Multi-scale dual morse complexes for representing terrain morphology

Danovaro, Emanuele; Floriani, Leila De; Vitali, Maria; Magillo, Paola

doi:10.1145/1341012.1341050

Cited by 9 publications

(7 citation statements)

References 23 publications

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“…The size of a morphological representation can be large for common models, which may consist of several millions of triangles. To deal with problem, we have been focusing on a multiresolution representation of the terrain morphology (see [13]), that allows concentrating on the areas of interest and producing approximate representations of the morphology at uniform and variable resolution. In our current work, we are developing a multiresolution model that combines the geometrical and morphological representations, where the morphological representation as an index on the geometrical model [14].…”

Section: Discussionmentioning

confidence: 99%

Computing Morse Decompositions for Triangulated Terrains: An Analysis and an Experimental Evaluation

Vitali

Floriani

Magillo

2011

Image Analysis and Processing – ICIAP 2011

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Abstract. We consider the problem of extracting the morphology of a terrain discretized as a triangle mesh. We discuss first how to transpose Morse theory to the discrete case in order to describe the morphology of triangulated terrains. We review algorithms for computing Morse decompositions, that we have adapted and implemented for triangulated terrains. We compare the the Morse decompositions produced by them, by considering two different metrics.

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Section: Discussionmentioning

confidence: 99%

Computing Morse Decompositions for Triangulated Terrains: An Analysis and an Experimental Evaluation

Vitali

Floriani

Magillo

2011

Image Analysis and Processing – ICIAP 2011

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“…Morse theory was expanded considerably for mapping and modeling applications (Robins, Wood, and Sheppard 2011;Bremer et al 2003;Čomić, De Floriani, and Papaleo 2005), multiscale terrain modeling began (Wood 1996;Danovaro et al 2003;Danovaro, De Floriani, and Vitali 2007;Schmidt and Andrew 2005), and grid-based surface patch methods emerged to compete with the TIN (Schneider 2005). Danovaro, De Floriani, and Vitali (2007) combined Morse methods and the multiscale approach, while Florinsky (2009) moved beyond the second to the third terrain derivatives. Rana (2004Rana ( , 2010 provided comprehensive reviews of methods and issues in topological surface networks, while others considered the uncertainties in the data and processing (Lindsay 2006;Pathmanabhan and Dinesh 2007;O'Neil and Shortridge 2013).…”

Section: Algorithmsmentioning

confidence: 99%

Exploring uncertainties in terrain feature extraction across multi-scale, multi-feature, and multi-method approaches for variable terrain

Romero

Clarke

2017

Cartography and Geographic Information Science

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In the field of terrain analysis, a primary goal is to effectively identify topographic features for a better understanding of their associated processes. The relationships among features are, therefore, of particular importance. The concept of the surface network, involving and defined by such features as peaks, pits, various saddles, ridge lines, and the opposite course lines, can be a beneficial construct for describing and modeling any mathematical surface and, perhaps, topographic surfaces, as well. However, limitations of terrain data collection, storage, and computational processing have presented difficulties when attempting to make the jump from such logical constructs and their supporting mathematical theories to the development of tools and mapped products representing the measured topography of a landscape. Compared to feature extraction, less attention has been given to the topological relationships among topographic features. This article provides a chronological review of the development of surface network and critical point theory, the study of topography, and the progression of terrain analysis with particular consideration given to the application of surface network theory to represent the topology of topography. Any possible true computed surface network is concluded to be scaledependent, fuzzy, and vague and its undisputed calculation elusive.

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“…Various visualization and image processing studies have been seeking to define Morse theory and watershed segmentation algorithms that work directly via the Delaunay tessellation of the discrete dataset [60], [59], [73], [74], [75], [64].…”

Section: E Tessellation Spinesmentioning

confidence: 99%

Geometry and Morphology of the Cosmic Web: Analyzing Spatial Patterns in the Universe

Weygaert

Jones

Platen

et al. 2009

2009 Sixth International Symposium on Voronoi Diagrams

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We review the analysis of the Cosmic Web by means of an extensive toolset based on the use of Delaunay and Voronoi tessellations. The Cosmic Web is the salient and pervasive foamlike pattern in which matter has organized itself on scales of a few up to more than a hundred Megaparsec. The weblike spatial arrangement of galaxies and mass into elongated filaments, sheetlike walls and dense compact clusters, the existence of large near-empty void regions and the hierarchical nature of this mass distribution are three major characteristics of the comsic matter distribution.First, we describe the Delaunay Tessellation Field Estimator.Using the unique adaptive qualities of Voronoi and Delaunay tessellations, DTFE infers the density field from the (contiguous) Voronoi tessellation of a sampled galaxy or simulation particle distribution and uses the Delaunay tessellation as adaptive grid for defining continuous volumefilling fields of density and other measured quantities through linear interpolation. The resulting DTFE formalism is shown to recover the hierarchical nature and the anisotropic morphology of the cosmic matter distribution. The Multiscale Morphology Filter (MMF) uses the DTFE density field to extract the diverse morphological elements -filaments, sheets and clusters -on the basis of a ScaleSpace analysis which searches for these morphologies over a range of scales. Subsequently, we discuss the Watershed Voidfinder (WVF), which invokes the discrete watershed transform to identify voids in the cosmic matter distribution. The WVF is able to determine the location, size and shape of the voids. The watershed transform is also a key element in the SpineWeb analysis of the cosmic matter distribution. Finding its mathematical foundation in Morse theory, it allows the determination of the filamentary spine and connected walls in the cosmic matter density field through the identification of the singularities and corresponding separatrices. The first results of a direct implementation on the Delaunay tessellation itself are presented. Finally, we describe the concept of Alphashapes for assessing the topology of the cosmic matter distribution.

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Multi-scale dual morse complexes for representing terrain morphology

Cited by 9 publications

References 23 publications

Computing Morse Decompositions for Triangulated Terrains: An Analysis and an Experimental Evaluation

Computing Morse Decompositions for Triangulated Terrains: An Analysis and an Experimental Evaluation

Exploring uncertainties in terrain feature extraction across multi-scale, multi-feature, and multi-method approaches for variable terrain

Geometry and Morphology of the Cosmic Web: Analyzing Spatial Patterns in the Universe

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