Edge enhancement with image algebra

Illustrates an implementation method for edge enhancement algorithms, or other processes based on convolutions, through the application of image algebra. Standard convolution kernels are decomposed into orthogonal components to identify a small set of basis images that are combined to perform the desired functions. With this method, algorithms can easily be modified as they are not limited by the summation of fixed constants in convolution kernels. Though results are shown on a pixel basis, there is no effort in this paper to evaluate the relative performances of various algorithms. However, the image algebra approach naturally illuminates the fundamental properties of different algorithms. The approach is effective for software implementation as algorithms typically execute faster than implementations based on conventional convolutions