Computer Vision, Graphics, and Image Processing
The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
Self-dual morphological operators and filters
Journal of Mathematical Imaging and Vision
Attribute openings, thinnings, and granulometries
Computer Vision and Image Understanding
An improved seeded region growing algorithm
Pattern Recognition Letters
Auto-dual connected operators based on iterative merging algorithms
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Connected morphological operators for binary images
Computer Vision and Image Understanding
Mathematical morphology on complete semilattices and its applications to image processing
Fundamenta Informaticae - Special issue on mathematical morphology
Inf-Semilattice Approach to Self-Dual Morphology
Journal of Mathematical Imaging and Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Comparison of Algorithms for Connected Set Openings and Closings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Advances in the Analysis of Topographic Features on Discrete Images
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Annular filters for binary images
IEEE Transactions on Image Processing
Morphological Image Compositing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Iterative area filtering of multichannel images
Image and Vision Computing
On lexicographical ordering in multivariate mathematical morphology
Pattern Recognition Letters
Geodesy on label images, and applications to video sequence processing
Journal of Visual Communication and Image Representation
Constrained Connectivity and Transition Regions
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Advances in constrained connectivity
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Adjacency stable connected operators and set levelings
Image and Vision Computing
Morphological refinement of an image segmentation
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
Conditional Toggle Mappings: Principles and Applications
Journal of Mathematical Imaging and Vision
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Most morphological operators occur by pair of dual operators as highlighted by the erosion/dilation and opening/closing pairs. In practice, one decides to apply an operator or its dual depending on whether the targeted image structures are darker or brighter than their neighbourhood. Nevertheless, the same type of image structures may appear brighter than their neighbourhood in a region of the image definition domain but brighter in another. In this situation, self-dual rather than dual operators should be used. However, self-dual operators still assume that image structures roughly correspond to image extrema. Therefore, this model does not apply to complex images representing a partition of the space into image objects of arbitrary intensity values such as satellite images displaying landscapes with fields of various crop types. In this paper, we revisit the notion of self-duality, propose two new self-dual morphological filters, and show that it is possible to go beyond self-duality either by considering self-complementary operators or by substituting the image extrema paradigm with the more general concept of flat zones.