_B), _frecip(3)) * grn_rt_gb2) +
                    (mypowf((p_R * p_B * p_B), _frecip(3)) * grn_rt_rb2) +
                    (mypowf((p_G * p_R * p_R), _frecip(3)) * grn_rt_gr2) +
                    (mypowf((p_B * p_G * p_G), _frecip(3)) * grn_rt_bg2) +
                    (mypowf((p_B * p_R * p_R), _frecip(3)) * grn_rt_br2) +
                    (mypowf((p_R * p_G * p_B), _frecip(3)) * grn_rt_rgb) +
                    //  4
                    (mypowf((p_R * p_R * p_R * p_G), 0.25) * grn_rt_r3g) +
                    (mypowf((p_R * p_R * p_R * p_B), 0.25) * grn_rt_r3b) +
                    (mypowf((p_G * p_G * p_G * p_R), 0.25) * grn_rt_g3r) +
                    (mypowf((p_G * p_G * p_G * p_B), 0.25) * grn_rt_g3b) +
                    (mypowf((p_B * p_B * p_B * p_R), 0.25) * grn_rt_b3r) +
                    (mypowf((p_B * p_B * p_B * p_G), 0.25) * grn_rt_b3g) +
                    (mypowf((p_R * p_R * p_G * p_B), 0.25) * grn_rt_r2gb) +
                    (mypowf((p_G * p_G * p_R * p_B), 0.25) * grn_rt_g2rb) +
                    (mypowf((p_B * p_B * p_R * p_G), 0.25) * grn_rt_b2rg);

    float bFinal =  //  1
                    (p_R * blu_r) +
                    (p_G * blu_g) +
                    (p_B * blu_b) +
                    //  2
                    (mypowf((p_R * p_G), 0.5) * blu_rt_rg) +
                    (mypowf((p_G * p_B), 0.5) * blu_rt_gb) +
                    (mypowf((p_R * p_B), 0.5) * blu_rt_rb) +
                    //  3
                    (mypowf((p_R * p_G * p_G), _frecip(3)) * blu_rt_rg2) +
                    (mypowf((p_G * p_B * p_B), _frecip(3)) * blu_rt_gb2) +
                    (mypowf((p_R * p_B * p_B), _frecip(3)) * blu_rt_rb2) +
                    (mypowf((p_G * p_R * p_R), _frecip(3)) * blu_rt_gr2) +
                    (mypowf((p_B * p_G * p_G), _frecip(3)) * blu_rt_bg2) +
                    (mypowf((p_B * p_R * p_R), _frecip(3)) * blu_rt_br2) +
                    (mypowf((p_R * p_G * p_B), _frecip(3)) * blu_rt_rgb) +
                    //  4
                    (mypowf((p_R * p_R * p_R * p_G), 0.25) * blu_rt_r3g) +
                    (mypowf((p_R * p_R * p_R * p_B), 0.25) * blu_rt_r3b) +
                    (mypowf((p_G * p_G * p_G * p_R), 0.25) * blu_rt_g3r) +
                    (mypowf((p_G * p_G * p_G * p_B), 0.25) * blu_rt_g3b) +
                    (mypowf((p_B * p_B * p_B * p_R), 0.25) * blu_rt_b3r) +
                    (mypowf((p_B * p_B * p_B * p_G), 0.25) * blu_rt_b3g) +
                    (mypowf((p_R * p_R * p_G * p_B), 0.25) * blu_rt_r2gb) +
                    (mypowf((p_G * p_G * p_R * p_B), 0.25) * blu_rt_g2rb) +
                    (mypowf((p_B * p_B * p_R * p_G), 0.25) * blu_rt_b2rg);

    return make_float3(rFinal, gFinal, bFinal);
}

But for some reason when I try applying the DCTL in comparison to the LUT in Resolve, I get some really weird results and I have no clue as to why.

I don't suppose you have any idea what's going wrong here, do you? I'm assuming it's some Resolve limitation but I can't fathom what that would be at the moment.

Thank you in advance and I hope to hear back soon!

[ethan-ou]

Apologies for such a long delay! I think I tried to make the 4th degree polynomial work on my end but it became way too difficult to get a good match. It's because it has a lot of variables it's trying to optimise for and the amount of gain you get from those increased variables rarely leads to a better match. I think when I tried it I got results on the 2nd and 3rd degrees that was barely better than the standard linear transform.

Hopefully you get somewhere with this but I couldn't and that's why the DCTL folder in this repo doesn't have a 4th degree polynomial either.