II.1 - IMAGE SMOOTHING AND SHARPENING BY DISCRETE CONVOLUTION

Abstract

This chapter discusses image smoothing and sharpening by discrete convolution. Discrete convolution determines a new value for each pixel in an image by computing some function of that pixel and its neighbors. Often this function simply is a weighted sum of pixel values in a small neighborhood of the source pixel. These weights can be represented by a small matrix that sometimes is called a convolution kernel. The dimensions of the matrix must be odd so there will be a central cell to represent the weight of the original value of the pixel for which a new value is being computed. The new value is computed by multiplying each pixel value in the neighborhood of the central pixel by the corresponding weight in the matrix, summing all the weighted values, and dividing by the sum of the weights in the matrix. The chapter presents a pseudo-code that shows this computation for a 3 × 3 convolution kernel. It also highlights that there are a large number of useful ways to apply discrete convolution for image enhancement.