Wavelet Foveation

Abstract

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.

Experiential Sampling on Multiple Data Streams

“…There is also the foveation technique [13], [15] for maintaining a high-resolution area of interest in an image. A uniform-resolution image can be foveated to transform into a spatially varying resolution image by either a log-polar [13] or a wavelet approach [14]. All these approaches recognize the need for doing adaptive sampling.…”

“…This keeps the valuable information gain per unit cost near the maximal value. In contrast, the rate of gain of valuable information per unit cost for the local feature centered approach (if we only use (1) for content analysis) is equal to (14) where is number of times that the local analysis needs to be performed.…”

Robust image authentication using content based compression

“…This distribution of resolution provides a fast and simple way of reducing information in the visual field without sacrificing the size of the visual field and the resolution around the fovea. As the biological visual system is highly effective, its space-variant nature has inspired the design of many computer vision systems that resemble the biological foveated vision [1,4,21], video conferencing [2,8], image compression [5], and visualization systems [13]. The foveated image is obtained from the uniform resolution image through a space-variant smoothing process where the width of the smoothing function is small near the fovea but gradually increases toward the periphery.…”

“…The process of going from a uniform image to a foveated image is known as foveation. In this paper, we use the definition and techniques in [5]. The foveation of an image I : R 2 → R is determined by a smoothing function g : R 2 → R and a weight function w : R 2 → R ≥0 .…”

“…This fast algorithm plays an important role in both the signature creation and the authentication process. The reader is referred to [5] for the details of the approximation algorithm.…”