Geodesic Saliency of Watershed Contours and Hierarchical Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Modelling and segmentation of colour images in polar representations
Image and Vision Computing
A comparative study on multivariate mathematical morphology
Pattern Recognition
Morphological operators on the unit circle
IEEE Transactions on Image Processing
Hypercomplex Fourier Transforms of Color Images
IEEE Transactions on Image Processing
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The aim of the study is to structure multivariate data in cylindrical polar representation, in order to segment them by composing the Rn luminance and hue partitions accouding to that of the saturation. Remote sensing applications are in mind. This goal requires to equip with a total ordering the unit sphere in Rn, where the hue is ddistributed. The proposed orders, and the subsequent lattices, do not depend on absolute coordinates, but are adapted either to the whole image under study, or to the neighbouhoods necessary for processing the image. They are obtained by choosing a few maxima on the distribution of the spherical coordinates of the image. and by taking as new variables the infima of the distances to these various maxima. The case of four dimensions, usual when dealing with the principal components in remote sensing, is treated in detail. A comparison of the results in various dimentions is performed on a multispectral aerial image of the university of Pavia.