Why mathematical morphology needs complete lattices
Signal Processing
Morphological operators for image sequences
Computer Vision and Image Understanding
Complete ordering and multivariate mathematical morphology
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Outex - New Framework for Empirical Evaluation of Texture Analysis Algorithms
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 1 - Volume 1
Levelings, Image Simplification Filters for Segmentation
Journal of Mathematical Imaging and Vision
Morphological operators on complex signals
Signal Processing
A comparative study on multivariate mathematical morphology
Pattern Recognition
Beyond self-duality in morphological image analysis
Image and Vision Computing
Spatial morphological covariance applied to texture classification
MRCS'06 Proceedings of the 2006 international conference on Multimedia Content Representation, Classification and Security
Morphological operators on the unit circle
IEEE Transactions on Image Processing
A class of sparsely connected autoassociative morphological memories for large color images
IEEE Transactions on Neural Networks
Morphological description of color images for content-based image retrieval
IEEE Transactions on Image Processing
Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology
Information Sciences: an International Journal
Mathematical morphology on bipolar fuzzy sets: general algebraic framework
International Journal of Approximate Reasoning
Component-Trees and Multivalued Images: Structural Properties
Journal of Mathematical Imaging and Vision
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Since mathematical morphology is based on complete lattice theory, a vector ordering method becomes indispensable for its extension to multivariate images. Among the several approaches developed with this purpose, lexicographical orderings are by far the most frequent, as they possess certain desirable theoretical properties. However, their main drawback consists of the excessive priority attributed to the first vector dimension. In this paper, the existing solutions to solving this problem are recalled and two new approaches are presented. First, a generalisation of @a-modulus lexicographical ordering is introduced, making it possible to accommodate any quantisation function. Additionally, an input specific method is suggested, based on the use of a marker image. Comparative application results on colour noise reduction and texture classification are also provided.