Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Regularized Shock Filters and Complex Diffusion
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Detecting Codimension--Two Objects in an Image with Ginzburg-Landau Models
International Journal of Computer Vision
AIME '07 Proceedings of the 11th conference on Artificial Intelligence in Medicine
Complex Diffusion on Scalar and Vector Valued Image Graphs
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Complex diffusion on image graphs
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Morphological sharpening and denoising using a novel shock filter model
ICISP'10 Proceedings of the 4th international conference on Image and signal processing
A new fuzzy additive noise reduction method
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
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A framework that naturally unifies smoothing and enhancement processes is presented. We generalize the linear and nonlinear scale spaces in the complex domain, by combining the diffusion equation with the simplified Schr枚dinger equation. A fundamental solution for the linear case is developed. Preliminary analysis of the complex diffusion shows that the generalized diffusion has properties of both forward and inverse diffusion. An important observation, supported theoretically and numerically, is that the imaginary part can be regarded as an edge detector (smoothed second derivative), after rescaling by time, when the complex diffusion coefficient approaches the real axis. Based on this observation, a nonlinear complex process for ramp preserving denoising is developed.