Hierarchy construction schemes within the Scale set framework

Segmentation algorithms based on an energy minimisation framework often depend on a scale parameter which balances a fit to data and a regularising term. Irregular pyramids are defined as a stack of graphs successively reduced. Within this framework, the scale is often defined implicitly as the height in the pyramid. However, each level of an irregular pyramid can not usually be readily associated to the global optimum of an energy or a global criterion on the base level graph. This last drawback is addressed by the scale set framework designed by Guigues. The methods designed by this author allow to build a hierarchy and to design cuts within this hierarchy which globally minimise an energy. This paper studies the influence of the construction scheme of the initial hierarchy on the resulting optimal cuts. We propose one sequential and one parallel method with two variations within both. Our sequential methods provide partitions near the global optima while parallel methods require less execution times than the sequential method of Guigues even on sequential machines

Towards A regional resources strategy consultation

Report produced for emda to inform the agency's input into regional Waste and Resources Strategies. Reviews policy context, available data and views from key stakeholders

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

An enhanced classification of artificial ground

This report describes a detailed scheme for the mapping and recording of artificial ground. It presents codes and descriptions that underpin the entries in the British Geological Survey stratigraphical lexico

Structure-Aware Sampling: Flexible and Accurate Summarization

In processing large quantities of data, a fundamental problem is to obtain a summary which supports approximate query answering. Random sampling yields flexible summaries which naturally support subset-sum queries with unbiased estimators and well-understood confidence bounds. Classic sample-based summaries, however, are designed for arbitrary subset queries and are oblivious to the structure in the set of keys. The particular structure, such as hierarchy, order, or product space (multi-dimensional), makes range queries much more relevant for most analysis of the data. Dedicated summarization algorithms for range-sum queries have also been extensively studied. They can outperform existing sampling schemes in terms of accuracy on range queries per summary size. Their accuracy, however, rapidly degrades when, as is often the case, the query spans multiple ranges. They are also less flexible - being targeted for range sum queries alone - and are often quite costly to build and use. In this paper we propose and evaluate variance optimal sampling schemes that are structure-aware. These summaries improve over the accuracy of existing structure-oblivious sampling schemes on range queries while retaining the benefits of sample-based summaries: flexible summaries, with high accuracy on both range queries and arbitrary subset queries

Lagrangian theory of structure formation in relativistic cosmology III: gravitoelectric perturbation and solution schemes at any order

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the first-order trace solutions that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given together with extensions and applications for accessing the nonperturbative regime. We furnish here construction rules to obtain from Newtonian solutions the gravitoelectric class of relativistic solutions, for which we give the complete perturbation and solution schemes at any order of the perturbations. By construction, these schemes generalize the complete hierarchy of solutions of the Newtonian Lagrangian perturbation theory.Comment: 17 pages, a few minor extensions to match the published version in PR

A data cube model for analysis of high volumes of ambient data

Ambient systems generate large volumes of data for many of their application areas with XML often the format for data exchange. As a result, large scale ambient systems such as smart cities require some form of optimization before different components can merge their data streams. In data warehousing, the cube structure is often used for optimizing the analytics process with more recent structures such as dwarf, providing new orders of magnitude in terms of optimizing data extraction. However, these systems were developed for relational data and as a result, we now present the development of an XML dwarf to manage ambient systems generating XML data