A growth-geometry coding of bilevel images for transmission over low-capacity channels in a progressive fashion is described. In progressive techniques, a crude representation of the image is transmitted first, and the details are added later. Such presentation is desirable when a viewer wishes to recognize image content as soon as possible, and half transmission of unwanted detail, or initiate actions simultaneous to tranmsmission of the remaining detail. Progressive transmission is also desirable simply as a means to provide an aesthetically pleasing sequence which holds the viewer's attention. For these purposes, a progressive display is more effective than a line-by-line scanning display. Important applications of progressive display include bilevel aspects of teleconferencing, teleconsultation, still-picture broadcasting, remote plant surveillance, computer-graphics communication, and interactive visual search of large picture databases. In the growth-geometry approach, aggregates of picture elements (pels) within the image are identified as those which can be generated by applying specified growth processes to particular pels, called seed pels. The data transmitted consist of the location, type of growth, and number of growth stages for each seed pel. At the receiver, pels are attached in the neighborhood of each seed pel according to the indicated growth processes, and thus regenerate the image exactly. Inter-related aspects of coding efficiency, equipment complexity, and perceptual quality are discussed, coding methods for a number of growth processes and specific software and hardware implementations are described. While our experience with this coding is not extensive, we believe that it indicates this approach has the potential for desirable visual presentation, with relatively high coding efficiency and economical implementation. Possible extensions of this method to coding multilevel images, and an application of these processes to determining optimal routing for interconnections in electronic systems are also discussed.