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
Total ordering based on space filling curves for multivalued morphology
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Modelling and segmentation of colour images in polar representations
Image and Vision Computing
A comparative study on multivariate mathematical morphology
Pattern Recognition
Constrained Connectivity for Hierarchical Image Decomposition and Simplification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological operators on the unit circle
IEEE Transactions on Image Processing
Hypercomplex Fourier Transforms of Color Images
IEEE Transactions on Image Processing
Mathematical morphology for vector images using statistical depth
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
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The emergence of new data in multidimensional function lattices is studied. A typical example is the apparition of false colours when (R,G,B) images are processed. Two lattice models are specially analysed. Firstly, one considers a mixture of total and marginal orderings where the variations of some components are governed by other ones. This constraint yields the "pilot lattices". The second model is a cylindrical polar representation in n dimensions. In this model, data that are distributed on the unit sphere of n *** 1 dimensions need to be ordered. The proposed orders, and lattices are specific to each image. They are obtained from Voronoi tesselation of the unit sphere The case of four dimensions is treated in detail and illustrated.