Calculate y derivative of image - c++

Question

I want to implement the y derivative of an image.
Given is the following openCV function, who uses a Sobel Operator:
Sobel(gray_input_picture, y_derivative_picture, CV_32FC1 , 0, 1, 3, BORDER_DEFAULT);
There is an example how it looks like:
Now i need to implement it by myself without using this sobel function.
I found some help here: Gradient direction computation
What i now implemented was:
for(int x=0; x<gray_input_picture.rows; x++)
{
for(int y=0; y<gray_input_picture.cols; y++)
{
if(x == gray_input_picture.rows-1 || x == 0)
{
y_derivative.at<Vec3b>(x,y) = gray_input_picture.at<Vec3b>(x,y);
}
else
{
Vec3b color;
color[0] = gray_input_picture.at<Vec3b>(x+1,y)[0] - gray_input_picture.at<Vec3b>(x-1,y)[0];
color[1] = gray_input_picture.at<Vec3b>(x+1,y)[1] - gray_input_picture.at<Vec3b>(x-1,y)[1];
color[2] = gray_input_picture.at<Vec3b>(x+1,y)[2] - gray_input_picture.at<Vec3b>(x-1,y)[2];
y_derivative_picture.at<Vec3b>(x,y) = color;
}
}
}
bitwise_not ( y_derivative_picture, y_derivative_picture2 );
The x and y switch comes from openCV. That's why it's a little bit different. What i don't understand is, that i get a picture which i need to convert (black to white, white to black).
The Result is a little bit different too. It contains blue areas:
Anyone know how i can implement the y derivative better (that it looks similar to the Sobel function)?
Or does anyone know the problem in my implementation?
Thanks!

Answer 1

I think you would probably need to check out what Sobel operator does here:
http://en.wikipedia.org/wiki/Sobel_operator