Detecting edges in an image using powers-of-two coefficients

The process of detecting edges in an image includes the convolution of the image with an operator or template, whose coefficients are determined by the algorithm in use. By approximating these coefficients to the nearest power-of-two, the convolution operation is greatly speeded-up, since each multiplication can instead be performed by a shift operation. This is attractive both for a software as well as a hardware implementation, since the arithmetic shift operation can be implemented at a lower cost than multiplication. Methods for deriving an integer valued operator and a powers-of-two operator are discussed, and the results obtained with each operator are compared.