Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Handbook of image processing operators
Handbook of image processing operators
Nonlinear Filters for Image Processing
Nonlinear Filters for Image Processing
Bilateral Filtering and Anisotropic Diffusion: Towards a Unified Viewpoint
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Images as embedding maps and minimal surfaces: movies, color, and volumetric medical images
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Image filtering using morphological amoebas
Image and Vision Computing
Combining curvature motion and edge-preserving denoising
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Modified curvature motion for image smoothing and enhancement
IEEE Transactions on Image Processing
An axiomatic approach to image interpolation
IEEE Transactions on Image Processing
Morphological Amoebas Are Self-snakes
Journal of Mathematical Imaging and Vision
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This paper is concerned with amoeba median filtering, a structure-adaptive morphological image filter. It has been introduced by Lerallut et al. in a discrete formulation. Experimental evidence shows that iterated amoeba median filtering leads to segmentation-like results that are similar to those obtained by self-snakes, an image filter based on a partial differential equation. We investigate this correspondence by analysing a space-continuous formulation of iterated median filtering. We prove that in the limit of vanishing radius of the structuring elements, iterated amoeba median filtering indeed approximates a partial differential equation related to self-snakes and the well-known (mean) curvature motion equation. We present experiments with discrete iterated amoeba median filtering that confirm qualitative and quantitative predictions of our analysis.