Parameters Selection Of Morphological Scale-Space Decomposition For Hyperspectral Images Using Tensor Modeling

International audienceDimensionality reduction (DR) using tensor structures in morphological scale-space decomposition (MSSD) for HSI has been investigated in order to incorporate spatial information in DR.We present results of a comprehensive investigation of two issues underlying DR in MSSD. Firstly, information contained in MSSD is reduced using HOSVD but its nonconvex formulation implicates that in some cases a large number of local solutions can be found. For all experiments, HOSVD always reach an unique global solution in the parameter region suitable to practical applications. Secondly, scale parameters in MSSD are presented in relation to connected components size and the influence of scale parameters in DR and subsequent classification is studied

Vector ordering and multispectral morphological image processing

International audienceThis chapter illustrates the suitability of recent multivariate ordering approaches to morphological analysis of colour and multispectral images working on their vector representation. On the one hand, supervised ordering renders machine learning no-tions and image processing techniques, through a learning stage to provide a total ordering in the colour/multispectral vector space. On the other hand, anomaly-based ordering, automatically detects spectral diversity over a majority background, al-lowing an adaptive processing of salient parts of a colour/multispectral image. These two multivariate ordering paradigms allow the definition of morphological operators for multivariate images, from algebraic dilation and erosion to more advanced techniques as morphological simplification, decomposition and segmentation. A number of applications are reviewed and implementation issues are discussed in detail

Connected operators based on region-tree pruning strategies

This paper discusses region-based representations useful to create connected operators. The filtering approach involves three steps: 1) a region tree representation of the input image is constructed; 2) the simplification is obtained by pruning the tree; and 3) and output image is constructed from the pruned tree. The paper focuses in particular on the pruning strategies that can be used depending of the increasing of the simplification criteria.Peer ReviewedPostprint (published version

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Generalized Morphology using Sponges

Mathematical morphology has traditionally been grounded in lattice theory. For non-scalar data lattices often prove too restrictive, however. In this paper we present a more general alternative, sponges, that still allows useful definitions of various properties and concepts from morphological theory. It turns out that some of the existing work on “pseudo-morphology” for non-scalar data can in fact be considered “proper” mathematical morphology in this new framework, while other work cannot, and that this correlates with how useful/intuitive some of the resulting operators are

A study of observation scales based on Felzenswalb-Huttenlocher dissimilarity measure for hierarchical segmentation

International audienceHierarchical image segmentation provides a region-oriented scale-space, i.e., a set of image segmentations at different detail levels in which the segmentations at finer levels are nested with respect to those at coarser levels. Guimarães et al. proposed a hierarchical graph based image segmentation (HGB) method based on the Felzenszwalb-Huttenlocher dissimilarity. This HGB method computes, for each edge of a graph, the minimum scale in a hierarchy at which two regions linked by this edge should merge according to the dissimilarity. In order to generalize this method, we first propose an algorithm to compute the intervals which contain all the observation scales at which the associated regions should merge. Then, following the current trend in mathematical morphology to study criteria which are not increasing on a hierarchy, we present various strategies to select a significant observation scale in these intervals. We use the BSDS dataset to assess our observation scale selection methods. The experiments show that some of these strategies lead to better segmentation results than the ones obtained with the original HGB method

Representations for Morphological Image Operators and Analogies with Linear Operators

1.1 Why a representation theory?...............................