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Computer Vision, Graphics, and Image Processing - Lectures notes in computer science, Vol. 201 (G. Goos and J. Hartmanis, Eds.)
A nonlinear laplace operator as edge detector in noisy images
Computer Vision, Graphics, and Image Processing
The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
The algebraic basis of mathematical morphology
CVGIP: Image Understanding
On the construction of morphological operators which are self-dual and activity-extensive
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Journal of Mathematical Imaging and Vision
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
Spatial—color Clifford algebras for invariant image recognition
Geometric computing with Clifford algebras
Grey-Scale Morphology Based on Fuzzy Logic
Journal of Mathematical Imaging and Vision
Inf-Semilattice Approach to Self-Dual Morphology
Journal of Mathematical Imaging and Vision
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
The Viscous Watershed Transform
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Signal modeling for two-dimensional image structures
Journal of Visual Communication and Image Representation
Spatial and spectral quaternionic approaches for colour images
Computer Vision and Image Understanding
Quaternion color texture segmentation
Computer Vision and Image Understanding
Size-density spectra and their application to image classification
Pattern Recognition
A Metric Approach to nD Images Edge Detection with Clifford Algebras
Journal of Mathematical Imaging and Vision
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Journal of Visual Communication and Image Representation
IEEE Transactions on Signal Processing
Hypercomplex signals-a novel extension of the analytic signal tothe multidimensional case
IEEE Transactions on Signal Processing
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
IEEE Transactions on Image Processing
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The natural ordering of grey levels is used in classical mathematical morphology for scalar images to define the erosion/dilation and the evolved operators. Various operators can be sequentially applied to the resulting images always using the same ordering. In this paper we propose to consider the result of a prior transformation to define the imaginary part of a complex image, where the real part is the initial image. Then, total orderings between complex numbers allow defining subsequent morphological operations between complex pixels. More precisely, the total orderings are lexicographic cascades with the local modulus and phase values of these complex images. In this case, the operators take into account simultaneously the information of the initial image and the processed image. In addition, the approach can be generalized to the hypercomplex representation (i.e., real quaternion) by associating to each image three different operations, for instance directional filters. Total orderings initially introduced for colour quaternions are used to define the evolved morphological transformations. Effects of these new operators are illustrated with different examples of filtering.