# opencv brisk function refine1D?

Hello, I am a bit confusing with the brisk src code and I've found this function:

inline float
BriskScaleSpace::refine1D(const float s_05, const float s0, const float s05, float& max) const
{
int i_05 = int(1024.0 * s_05 + 0.5);
int i0 = int(1024.0 * s0 + 0.5);
int i05 = int(1024.0 * s05 + 0.5);

//   16.0000  -24.0000    8.0000
//  -40.0000   54.0000  -14.0000
//   24.0000  -27.0000    6.0000

int three_a = 16 * i_05 - 24 * i0 + 8 * i05;
// second derivative must be negative:
if (three_a >= 0)
{
if (s0 >= s_05 && s0 >= s05)
{
max = s0;
return 1.0f;
}
if (s_05 >= s0 && s_05 >= s05)
{
max = s_05;
return 0.75f;
}
if (s05 >= s0 && s05 >= s_05)
{
max = s05;
return 1.5f;
}
}

int three_b = -40 * i_05 + 54 * i0 - 14 * i05;
// calculate max location:
float ret_val = -float(three_b) / float(2 * three_a);
// saturate and return
if (ret_val < 0.75)
ret_val = 0.75;
else if (ret_val > 1.5)
ret_val = 1.5; // allow to be slightly off bounds ...?
int three_c = +24 * i_05 - 27 * i0 + 6 * i05;
max = float(three_c) + float(three_a) * ret_val * ret_val + float(three_b) * ret_val;
max /= 3072.0f;
return ret_val;
}


I found that this function is the implementation of the BRISK paper to fit a 1D parabola and get the maximum given three values. However, I just can't understand the code, what is 1D parabola fitting and how can it just use a hardcoded matrix to fit the parabola? What is the purpose of i05,i0... by multiplying 1024.0f? Can someone explain the function for me, I guess there must be some formula convention behind this.

Thanks.

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