RGB To Gray Or To Lab

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To implement Spectral Residual Approach， I need to transform the images from RGB space into Gray space.

RGB To Gray

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Gray = R*0.299 + G*0.587 + B*0.114

RGB To Lab

To implement Frequency Tuned Approach， I need to transform the images from RGB space into Lab space.

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void RGB2Lab(double R, double G, double B, double &L, double &a, double &b)
{
	double X, Y, Z, fX, fY, fZ;
	X = 0.412453*R + 0.357580*G + 0.180423*B;
	Y = 0.212671*R + 0.715160*G + 0.072169*B;
	Z = 0.019334*R + 0.119193*G + 0.950227*B;
	X /= (255 * 0.950456);
	Y /=  255;
	Z /= (255 * 1.088754);
	if (Y > 0.008856)
	{
		fY = pow(Y, 1.0/3.0);
		L = 116.0*fY - 16.0;
	}
	else
	{
		fY = 7.787*Y + 16.0/116.0;
		L = 903.3*Y;
	}
	if (X > 0.008856) {
		fX = pow(X, 1.0/3.0);
	}
	else {
		fX = 7.787*X + 16.0/116.0;
	}
	if (Z > 0.008856) {
		fZ = pow(Z, 1.0/3.0);
	}
	else {
		fZ = 7.787*Z + 16.0/116.0;
	}
	a = 500.0*(fX - fY);
	b = 200.0*(fY - fZ);
}

Transformation Formulas (Page 18-19, Formula 4-4 To 4-9)

References