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
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Signal and image restoration using shock filters and anisotropic diffusion
SIAM Journal on Numerical Analysis
KCS-new kernel family with compact support in scale space: formulation and impact
IEEE Transactions on Image Processing
Shock Filters for Character Image Enhancement and Peeling
ICDAR '03 Proceedings of the Seventh International Conference on Document Analysis and Recognition - Volume 2
Theoretical foundations for spatially discrete 1-D shock filtering
Image and Vision Computing
Morphological sharpening and denoising using a novel shock filter model
ICISP'10 Proceedings of the 4th international conference on Image and signal processing
Adaptive Continuous-Scale Morphology for Matrix Fields
International Journal of Computer Vision
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Considerable interest has recently been given to signal processing models based on partial differential equations. Successively improved models based on hyperbolic partial differential equation types are proposed in the literature. These models yield interesting results; however, it would be of great interest to generalize them in order to increase their efficiency. In this paper, we propose a generalized shock filter model for one-dimensional signal restoration. After justifying the existence and uniqueness of the solutions in an adequate vector space, we propose an effective numerical scheme to discretize the proposed model, and derive a two-dimensional numerical scheme directly from the one-dimensional model following a space-split strategy. We then prove a stability result for both schemes. We conclude our study by providing high-quality experimental results for one- and two-dimensional signal enhancement and restoration, and showing the influence the shock speed control has on processing time.