Implementation:

The difference operators in Eqn. 44 correspond to convolving the image with the two masks in Fig. 22.
This is easy to compute:

• The top left-hand corner of the appropriate mask is superimposed over each pixel of the image in turn,
• A value is calculated for or by using the mask coefficients in a weighted sum of the value of pixel (i,j) and its neighbours.
• These masks are referred to as convolution masks or sometimes convolution kernels.

 

Fig. 22 Edge operator convolution masks
Instead of finding approximate gradient components along the x and y directions we can also approximate gradient components along directions at and to the axes respectively. In this case the following equations are used:
 

This form of operator is known as the Roberts edge operator and was one of the first operators used to detect edges in images. The corresponding convolution masks are given by:  

Fig. 23 The C Compilation Model
Many edge detectors have been designed using convolution mask techniques, often using mask sizes or even larger.
An advantage of using a larger mask size is that errors due to the effects of noise are reduced by local averaging within the neighbourhood of the mask.
An advantage of using a mask of odd size is that the operators are centred and can therefore provide an estimate that is biased towards a centre pixel (i,j).
One important edge operator of this type is the Sobel edge operator. The Sobel edge operator masks are given in Fig 24.  

Fig. 24 Sobel edge operator convolution masks