A New Method of Image Compression
We suggest a new method of image compression based on edge detection. The idea is based on the supposition that important information in an image is located in pixels lying near the edges. All other pixels contain only a homogeneous distribution of colors that can by reconstructed by solving numerically a partial differential equation with the methods of finite differences. We use here edge detection with the method described in the previous chapter. We represent edges as an ACC, described in Chapter 7. This representation has advantages because an element of the edge is defined by the difference of colors of two adjacent pixels. Thus an element of the edge belongs to neither of these two pixels, but rather to a space element lying between these pixels. Such a space element does not exist in a digital image; however, it exists in an ACC. This is the one-dimensional cell called the crack, whereas pixels are two-dimensional cells. The ends of a crack are zero-dimensional cells called points. When considering pixels as small squares, cracks are the sides of these squares; points are their corners and the end points of the cracks.