On morphological hierarchical representations for image processing and spatial data clustering

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 briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

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

On the equivalence between hierarchical segmentations and ultrametric watersheds

We study hierarchical segmentation in the framework of edge-weighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical segmentations. We end this paper by showing how to use the proposed framework in practice in the example of constrained connectivity; in particular it allows to compute such a hierarchy following a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.Comment: 19 pages, double-colum

An Efficient Image Segmentation Approach through Enhanced Watershed Algorithm

Image segmentation is a significant task for image analysis which is at the middle layer of image engineering. The purpose of segmentation is to decompose the image into parts that are meaningful with respect to a particular application. The proposed system is to boost the morphological watershed method for degraded images. Proposed algorithm is based on merging morphological watershed result with enhanced edge detection result obtain on pre processing of degraded images. As a post processing step, to each of the segmented regions obtained, color histogram algorithm is applied, enhancing the overall performance of the watershed algorithm. Keywords – Segmentation, watershed, color histogra

The Spine of the Cosmic Web

We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes the local adjacency properties of the boundaries between the watershed basins to trace the critical points in the density field and the separatrices defined by them. The separatrices are classified into walls and the spine, the network of filaments and nodes in the matter distribution. Testing the method with a heuristic Voronoi model yields outstanding results. Following the discussion of the test results, we apply the SpineWeb method to a set of cosmological N-body simulations. The latter illustrates the potential for studying the structure and dynamics of the Cosmic Web.Comment: Accepted for publication HIGH-RES version: http://skysrv.pha.jhu.edu/~miguel/SpineWeb

A GIS- and field-based investigation of main channel morphological sensitivity to tributary inputs at the watershed scale in Québec

Confluences are key nodes of river networks, as a result of the dynamic mixing of water, sediment, wood or ice between tributaries and receiving channels. Geomorphically active tributaries have the potential to disrupt the balance of erosional and depositional processes along main river channels, thereby resetting downstream longitudinal patterns. In turn, main channels respond to or absorb these changes as a function of their spatial and temporal sensitivity, which varies with topography, energy conditions and the system’s capacity to recover following major past events. Consequently, confluence zones are areas of increased spatial heterogeneity, with important implications for the resilience of river ecosystems and their management. However, due to their complexity, tributary-main channel interactions represent a relatively understudied component in fluvial geomorphology. The objectives of this study are to 1) improve our understanding of the morphodynamics of active confluences characterized by high sediment load tributaries based on field observations in Gaspésie, Québec and 2) propose a novel semi-automated GIS model that uses a fuzzy approach to integrate multiple key factors (unit stream power, valley confinement and sediment connectivity potential) to assess main channel confluence morphological sensitivity (CMS) to active tributaries at the scale of whole watersheds. The model was tested using digital elevation models (DEM) in Coaticook and Gaspésie watersheds, Québec. Results of the field survey showed that despite all confluences being located in a generally homogeneous geological setting, considerable disparities in the morphological effect of tributaries exist. The fuzzy GIS model was able to identify sensitive locations along the main channel associated to geomorphically active tributaries and has thus the potential to be used as part of watershed geomorphic assessments, particularly when high-resolution (LiDAR) DEMs are available. These findings highlight the spatially contingent distribution of resisting and impelling forces along main channels, including tributary-main channel interactions, in influencing river behaviour