Performance of three recursive algorithms for fast space-variant Gaussian filtering

摘要

Animal visual systems have solved the problem of limited resources by allocating more processing power to central than peripheral vision. Foveation considerably reduces the amount of data per image by progressively decreasing the resolution at the periphery while retaining a sharp center of interest. This strategy has important applications in the design of autonomous systems for navigation, tracking and surveillance. Central to foveation is a space-variant Gaussian filtering scheme that gradually blurs out details as the distance to the image center increases. Unfortunately Gaussian convolution is a computationally expensive operation, which can severely limit the real-time applicability of foveation. In the space-variant case, the problem is even more difficult as traditional techniques such as the fast Fourier transform cannot be employed because the convolution kernel is different at each pixel. We show that recursive filtering, which was introduced to approximate Gaussian convolution, can be extended to the space-variant case and leads to a very simple implementation that makes it ideal for that application. Three main recursive algorithms have emerged, produced by independent derivation methods. We assess and compare their performance in traditional filtering applications and in our specific space-variant case. All three methods drastically cut down the cost of Gaussian filtering to a limited number of operations per pixel that is independent of the scale selected. In addition we show that two of those algorithms have excellent accuracy in that the output they produce differs from the output obtained performing real Gaussian convolution by less than 1%.