HOW TO APPLY SOBEL OPERATOR TO AN IMAGE

private static Bitmap ConvolutionFilter(Bitmap sourceImage,
    double[,] xkernel,
    double[,] ykernel, double factor = 1, int bias = 0, bool grayscale = false)
{

    //Image dimensions stored in variables for convenience
    int width = sourceImage.Width;
    int height = sourceImage.Height;

    //Lock source image bits into system memory
    BitmapData srcData = sourceImage.LockBits(new Rectangle(0, 0, width, height), ImageLockMode.ReadOnly, PixelFormat.Format32bppArgb);

    //Get the total number of bytes in your image - 32 bytes per pixel x image width x image height -> for 32bpp images
    int bytes = srcData.Stride * srcData.Height;

    //Create byte arrays to hold pixel information of your image
    byte[] pixelBuffer = new byte[bytes];
    byte[] resultBuffer = new byte[bytes];

    //Get the address of the first pixel data
    IntPtr srcScan0 = srcData.Scan0;

    //Copy image data to one of the byte arrays
    Marshal.Copy(srcScan0, pixelBuffer, 0, bytes);

    //Unlock bits from system memory -> we have all our needed info in the array
    sourceImage.UnlockBits(srcData);

//Convert your image to grayscale if necessary
if (grayscale == true)
{
    float rgb = 0;
    for (int i = 0; i < pixelBuffer.Length; i += 4)
    {
        rgb = pixelBuffer[i] * .21f;
        rgb += pixelBuffer[i + 1] * .71f;
        rgb += pixelBuffer[i + 2] * .071f;
        pixelBuffer[i] = (byte)rgb;
        pixelBuffer[i + 1] = pixelBuffer[i];
        pixelBuffer[i + 2] = pixelBuffer[i];
        pixelBuffer[i + 3] = 255;
    }
}

//Create variable for pixel data for each kernel
double xr = 0.0;
double xg = 0.0;
double xb = 0.0;
double yr = 0.0;
double yg = 0.0;
double yb = 0.0;
double rt = 0.0;
double gt = 0.0;
double bt = 0.0;

//This is how much your center pixel is offset from the border of your kernel
//Sobel is 3x3, so center is 1 pixel from the kernel border
int filterOffset = 1;
int calcOffset = 0;
int byteOffset = 0;

//Start with the pixel that is offset 1 from top and 1 from the left side
//this is so entire kernel is on your image
for (int OffsetY = filterOffset; OffsetY < height - filterOffset; OffsetY++)
{
    for (int OffsetX = filterOffset; OffsetX < width - filterOffset; OffsetX++)
    {
        //reset rgb values to 0
        xr = xg = xb = yr = yg = yb = 0;
        rt = gt = bt = 0.0;

        //position of the kernel center pixel
        byteOffset = OffsetY * srcData.Stride + OffsetX * 4;

    //Create new bitmap which will hold the processed data
    Bitmap resultImage = new Bitmap(width, height);

    //Lock bits into system memory
    BitmapData resultData = resultImage.LockBits(new Rectangle(0, 0, width, height), ImageLockMode.WriteOnly, PixelFormat.Format32bppArgb);

    //Copy from byte array that holds processed data to bitmap
    Marshal.Copy(resultBuffer, 0, resultData.Scan0, resultBuffer.Length);

    //Unlock bits from system memory
    resultImage.UnlockBits(resultData);

    //Return processed image
    return resultImage;
}

//Sobel operator kernel for horizontal pixel changes
private static double[,] xSobel
{
    get
    {
        return new double[,]
        {
            { -1, 0, 1 },
            { -2, 0, 2 },
            { -1, 0, 1 }
        };
    }
}

//Sobel operator kernel for vertical pixel changes
private static double[,] ySobel
{
    get
    {
        return new double[,]
        {
            {  1,  2,  1 },
            {  0,  0,  0 },
            { -1, -2, -1 }
        };
    }
}