Raising in watershed lattices

International audienc

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 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

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

The effect of spatial and temporal planning scale on the trade-off between the financial value and carbon storage in production forests

Background: Increasing carbon stock in standing forests is one of the proposed ways to mitigate climate change. However, in production forests, this typically would lead to reduced harvesting possibilities and thus reduced financial gain for the forest owners. The size of this reduction should depend on the chosen target level of the carbon stock as well as the required speed of accumulation. Furthermore, due to landscape heterogeneity, the size of the loss can be expected to vary the planning scale, often related to forest property size.Aim: This study aimed to quantify the effects of spatial and temporal planning scales on the severity of the tradeoff between Net Present Value (NPV) of future timber sales and carbon storage in production forests in Southern Sweden.Methods: We used the Heureka PlanWise forest decision support system with built-in Linear Programming functionality. We created six Production Possibility Frontiers (PPF) that quantified the trade-off for the combinations of two scenarios for timing of carbon accumulation (either by 2100 or by 2100 with an intermediate target by 2045) and three spatial management scales (-3300 ha, -300 ha, and -60 ha; 1068 stands).Results: There was a strong effect of temporal scale, with consistently lower NPV, with the same carbon stock in 2100, when the intermediate target for 2045 was applied. The effect of the spatial scale was only apparent between the smallest (50 ha) scale and the larger scales (300 and 3300 ha), with consistently lower NPV with the same carbon stock at the smallest scale.Conclusion: We conclude that both the effects of spatial management scale and temporal scale on the cost of carbon storage should be considered in relation to potential climate policies

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

Interpreting wind damage risk-how multifunctional forest management impacts standing timber at risk of wind felling

Landscape multifunctionality, a widely accepted challenge for boreal forests, aims to simultaneously provide timber, non-timber ecosystem services, and shelter for biodiversity. However, multifunctionality requires the use of novel forest management regimes optimally combined over the landscape, and an increased share of sets asides. It remains unclear how this combination will shape stand vulnerability to wind disturbances and exposed timber volume. We combined forest growth simulations and multi-objective optimization to create alternative landscape level forest management scenarios. Management choices were restricted to 1) rotation forestry, 2) continuous cover forestry, and 3) all regimes allowed over a harvest intensity gradient from completely set aside landscapes to maximal economic gain. Estimates for the stands' structural and environmental characteristics were used to predict the stand level wind damage probability. We evaluated averaged wind-exposed standing timber volume and changing forest structure under management scenarios. Intensive rotation forestry reduced tree heights and wind damage risk, but also reduced landscape multifunctionality. Conversely, continuous cover forestry maintained multifunctionality but increased wind damage probability due to taller trees and higher thinning frequency. Overall, continuous cover forestry lowers the total volume of wind exposed timber at any given time compared with rotation forestry. Nevertheless, a selective application of rotation forestry contributes to high economic gains and increases landscape heterogeneity. A combination of management approaches across landscapes provides an efficient way to reduce the amount of wind-exposed timber volume while also increasing habitat for vertebrate and non-vertebrate species and satisfying high timber demands

Sharing Public Land Decision Making: The Quincy Library Group Experience [includes first three items from Appendix A]

25 pages (includes illustrations). Contains 1 reference. Includes first three items from Appendix A

Weighted fusion graphs: merging properties and watersheds

International audienc