A note on the gradient of a multi-image
Computer Vision, Graphics, and Image Processing - Lectures notes in computer science, Vol. 201 (G. Goos and J. Hartmanis, Eds.)
Morphological operators for image sequences
Computer Vision and Image Understanding
Clifford algebras with numeric and symbolic computations
Clifford algebras with numeric and symbolic computations
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
Spatial—color Clifford algebras for invariant image recognition
Geometric computing with Clifford algebras
Digital Video and HDTV Algorithms and Interfaces
Digital Video and HDTV Algorithms and Interfaces
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Modelling and segmentation of colour images in polar representations
Image and Vision Computing
Quaternion involutions and anti-involutions
Computers & Mathematics with Applications
Computer Vision and Image Understanding
Spatial and spectral quaternionic approaches for colour images
Computer Vision and Image Understanding
Quaternion color texture segmentation
Computer Vision and Image Understanding
A comparative study on multivariate mathematical morphology
Pattern Recognition
A general framework for low level vision
IEEE Transactions on Image Processing
Color image processing by using binary quaternion-moment-preserving thresholding technique
IEEE Transactions on Image Processing
Hypercomplex Fourier Transforms of Color Images
IEEE Transactions on Image Processing
Morphological grayscale reconstruction in image analysis: applications and efficient algorithms
IEEE Transactions on Image Processing
Body color sets: A compact and reliable representation of images
Journal of Visual Communication and Image Representation
Hypercomplex Mathematical Morphology
Journal of Mathematical Imaging and Vision
Component-Trees and Multivalued Images: Structural Properties
Journal of Mathematical Imaging and Vision
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The definition of morphological operators for colour images requires a total ordering for colour points. A colour can be represented by different algebraic structures, in this paper we focus on real quaternions. The paper presents two main contributions. On the one hand, we have studied different alternatives to introduce the scalar part to obtain full colour quaternions. On the other hand, several total lexicographic orderings for quaternions have been defined, according to the various quaternion decompositions. The properties of these quaternionic orderings have been characterised to enable the identification of the most useful ones to define colour morphological operators. The theoretical results are illustrated with examples of processed images which show the usefulness of the proposed operators for real life complex problems.