An overview of morphological filtering
Circuits, Systems, and Signal Processing - Special issue: median and morphological filters
Self-dual morphological operators and filters
Journal of Mathematical Imaging and Vision
Connected morphological operators for binary images
Computer Vision and Image Understanding
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: modeling, learning, sampling and computing, Part I
Edge Detection by Helmholtz Principle
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Fast computation of a contrast-invariant image representation
IEEE Transactions on Image Processing
Journal of Mathematical Imaging and Vision
Significance Tests and Statistical Inequalities for Region Matching
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
A probabilistic grouping principle to go from pixels to visual structures
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
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Area openings and closings are morphological filters which efficiently suppress impulse noise from an image, by removing small connected components of level sets. The problem of an objective choice of threshold for the area remains open. Here, a mathematical model for random images will be considered. Under this model, a Poisson approximation for the probability of appearance of any local pattern can be computed. In particular, the probability of observing a component with size larger than k in pure impulse noise has an explicit form. This permits the definition of a statistical test on the significance of connected components, thus providing an explicit formula for the area threshold of the denoising filter, as a function of the impulse noise probability parameter. Finally, using threshold decomposition, a denoising algorithm for grey level images is proposed.