For the image find the first derivative and second derivatives or the enhanced image can find an edge image.
First Derivative:
We know that in a mathematical method for finding the first derivative is:
Since the graphics image is composed of discrete pixels by, the minimum h value is 1, so the calculation:
Therefore, the rate of change of the derivative of the luminance image is an image of the first order, for a grayscale image, he first derivative is calculated as follows:
Gray-scale image matrix:
ABC
DEF
GHI
then the central pixel E:
DX = Fe (or FD)
Dy = of He (or hi)
Of course, if using the sobel operator, then
dx = (c + 2f + i ) - (a + 2d + G)
Dy = (G + 2H + I) - (A + 2B + C)
Therefore, the image edge detection, sobel operator of convolution factors:
It can be seen that the convolution factor sobel operator is actually requested image, the first derivative.
Second Derivative:
Therefore, when h = 1 when:
Then you can simplify:
This step is derived as (mathematical difference I saw was a morning read) in mathematics:
So that x = x-1
then:
In the x and y directions, are:
The combination of the second derivative of x and y directions:
This essentially is the famous second-order differential Laplace operator (Laplacian), Laplace second derivative as well as other forms, such as:
So convolution factor Laplacian operator of the following two: