Wavelet foveation

A foveated image is a nonuniform resolution image whose resolution is highest at a point (fovea) but falls off away from the fovea. It can be obtained from a uniform image through a space-variant smoothing process, where the width of the smoothing function is small near the fovea and gradually expanding as the distance from the fovea increases. We treat this process as an integral operator and analyze its kernel. This kernel is dominated by its diagonal in the wavelet bases and thus permits a fast algorithm for foveating images. In addition, the transformed kernel takes a simple form which can be easily computed using a look-up table. This is useful, since in applications the fovea changes rapidly. We describe an application of our approximation algorithm in image visualization over the Internet.