相关论文: On the equivalence between hierarchical segmentati…

We present an algebraic approach to the watershed adapted to edge or node weighted graphs. Starting with the flooding adjunction, we introduce the flooding graphs, for which node and edge weights may be deduced one from the other. Each node…

Watersheds have been defined both for node and edge weighted graphs. We show that they are identical: for each edge (resp.\ node) weighted graph exists a node (resp. edge) weighted graph with the same minima and catchment basin.

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we…

Image segmentation is the process of partitioning an image into meaningful segments. The meaning of the segments is subjective due to the definition of homogeneity is varied based on the users perspective hence the automation of the…

An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or…

We present a method for hierarchical image segmentation that defines a disaffinity graph on the image, over-segments it into watershed basins, defines a new graph on the basins, and then merges basins with a modified, size-dependent version…

Ultametrics are an important class of distances used in applications such as phylogenetics, clustering and classification theory. Ultrametrics are essentially distances that can be represented by an edge-weighted rooted tree so that all of…

A novel method to obtain hierarchical and overlapping clusters from network data -i.e., a set of nodes endowed with pairwise dissimilarities- is presented. The introduced method is hierarchical in the sense that it outputs a nested…

The watershed is one of the most used tools in image segmentation. We present how its concept is born and developed over time. Its implementation as an algorithm or a hardwired device evolved together with the technology which allowed it.…

The watershed is a powerful tool for segmenting objects whose contours appear as crest lines on a gradient image. The watershed transform associates to a topographic surface a partition into catchment basins, defined as attraction zones of…

An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a natural hierarchical embedding. Such hierarchical structure can be global in the data…

The present paper develops a general methodology for the morphological segmentation of hyperspectral images, i.e., with an important number of channels. This approach, based on watershed, is composed of a spectral classification to obtain…

Learned boundary maps are known to outperform hand- crafted ones as a basis for the watershed algorithm. We show, for the first time, how to train watershed computation jointly with boundary map prediction. The estimator for the merging…

Many image processing applications rely on partitioning an image into disjoint regions whose pixels are 'similar.' The watershed and waterfall transforms are established mathematical morphology pixel clustering techniques. They are both…

Hyperspectral image (HSI) classification is a topic of active research. One of the main challenges of HSI classification is the lack of reliable labelled samples. Various semi-supervised and unsupervised classification methods are proposed…

The segmentation, seen as the association of a partition with an image, is a difficult task. It can be decomposed in two steps: at first, a family of contours associated with a series of nested partitions (or hierarchy) is created and…

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…

An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…

Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…

We study the notion of hierarchy in the context of visualizing textual data and navigating text collections. A formal framework for ``hierarchy'' is given by an ultrametric topology. This provides us with a theoretical foundation for…