Generate a Gaussian template (C ++)

 

Figure 1. Normal distribution equation in n-dimensional space (the formula is the same as that in figure 2)

 

Gaussian Blur is an image fuzzy filter that uses normal distribution to calculate the transformation of each pixel in an image.
The normal distribution equation of n-dimensional space is

(Figure 2)
In two-dimensional space, it is defined

(Figure 3)
Here, R is The Blur radius (R2 = u2 + V2), and σ is the standard deviation of normal distribution.
In two-dimensional space, the contour lines of the surface generated by this formula are concentric circles with normal distribution starting from the center. The convolution matrix composed of pixels with a non-zero distribution is transformed with the original image.

 

/*

E's X power function
For example
Exp (1) = 1 power of e = E = 2. 718281828...
Exp (0) = 0 power of e = 1
Exp (2) = E square = 3890561...
E is a constant, equal to 2. 718281828...

*/

A 5x5 Gaussian convolution kernel with a standard deviation of 1.4:
2 4 5 4 2
4 9 12 9 4
5 12 15 12 5
4 9 12 9 4
2 4 5 4 2
Last multiplied by the ratio of 1/115
// Code
// Code 1 (self-implemented)
Void makegauss ()
{
Double Sigma = 1.4; // σ is the standard deviation of normal distribution. Here it is 1.4.
Double dresult [5] [5]; // used to store results
Double dresult1 [5] [5]; // used to store results
 
// Center of the array
Int ncenterx = 2, ncentery = 2; // start with 1 at the center point.
Int nsize = 5;
// The distance from a point in the array to the center point
Double DDIs;
Double Pi = 3.1415926535;
// Intermediate variable
Double dvalue;
Double dsum;
Dsum = 0;
Int I, J;
 
For (I = 0; I <nsize; ++ I)
{
For (j = 0; j <nsize; ++ J)
{
DDIs = (I-ncenterx) * (I-ncenterx) + (J-ncentery) * (J-ncentery );
Dvalue = exp (-DDIs/(2 * Sigma * sigma ))/
(2 * pI * Sigma * sigma );
Dresult [I] [J] = dvalue;
Dsum + = dvalue;
}
}
// Normalization
For (I = 0; I <nsize; ++ I)
{
For (j = 0; j <nsize; ++ J)
{
Dresult1 [I] [J] = dresult [I] [J]/dsum;
}
}
STD: cout <dsum <STD: Endl;
For (I = 0; I <nsize; ++ I)
{
For (j = 0; j <nsize; ++ J)
{
// Dresult1 is the result of Gauss, but dresult * 1.95*100 is the result of the article.
// A convolution kernel of 5x5 Gaussian with a standard deviation of 1.4
// Do not know why.
STD: cout <(INT) (dresult [I] [J] * 1.95*100) <"";
}
STD: cout <STD: Endl;
}
}
// Code 2 (found online)
Void Gauss ()
{
Int h_size;
Float siz, sigma;
Int I, J;
Printf ("Please input size of Gaussian Core/N ");
Scanf ("% d", & h_size );
Printf ("Please input Sigma:/N ");
Scanf ("% F", & sigma );
Siz = (h_size-1)/2;
Float ** A, ** B;
A = new float * [h_size];
For (INT I = 0; I B = new float * [h_size];
For (I = 0; I 
For (I = 0; I {
For (j = 0; j {
A [I] [J] =-siz + J;
Printf ("% 4.2f", a [I] [J]);
}
Printf ("/N ");
}
Printf ("/N ");
For (I = 0; I {
For (j = 0; j {
B [I] [J] = A [J] [I];
Printf ("% 4.2f", B [I] [J]);
}
Printf ("/N ");
}
Printf ("/N ");
Float h_sum = 0;
For (I = 0; I {
For (j = 0; j {
A [I] [J] = A [I] [J] * A [I] [J];
B [I] [J] = B [I] [J] * B [I] [J];
A [I] [J] =-(A [I] [J] + B [I] [J])/(2 * Sigma * sigma );
A [I] [J] = exp (A [I] [J]);
If (A [I] [J] <0.0001) A [I] [J] = 0;
H_sum = h_sum + A [I] [J];
}
}
 
For (I = 0; I {
For (j = 0; j {
A [I] [J] = A [I] [J]/h_sum;
}
}
For (I = 0; I {
For (j = 0; j {
Printf ("% 4.4f", a [I] [J]);
}
Printf ("/N ");
}
}