Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Toward a computational theory of shape: an overview
ECCV 90 Proceedings of the first european conference on Computer vision
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
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Numerical Geometry of Images: Theory, Algorithms, and Applications
Numerical Geometry of Images: Theory, Algorithms, and Applications
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
From adaptive averaging to accelerated nonlinear diffusion filtering
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Adaptive smoothing respecting feature directions
IEEE Transactions on Image Processing
A Nonlinear Probabilistic Curvature Motion Filter for Positron Emission Tomography Images
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Differential Equations for Morphological Amoebas
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Morphological Amoebas Are Self-snakes
Journal of Mathematical Imaging and Vision
Numerical scheme for efficient colour image denoising
Computers & Mathematics with Applications
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
| Hi-index | 0.00 |
In this paper we investigate a family of partial differential equations (PDEs) for image processing which can be regarded as isotropic nonlinear diffusion with an additional factor on the right-hand side. The one-dimensional analogues to this filter class have been motivated as scaling limits of one-dimensional adaptive averaging schemes. In 2-D, mean curvature motion is one of the most prominent examples of this family of PDEs. Other representatives of the filter class combine properties of curvature motion with the enhanced edge preservation of Perona-Malik diffusion. It becomes appearent that these PDEs require a careful discretisation. Numerical experiments display the differences between Perona-Malik diffusion, classical mean curvature motion and the proposed extensions.We consider, for example, enhanced edge sharpness, the question of morphological invariance, and the behaviour with respect to noise.