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I have found the possible bug in my code which is the Noise Mat type(Unsigned char). This will trim the Negative values from the Noise Mat, so that image will look brighter! Here is my updated code!

Mat mNoise_Bgr = Mat(mSource_Bgr.size(),CV_8UC3);
Mat mGaussian_noise = Mat(mSource_Bgr.size(),CV_16SC3);
randn(mGaussian_noise,0,m_NoiseStdDev);

for (int Rows = 0; Rows < mSource_Bgr.rows; Rows++)
{
    for (int Cols = 0; Cols < mSource_Bgr.cols; Cols++)
    {
        Vec3b Source_Pixel= mSource_Bgr.at<Vec3b>(Rows,Cols);
        Vec3b &Des_Pixel= mNoise_Bgr.at<Vec3b>(Rows,Cols);
        Vec3s Noise_Pixel= mGaussian_noise.at<Vec3s>(Rows,Cols);

        for (int i = 0; i < 3; i++)
        {
            int Dest_Pixel= Source_Pixel.val[i] + Noise_Pixel.val[i];
            Des_Pixel.val[i]= Clamp(Dest_Pixel);
        }
    }
}

imshow("Noise Window",mNoise_Bgr);

I have found the possible bug in my code which is the Noise Mat type(Unsigned char). This will trim the Negative values from the Noise Mat, so that image will look brighter! Here is my updated code!

Mat mNoise_Bgr #include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"

#include <iostream>

using namespace cv;
using namespace std;

inline BYTE Clamp(int n)
{
    n = Mat(mSource_Bgr.size(),CV_8UC3);
n>255 ? 255 : n;
    return n<0 ? 0 : n;
}

bool AddGaussianNoise(const Mat mSrc, Mat &mDst,double Mean=0.0, double StdDev=10.0)
{
    if(mSrc.empty())
    {
        cout<<"[Error]! Input Image Empty!";
        return 0;
    }

    Mat mGaussian_noise = Mat(mSource_Bgr.size(),CV_16SC3);
randn(mGaussian_noise,0,m_NoiseStdDev);

Mat(mSrc.size(),CV_16SC3);
    randn(mGaussian_noise,Scalar::all(Mean),Scalar::all(StdDev));

    for (int Rows = 0; Rows < mSource_Bgr.rows; mSrc.rows; Rows++)
{
    {
        for (int Cols = 0; Cols < mSource_Bgr.cols; mSrc.cols; Cols++)
    {
    {
            Vec3b Source_Pixel= mSource_Bgr.at<Vec3b>(Rows,Cols);
mSrc.at<Vec3b>(Rows,Cols);
            Vec3b &Des_Pixel= mNoise_Bgr.at<Vec3b>(Rows,Cols);
mDst.at<Vec3b>(Rows,Cols);
            Vec3s Noise_Pixel= mGaussian_noise.at<Vec3s>(Rows,Cols);

         for (int i = 0; i < 3; i++)
        {
    {
                int Dest_Pixel= Source_Pixel.val[i] + Noise_Pixel.val[i];
             Des_Pixel.val[i]= Clamp(Dest_Pixel);
        }
    }
}

imshow("Noise Window",mNoise_Bgr);
    }
        }
    }

    return true;
}

bool AddGaussianNoise_Opencv(const Mat mSrc, Mat &mDst,double Mean=0.0, double StdDev=10.0)
{
    if(mSrc.empty())
    {
        cout<<"[Error]! Input Image Empty!";
        return 0;
    }
    Mat mSrc_16SC;
    Mat mGaussian_noise = Mat(mSrc.size(),CV_16SC3);
    randn(mGaussian_noise,Scalar::all(Mean), Scalar::all(StdDev));

    mSrc.convertTo(mSrc_16SC,CV_16SC3);
    addWeighted(mSrc_16SC, 1.0, mGaussian_noise, 1.0, 0.0, mSrc_16SC);
    mSrc_16SC.convertTo(mDst,mSrc.type());

    return true;
}


int main(int argc, const char* argv[])
{
    Mat mSource= imread("input.png",1); 
    imshow("Source Image",mSource);

    Mat mColorNoise(mSource.size(),mSource.type());

    AddGaussianNoise(mSource,mColorNoise,0,10.0);

    imshow("Source + Color Noise",mColorNoise); 

    AddGaussianNoise_Opencv(mSource,mColorNoise,0,10.0);

    imshow("Source + Color Noise OpenCV",mColorNoise);  

    waitKey();
    return 0;
}

I have found the possible bug in my code which is the Noise Mat type(Unsigned char). This will trim the Negative values from the Noise Mat, so that image will look brighter! Here is my updated code!

#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"

#include <iostream>

using namespace cv;
using namespace std;

inline BYTE Clamp(int n)
{
    n = n>255 ? 255 : n;
    return n<0 ? 0 : n;
}

bool AddGaussianNoise(const Mat mSrc, Mat &mDst,double Mean=0.0, double StdDev=10.0)
{
    if(mSrc.empty())
    {
        cout<<"[Error]! Input Image Empty!";
        return 0;
    }

    Mat mGaussian_noise = Mat(mSrc.size(),CV_16SC3);
    randn(mGaussian_noise,Scalar::all(Mean),Scalar::all(StdDev));

    for (int Rows = 0; Rows < mSrc.rows; Rows++)
    {
        for (int Cols = 0; Cols < mSrc.cols; Cols++)
        {
            Vec3b Source_Pixel= mSrc.at<Vec3b>(Rows,Cols);
            Vec3b &Des_Pixel= mDst.at<Vec3b>(Rows,Cols);
            Vec3s Noise_Pixel= mGaussian_noise.at<Vec3s>(Rows,Cols);

            for (int i = 0; i < 3; i++)
            {
                int Dest_Pixel= Source_Pixel.val[i] + Noise_Pixel.val[i];
                Des_Pixel.val[i]= Clamp(Dest_Pixel);
            }
        }
    }

    return true;
}

bool AddGaussianNoise_Opencv(const Mat mSrc, Mat &mDst,double Mean=0.0, double StdDev=10.0)
{
    if(mSrc.empty())
    {
        cout<<"[Error]! Input Image Empty!";
        return 0;
    }
    Mat mSrc_16SC;
    Mat mGaussian_noise = Mat(mSrc.size(),CV_16SC3);
    randn(mGaussian_noise,Scalar::all(Mean), Scalar::all(StdDev));

    mSrc.convertTo(mSrc_16SC,CV_16SC3);
    addWeighted(mSrc_16SC, 1.0, mGaussian_noise, 1.0, 0.0, mSrc_16SC);
    mSrc_16SC.convertTo(mDst,mSrc.type());

    return true;
}


int main(int argc, const char* argv[])
{
    Mat mSource= imread("input.png",1); 
    imshow("Source Image",mSource);

    Mat mColorNoise(mSource.size(),mSource.type());

    AddGaussianNoise(mSource,mColorNoise,0,10.0);

    imshow("Source + Color Noise",mColorNoise); 

    AddGaussianNoise_Opencv(mSource,mColorNoise,0,10.0);

    AddGaussianNoise_Opencv(mSource,mColorNoise,0,10.0);//I recommend to use this way!

    imshow("Source + Color Noise OpenCV",mColorNoise);  

    waitKey();
    return 0;
}

I have found the possible bug in my code which is the Noise Mat type(Unsigned char). This will trim the Negative values from the Noise Mat, so that image will look brighter! Here is my updated code!

#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"

#include <iostream>

using namespace cv;
using namespace std;

inline BYTE uchar Clamp(int n)
{
    n = n>255 ? 255 : n;
    return n<0 ? 0 : n;
}

bool AddGaussianNoise(const Mat mSrc, Mat &mDst,double Mean=0.0, double StdDev=10.0)
{
    if(mSrc.empty())
    {
        cout<<"[Error]! Input Image Empty!";
        return 0;
    }

    Mat mGaussian_noise = Mat(mSrc.size(),CV_16SC3);
    randn(mGaussian_noise,Scalar::all(Mean),Scalar::all(StdDev));

    for (int Rows = 0; Rows < mSrc.rows; Rows++)
    {
        for (int Cols = 0; Cols < mSrc.cols; Cols++)
        {
            Vec3b Source_Pixel= mSrc.at<Vec3b>(Rows,Cols);
            Vec3b &Des_Pixel= mDst.at<Vec3b>(Rows,Cols);
            Vec3s Noise_Pixel= mGaussian_noise.at<Vec3s>(Rows,Cols);

            for (int i = 0; i < 3; i++)
            {
                int Dest_Pixel= Source_Pixel.val[i] + Noise_Pixel.val[i];
                Des_Pixel.val[i]= Clamp(Dest_Pixel);
            }
        }
    }

    return true;
}

bool AddGaussianNoise_Opencv(const Mat mSrc, Mat &mDst,double Mean=0.0, double StdDev=10.0)
{
    if(mSrc.empty())
    {
        cout<<"[Error]! Input Image Empty!";
        return 0;
    }
    Mat mSrc_16SC;
    Mat mGaussian_noise = Mat(mSrc.size(),CV_16SC3);
    randn(mGaussian_noise,Scalar::all(Mean), Scalar::all(StdDev));

    mSrc.convertTo(mSrc_16SC,CV_16SC3);
    addWeighted(mSrc_16SC, 1.0, mGaussian_noise, 1.0, 0.0, mSrc_16SC);
    mSrc_16SC.convertTo(mDst,mSrc.type());

    return true;
}


int main(int argc, const char* argv[])
{
    Mat mSource= imread("input.png",1); 
    imshow("Source Image",mSource);

    Mat mColorNoise(mSource.size(),mSource.type());

    AddGaussianNoise(mSource,mColorNoise,0,10.0);

    imshow("Source + Color Noise",mColorNoise); 


    AddGaussianNoise_Opencv(mSource,mColorNoise,0,10.0);//I recommend to use this way!

    imshow("Source + Color Noise OpenCV",mColorNoise);  

    waitKey();
    return 0;
}