Quadtrees, Transforms and Image Coding

Transforms and quadtrees are both methods of representing information in an image in terms of the presence of information at di#ering length scales. This paper presents a mathematical relationship between these two approaches to describing images in the particular case when Walsh transforms are used. Furthermore, both methods have been used for the compression of images for transmission. This paper notes that under certain circumstances, quadtree compression produces identical results to Walsh transform coding, but requires less computational e#ort to do so