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
Signal and image restoration using shock filters and anisotropic diffusion
SIAM Journal on Numerical Analysis
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
A Note on Two Classical Shock Filters and Their Asymptotics
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Complex Diffusion Processes for Image Filtering
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Anisotropic selective inverse diffusion for signal enhancement in the presence of noise
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 01
Rough Interface Reconstruction Using the Level Set Method
VIS '04 Proceedings of the conference on Visualization '04
Theoretical foundations for spatially discrete 1-D shock filtering
Image and Vision Computing
Total variation minimizing blind deconvolution with shock filter reference
Image and Vision Computing
An extension of min/max flow framework
Image and Vision Computing
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
C-arm tracking by intensity-based registration of a fiducial in prostate brachytherapy
IPCAI'10 Proceedings of the First international conference on Information processing in computer-assisted interventions
Two-phase kernel estimation for robust motion deblurring
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I
Adaptive Continuous-Scale Morphology for Matrix Fields
International Journal of Computer Vision
Adaptive coupled diffusion model for vessel image enhancement
International Journal of Computational Science and Engineering
Edge-preserving single image super-resolution
MM '11 Proceedings of the 19th ACM international conference on Multimedia
Shock coupled fourth-order diffusion for image enhancement
Computers and Electrical Engineering
Structure-preserving image smoothing via region covariances
ACM Transactions on Graphics (TOG)
Conditional Toggle Mappings: Principles and Applications
Journal of Mathematical Imaging and Vision
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We address the issue of regularizing Osher and Rudin's shock filter, used for image deblurring, in order to allow processes that are more robust against noise. Previous solutions to the problem suggested adding some sort of diffusion term to the shock equation. We analyze and prove some properties of coupled shock and diffusion processes. Finally we propose an original solution of adding a complex diffusion term to the shock equation. This new term is used to smooth out noise and indicate inflection points simultaneously. The imaginary value, which is an approximated smoothed second derivative scaled by time, is used to control the process. This results in a robust deblurring process that performs well also on noisy signals.