A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Synthesis of Gaussian Filters by Cascaded Uniform Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Representation of local geometry in the visual system
Biological Cybernetics
The cortex transform: rapid computation of simulated neural images
Computer Vision, Graphics, and Image Processing
Multiresolution Feature Extraction and Selection for Texture Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Algorithms for Low-Level Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Space variant image processing
International Journal of Computer Vision
Recursive implementation of the Gaussian filter
Signal Processing
Digital signal processing (3rd ed.): principles, algorithms, and applications
Digital signal processing (3rd ed.): principles, algorithms, and applications
Signals & systems (2nd ed.)
Recursive implementation of LoG filtering
Real-Time Imaging
A real-time foveated sensor with overlapping receptive fields
Real-Time Imaging - Special issue on natural and artificial real-time imaging and vision
Optical normal flow estimation on log-polar images. A solution for real-time binocular vision
Real-Time Imaging - Special issue on natural and artificial real-time imaging and vision
A review of biologically motivated space-variant data reduction models for robotic vision
Computer Vision and Image Understanding
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Adaptive resolution system for distributed surveillance
Real-Time Imaging
Fast Anisotropic Gauss Filtering
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Recursive Gaussian Derivative Filters
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 1 - Volume 1
Robot Navigation by Combining Central and Peripheral Optical Flow Detection on a Space-Variant Map
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 2 - Volume 2
IEEE Transactions on Signal Processing
A fast algorithm for convolution integrals with space and time variant kernels
Journal of Computational Physics
Improving Deriche-style Recursive Gaussian Filters
Journal of Mathematical Imaging and Vision
ISCGAV'08 Proceedings of the 8th conference on Signal processing, computational geometry and artificial vision
Accelerating space variant Gaussian filtering on graphics processing unit
EUROCAST'07 Proceedings of the 11th international conference on Computer aided systems theory
Accurate and efficient method for smoothly space-variant Gaussian blurring
IEEE Transactions on Image Processing
Fast space-variant elliptical filtering using box splines
IEEE Transactions on Image Processing
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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%.