Representations based on zero-crossings in scale-space
Readings in computer vision: issues, problems, principles, and paradigms
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection
Image and Vision Computing - Special issue on the first ECCV 1990
Active vision based on space-variant sensing
The fifth international symposium on Robotics research
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Nonlinear Image Filtering with Edge and Corner Enhancement
IEEE Transactions on Pattern Analysis and Machine Intelligence
A multi-scale approach to nonuniform diffusion
CVGIP: Image Understanding
Geometry-limited diffusion in the characterization of geometric patches in images
CVGIP: Image Understanding
Signal and image restoration using shock filters and anisotropic diffusion
SIAM Journal on Numerical Analysis
Solution of nonlinear diffusion appearing in image smoothing and edge detection
Applied Numerical Mathematics
An active foveated vision system: attentional mechanisms and scan path convergence measures
Computer Vision and Image Understanding
Learning an Integral Equation Approximation to Nonlinear Anisotropic Diffusion in Image Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fourier analysis and cortical architectures: the exponential chirp transform
Real-Time Imaging - Special issue on natural and artificial real-time imaging and vision
The local structure of space-variant images
Neural Networks
Space-Variant Fourier Analysis: The Exponential Chirp Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
A Common Framework for Curve Evolution, Segmentation and Anisotropic Diffusion
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Lie groups, Space-Variant Fourier Analysis and the Exponential Chirp Transform
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Learned Adaptive Nonlinear Filtering for Anisotropic Diffusion Approximation in Image Processing
ICPR '96 Proceedings of the International Conference on Pattern Recognition (ICPR '96) Volume IV-Volume 7472 - Volume 7472
Optical Flow in Log-Mapped Image Plane-A New Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optical Flow in Log-mapped Image Plane (A New Approach)
RobVis '01 Proceedings of the International Workshop on Robot Vision
A Binocular Stereo Algorithm for Log-Polar Foveated Systems
BMCV '02 Proceedings of the Second International Workshop on Biologically Motivated Computer Vision
A review of log-polar imaging for visual perception in robotics
Robotics and Autonomous Systems
A Novel Space Variant Image Representation
Journal of Mathematical Imaging and Vision
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Many computer and robot vision applications requiremulti-scale image analysis. Classically, this has been accomplishedthrough the use of a linear scale-space, which is constructed byconvolution of visual input with Gaussian kernels of varying size(scale). This has been shown to be equivalent to the solution of a linear diffusion equation on an infinite domain, as the Gaussian isthe Green‘s function of such a system (Koenderink, 1984).Recently, much work has been focused on the use of a variableconductance function resulting in anisotropic diffusion described bya nonlinear partial differential equation (PDE). The use of anisotropic diffusion with a conductance coefficient which is adecreasing function of the gradient magnitude has been shown toenhance edges, while decreasing some types of noise (Perona andMalik, 1987). Unfortunately, the solution of the anisotropicdiffusion equation requires the numerical integration of a nonlinear PDE which is a costly process when carried out on a uniform mesh suchas a typical image. In this paper we show that the complex logtransformation, variants of which are universally used in mammalianretino-cortical systems, allows the nonlinear diffusion equation tobe integrated at exponentially enhanced rates due to the nonuniformmesh spacing inherent in the log domain. The enhanced integrationrates, coupled with the intrinsic compression of the complex logtransformation, yields a speed increase of between two and threeorders of magnitude, providing a means of performing rapid imageenhancement using anisotropic diffusion.