The problems that the presence of noise causes when using edge detectors means we should try to reduce the noise in an image prior to or in conjunction with the edge detection process. We have already discussed some methods of reducing or smoothing noise in the Image Processing Section. Some of these methods may be of use here. Another smoothing method is Gaussian smoothing Gaussian smoothing is performed by convolving an image with a Gaussian operator which is defined below. By using Gaussian smoothing in conjunction with the Laplacian operator, or another Gaussian operator, it is possible to detect edges.
Lets look at the Gaussian smoothing process first.
26 and is defined by where is the standard deviation representing the width of the Gaussian distribution. The shape of the distribution and hence the amount of smoothing can be controlled by varying . Thus the edge pixels in an image are determined by a single convolution operation. This method of edge detection was first proposed by Marr and Hildreth at MIT who introduced the principle of the zero-crossing method. The basic principle of this method is to find the position in an image where the second derivatives become zero.