Progressive Image Transmission: an Adaptive Quadtree-Pruning Approach *

Progressive, adaptive and hierarchical modes are desirable image coding features. This paper presents a quadtree-pruning pyramid coding scheme satisfying all these objectives. Pyramid coding is an approach suitable for progressive image tramsmission, where the original image is divided into different levels that correspond to successive approximants of the original one. Starting from the original image, a sequence of reduced-size images is formed by averaging intensity values over 2 x 2-pixel blocks. This sequence, called mean pyramid, ends with an image with only one pixel. Then another sequence of images, called the difference pyramid which can be further encoded via vector quantization, is formed by taking the difference of two consecutive images in the mean pyramid. Our quadtree-pruning approach uses only the mean pyramid. In order to achieve the adaptability goal, a threshold function is introduced which controls the resolution requirement at various parts of an image. The input to the encoder is the original image and a threshold function. The original image is first decomposed into a mean pyramid in a hierarchical quadtree format. This quadtree is then pruned under the constraint that the difference of intensity values between the original and compressed images does not exceed the corresponding value of the threshold function. The compressed image is retrieved from the leaves of the pruned quadtree in a bitstream format. The task for the decoder is straight forward: retrieve bits from the bitstream and decipher their meaning. The quadtree-pruning pyramid approach adaptively decorrelates spatial redundance of the original image by tree pruning. It is optimal in the sense that the image fidelity is controlled by the threshold function. Our method has advantages over the classical one in several ways. First, the difference pyramid is no longer needed and thereby computationly more efficient, both in time and space complexity. Second, vector quantization techniques are not needed to achieve a high compression rate. The various levels of the mean pyramid contain the spatial correlation of the original image, of which full use is made in the quadtreepruning procedure. Finally, to perfectly reconstruct the original image, special error delivery procedures and entropy coders are not required. Experiments show that the quadtree-pruning pyramid method is quite efficient for lossy compression. Our approach can also be used for lossless compression by simply setting the threshold function to be zero.