Watersheds, waterfalls, on edge or node weighted graphs

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 weighted or edge weighted graph may be transformed in a flooding graph, showing that there is no superiority in using one or the other, both being equivalent. We then introduce pruning operators extract subgraphs of increasing steepness. For an increasing steepness, the number of never ascending paths becomes smaller and smaller. This reduces the watershed zone, where catchment basins overlap. A last pruning operator called scissor associates to each node outside the regional minima one and only one edge. The catchment basins of this new graph do not overlap and form a watershed partition. Again, with an increasing steepness, the number of distinct watershed partitions contained in a graph becomes smaller and smaller. Ultimately, for natural image, an infinite steepness leads to a unique solution, as it is not likely that two absolutely identical non ascending paths of infinite steepness connect a node with two distinct minima. It happens that non ascending paths of a given steepness are the geodesics of lexicographic distance functions of a given depth. This permits to extract the watershed partitions as skeletons by zone of influence of the minima for such lexicographic distances. The waterfall hierarchy is obtained by a sequence of operations. The first constructs the minimum spanning forest which spans an initial watershed partition. The contraction of the trees into one node produces a reduced graph which may be submitted to the same treatment. The process is iterated until only one region remains. The union of the edges of all forests produced constitutes a minimum spanning tree of the initial graph

Watersheds on edge or node weighted graphs

The literature on the watershed is separated in two families: the watersheds on node weighted graphs and the watersheds on edge weighted graphs. The simplest node weighted graphs are images, where the nodes are the pixels ; neighboring pixels being linked by unweighted pixels. The edge weights on an edge weighted graph express dissimilarities between the unweighted nodes. Distinct definitions of minima and catchment basins have been given for both types of graphs from which different algorithms have been derived. This paper aims at showing that watersheds on edge or node weighted graphs are strictly equivalent. Moreover, all algorithms developed for edge weighted graphs may be applied on node weighted graphs and vice versa. From any node or edge weighted graph it is possible to derive a flooding graph with node and edge weights. Its regional minima and catchment basins are identical whether one considers the node weights alone or the edge weights alone. A lexicographic order relation permits to compare non ascending paths with the same origin according to their steepness. Overlapping zones between neighboring catchment basins are reduced or even suppressed by pruning edges in the flooding graph through which does not pass a steepest path and reduces, without arbitrary choices the overlapping zones between adjacent catchment basins. We propose several ways to break the remaining ties, the simplest being to assign slightly distinct weights to regional minima with the same weight. Like that each node is linked with only one regional minimum by a path of maximal steepness

Interactive Segmentation and Visualization of DTI Data Using a Hierarchical Watershed Representation

Magnetic resonance diffusion tensor imaging (DTI) measures diffusion of water molecules and is used to characterize orientation of white matter fibers and connectivity of neurological structures. Segmentation and visualization of DT images is challenging, because of low data quality and complexity of anatomical structures. In this paper, we propose an interactive segmentation approach, based on a hierarchical representation of the input DT image through a tree structure. The tree is obtained by successively merging watershed regions, based on the morphological waterfall approach, hence the name watershed tree. Region merging is done according to a combined similarity and homogeneity criterion. We introduce filters that work on the proposed tree representation, and that enable region-based attribute filtering of DTI data. Linked views between the visualizations of the simplified DT image and the tree enable a user to visually explore both data and tree at interactive rates. The coupling of filtering, semiautomatic segmentation by labeling nodes in the tree, and various interaction mechanisms support the segmentation task. Our method is robust against noise, which we demonstrate on synthetic and real DTI data

Riverscape genetics of Oncorhynchus tshawytscha (Chinook salmon) in Siletz River, OR

Traditional analysis in population genetics evaluates differences among groups of individuals and, in some cases, considers the effects of distance or potential barriers to gene flow. However, many forces may shape genetic variation of organisms in riverine systems. Similarly complex research linking habitat heterogeneity and configuration to genetic structure has integrated methods from landscape ecology, population genetics, and spatial statistics in approaches known as landscape or seascape genetics. However, challenges exist when translating these approaches into freshwater river networks due to functional differences in riverscape topography that create constrained pathways for movement. The overall goal of my dissertation was to combine the approaches applied in population genetics to identify genetic diversity within and among populations, with concepts derived from network theory to better understand how the riverscape influenced spatial genetic structure of Chinook salmon (Oncorhynchus tshawytscha) populations in Siletz River. I provide a perspective on how riverscape genetics could be used to provide a more comprehensive conceptual and applied understanding of connectivity and dispersal in freshwater systems. I describe four thematic areas of study representing current and future research opportunities and propose a basic methodology for conducting riverscape genetics analysis. I applied the proposed riverscape genetics method to attempt a novel analysis of spatial genetic structure of Chinook salmon within Siletz River, Oregon and compared results with interpretation of spatial genetic structure using traditional population genetics methods. Chinook salmon are a culturally important and economically valuable fish that express diverse life histories characterized by the season of their return migration to spawning habitat (called a “run”) and duration of freshwater or estuarine residence. Population structure among Chinook salmon of alternate run times observed in the Siletz River was investigated using 11 microsatellite markers, 96 Single Nucleotide Polymorphisms (SNPs), and three candidate gene markers that are linked to spawn time and body size. Results from all marker types identified two genetically distinct populations in the watershed (microsatellites; FST = 0.02, p < 0.05) that included a previously unrecognized spring run. This finding is an important consideration for management of the species, as spring run populations have not been recognized in smaller watersheds. Using riverscape genetics methods I characterized the spatial relationships among fall run Chinook salmon. Analysis assessed the effect of indicators of hydrology on dispersal and identified patterns of genetic variation were associated with site-specific differences in elevation of spawning habitat (MRDM; R2 = 0.11 p < 0.05). Further investigation using path-based methodology identified that the cumulative changes in gradient among stream reaches also significantly affected spatial genetic structure (MRDM; R2 = 0.14 p < 0.01). The combination of approaches that were used to investigate spatial genetic variation highlighted the utility of riverscape genetics to enhance our understanding of the relationships that contributed to observed population structure. Although fall run Chinook salmon within Siletz River exhibited high gene flow and were considered a single spawning population using traditional population genetic methods, there was evidence of differential habitat use within the group that was driven by the location of spawning habitat and the resistance to dispersal caused by habitat between these locations. Chinook salmon that traveled over steeper gradients to reach spawning habitat at higher elevations were different than individuals that traveled over shallower gradients to reach spawning habitat at lower elevations. The riverscape genetics approach applied in this chapter enhanced our understanding of habitat heterogeneity in shaping gene flow and spatial genetic structure at a fine spatial scale. Expanding quantitative genetic research, in river systems to explicitly consider riverscape scale network configurations would help develop a clear understanding of the importance of these factors in terms of population persistence.Keywords: spatial genetic variation, population genetics, Single Nucleotide Polymorphism, connectivity, gene flow, Siletz River, GIS, Chinook salmon, effective distance, microsatellite, SNPs, selection, riverscape genetics, adaptive genetic variation, riverscape, dispersal, population structur

Feature-rich distance-based terrain synthesis

This thesis describes a novel terrain synthesis method based on distances in a weighted graph. The method begins with a regular lattice with arbitrary edge weights; heights are determined by path cost from a set of generator nodes. The shapes of individual terrain features, such as mountains, hills, and craters, are specified by a monotonically decreasing profile describing the cross-sectional shape of a feature, while the locations of features in the terrain are specified by placing the generators. Pathing places ridges whose initial location have a dendritic shape. The method is robust and easy to control, making it possible to create pareidolia effects. It can produce a wide range of realistic synthetic terrains such as mountain ranges, craters, faults, cinder cones, and hills. The algorithm incorporates random graph edge weights, permits the inclusion of multiple topography profiles, and allows precise control over placement of terrain features and their heights. These properties all allow the artist to create highly heterogeneous terrains that compare quite favorably to existing methods

Improving connectivity for river fish

Doutoramento em Engenharia Florestal e dos Recursos Naturais - Instituto Superior de Agronomi

LIPIcs, Volume 277, GIScience 2023, Complete Volume

LIPIcs, Volume 277, GIScience 2023, Complete Volum

Forest landscapes and global change. New frontiers in management, conservation and restoration. Proceedings of the IUFRO Landscape Ecology Working Group International Conference

This volume contains the contributions of numerous participants at the IUFRO Landscape Ecology Working Group International Conference, which took place in Bragança, Portugal, from 21 to 24 of September 2010. The conference was dedicated to the theme Forest Landscapes and Global Change - New Frontiers in Management, Conservation and Restoration. The 128 papers included in this book follow the structure and topics of the conference. Sections 1 to 8 include papers relative to presentations in 18 thematic oral and two poster sessions. Section 9 is devoted to a wide-range of landscape ecology fields covered in the 12 symposia of the conference. The Proceedings of the IUFRO Landscape Ecology Working Group International Conference register the growth of scientific interest in forest landscape patterns and processes, and the recognition of the role of landscape ecology in the advancement of science and management, particularly within the context of emerging physical, social and political drivers of change, which influence forest systems and the services they provide. We believe that these papers, together with the presentations and debate which took place during the IUFRO Landscape Ecology Working Group International Conference – Bragança 2010, will definitively contribute to the advancement of landscape ecology and science in general. For their additional effort and commitment, we thank all the participants in the conference for leaving this record of their work, thoughts and science