Paola Magillo

Professore Associato

Indirizzo Via Dodecaneso, 35 - 16146 Genova
Ufficio Valletta Puggia - 305
E-mail
Telefono ufficio (+39) 010353 - 6705
Fax (+39) 010353 - 6699
Pagina personale https://person.dibris.unige.it/magillo-paola/

CV

Paola Magillo ha conseguito la Laurea in Scienze dell'Informazione nel 1992 e il Dottorato di ricerca in Informatica nel 1999, entrambi all'Universita' degli Studi di Genova.
Presso la stessa Universita' e' diventata Ricercatore nel 1992 e Professore associato nel 2004.
E' attualmente affiliata al Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi - DIBRIS (in passato al Dipartimento di Informatica e Scienze dell'Informazione - DISI) dell'Universita' degli Studi di Genova.
I suoi interessi di ricerca comprendono geometria computazionale, modellazione geometrica, sistemi informativi geografici, computer grafica,immagini.

Publications

Paola Magillo - Publications

See also: DBPL page

Years 2010 - today

  • Title: Repairing 3D binary images using the BCC grid with a 4-valued combinatorial coordinate system
    Authors: Comic, Lidija; Magillo, Paola
    Year: 2018
    Journal: Information Sciences
    Abstract: A 3D binary image I is called well-composed if the set of points in the topological boundary of the cubes in I is a 2-manifold. Repairing a 3D binary image is a process which produces a well composed image (or a polyhedral complex) from the non-well-composed image I.We propose here to repair 3D images by associating the Body-Centered Cubic grid (BCC grid) to the cubical grid. The obtained polyhedral complex is well composed, since two voxels in the BCC grid either share an entire face or are disjoint. We show that the obtained complex is homotopy equivalent to the cubical complex naturally associated with the image I.To efficiently encode and manipulate the BCC grid, we present an integer 4-valued combinatorial coordinate system that addresses cells of all dimensions (voxels, faces, edges and vertices), and allows capturing all the topological incidence and adjacency relations between cells by using only integer operations.We illustrate an application of this coordinate system on two tasks related with the repaired image: boundary reconstruction and computation of the Euler characteristic.
    Digital Object Identifier (DOI): 10.1016/j.ins.2018.02.049

  • Title: Computing a discrete Morse gradient from a watershed decomposition
    Authors: Comic, Lidija; De Floriani, Leila; Iuricich, Federico; Magillo, Paola
    Year: 2016
    Journal: COMPUTERS & GRAPHICS, Volume: 58, Pages: 43-52
    Abstract: We consider the problem of segmenting triangle meshes endowed with a discrete scalar function f based on the critical points of f. The watershed transform induces a decomposition of the domain of function f into regions of influence of its minima, called catchment basins. The discrete Morse gradient induced by f allows recovering not only catchment basins but also a complete topological characterization of the function and of the shape on which it is defined through a Morse decomposition. Unfortunately, discrete Morse theory and related algorithms assume that the input scalar function has no flat areas, whereas such areas are common in real data and are easily handled by watershed algorithms. We propose here a new approach for building a discrete Morse gradient on a triangulated 3D shape endowed by a scalar function starting from the decomposition of the shape induced by the watershed transform. This allows for treating flat areas without adding noise to the data. Experimental results show that our approach has significant advantages over existing ones, which eliminate noise through perturbation: it is faster and always precise in extracting the correct number of critical elements.
    Digital Object Identifier (DOI): 10.1016/j.cag.2016.05.020

  • Title: Morse complexes for shape segmentation and homological analysis: discrete models and algorithms
    Authors: De Floriani, Leila; Fugacci, Ulderico; Iuricich, Federico; Magillo, Paola
    Year: 2015
    Journal: COMPUTER GRAPHICS FORUM, Volume: 34(2), Pages: 761-785
    Abstract: Morse theory offers a natural and mathematically-sound tool for shape analysis and understanding. It allows studying the behavior of a scalar function defined on a manifold. Starting from a Morse function, we can decompose the domain of the function into meaningful regions associated with the critical points of the function. Such decompositions, called Morse complexes, provide a segmentation of a shape and are extensively used in terrain modeling and in scientific visualization. Discrete Morse theory, a combinatorial counterpart of smooth Morse theory defined over cell complexes, provides an excellent basis for computing Morse complexes in a robust and efficient way. Moreover, since a discrete Morse complex computed over a given complex has the same homology as the original one, but fewer cells, discrete Morse theory is a fundamental tool for efficiently detecting holes in shapes through homology and persistent homology. In this survey, we review, classify and analyze algorithms for computing and simplifying Morse complexes in the context of such applications with an emphasis on discrete Morse theory and on algorithms based on it.
    Digital Object Identifier (DOI): 10.1111/cgf.12596

  • Title: Morphological Modeling of Terrains and Volume Data
    Authors: L.Comic; L.De Floriani; P.Magillo; F.Iuricich
    Year: 2014
    Pages: 116
    Series: SpringerBriefs in Computer Science
    Digital Object Identifier (DOI): 10.1007/978-1-4939-2149-2

  • Title: Morphologically-aware elimination of flat edges from a TIN
    Authors: P.Magillo; L.De Floriani; F.Iuricich
    Year: 2013
    Conference: ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
    Place: Orlando, Florida, Dates: November 5-8, 2013
    Book title: Proceedings 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
    Pages: 244-253
    Abstract: We propose a new technique for eliminating flat edges from a Triangulated Irregular Network (TIN) in a morphologically consistent way. The algorithm is meant to be a preprocessing step for performing morphological computations on a terrain. Terrain morphology is rooted in Morse theory for smooth functions. Segmentation algorithms have been defined for TINs, mostly based on discrete versions of Morse theory, and under the assumption that the terrain model does not include flat edges. On the other hand, flat edges often occur in real data, and thus either they are eliminated through data perturbation, or the segmentation algorithms must be able to deal with them. In both cases, the resulting Morse segmentations are highly affected by the presence of flat edges. The new technique we propose provides a better solution, as it preserves the set of maxima and minima of the original terrain, and improves consistency among the terrain decompositions produced by different segmentation algorithms.
    Digital Object Identifier (DOI): 10.1145/2525314.2525341

  • Title: Discrete Morse versus watershed decompositions of tessellated manifolds
    Authors: L.De Floriani; F.Iuricich; P.Magillo; P.Simari
    Year: 2013
    Book title: Image Analysis and Processing (ICIAP 2013)
    Series: Lecture Notes in Computer Science
    Volume: 8157
    Pages: 339-348
    Abstract: With improvements in sensor technology and simulation methods, datasets are growing in size, calling for the investigation of efficient and scalable tools for their analysis. Topological methods, able to extract essential features from data, are a prime candidate for the development of such tools. Here, we examine an approach based on discrete Morse theory and compare it to the well-known watershed approach as a means of obtaining Morse decompositions of tessellated manifolds endowed with scalar fields, such as triangulated terrains or tetrahedralized volume data. We examine the theoretical aspects as well as present empirical results based on synthetic and real-world data describing terrains and 3D scalar fields. We will show that the approach based on discrete Morse theory generates segmentations comparable to the watershed approach while being theoretically sound, more efficient with regard to time and space complexity, easily parallelizable, and allowing for the computation of all descending and ascending i-manifolds and the topological structure of the two Morse complexes.
    Digital Object Identifier (DOI): 10.1007/978-3-642-41184-7_35

  • Title: Concentrated curvature for mean curvature estimation in triangulated surfaces
    Authors: M.M. Mesmoudi; L. De Floriani; P. Magillo
    Year: 2012
    Book title: Computational Topology in Image Context
    Pages: 79-87
    Series: Lecture Notes in Computer Science
    Volume: 7309
    Abstract: We present a mathematical result that allows computing the discrete mean curvature of a polygonal surface from the so-called concentrated curvature generally used for Gaussian curvature estimation. Our result adds important value to concentrated curvature as a geometric and metric tool to study accurately the morphology of a surface.
    Digital Object Identifier (DOI): 10.1007/978-3-642-30238-1_9

  • Title: Discrete Curvature Estimation Methods for Triangulated Surfaces
    Authors: Mohammed Mostefa Mesmoudi; Leila De Floriani; Paola Magillo
    Year: 2012
    Book title: Applications of Discrete Geometry and Mathematical Morphology
    Series: Lecture Notes in Computer Science
    Volume: 7346
    Pages: 28-42
    Abstract: We review some recent approaches to estimate discrete Gaussian and mean curvatures for triangulated surfaces, and discuss their characteristics. We focus our attention on concentrated curvature which is generally used to estimate Gaussian curvature. We present a result that shows that concentrated curvature can also be used to estimate mean curvature and hence principal curvatures. This makes concentrated curvature one of the fundamental notions in discrete computational geometry.
    Digital Object Identifier (DOI): 10.1007/978-3-642-32313-3_3

  • Title: Discrete Distortion for 3D Data Analysis
    Authors: L. De Floriani; F. Iuricich; P.Magillo; M. M.Mesmoudi; K. Weiss
    Year: 2012
    Book title: Visualization in Medicine and Life Sciences II
    Pages: 3-25
    Publisher: Springer, Berlin, Heidelberg
    Series: MATHEMATICS AND VISUALIZATION
    Abstract: We investigate a morphological approach to the analysis and understanding of three-dimensional scalar fields, and we consider applications to 3D medical and molecular images as examples.We consider a discrete model of the scalar field obtained by discretizing its 3D domain into a tetrahedral mesh. In particular, our meshes correspond to approximations at uniform or variable resolution extracted from a multi-resolution model of the 3D scalar field, that we call a hierarchy of diamonds. We analyze the images based on the concept of discrete distortion, that we have introduced in [26], and on segmentations based on Morse theory. Discrete distortion is defined by considering the graph of the discrete 3D field, which is a tetrahedral hypersurface in R 4, and measuring the distortion of the transformation which maps the tetrahedral mesh discretizing the scalar field domain into the mesh representing its graph in R 4. We describe a segmentation algorithm to produce Morse decompositions of a 3D scalar field which uses a watershed approach and we apply it to 3D images by using as scalar field both intensity and discrete distortion. We present experimental results by considering the influence of resolution on distortion computation. In particular, we show that the salient features of the distortion field appear prominently in lower resolution approximations to the dataset.
    Digital Object Identifier (DOI): 10.1007/978-3-642-21608-4_1

  • Title: Computing Morse decompositions for triangulated terrains: an analysis and an experimental evaluation
    Authors: M.Vitali; L.De Floriani; P.Magillo
    Year: 2011
    Book title: Image Analysis and Processing - ICIAP 2011
    Volume: 6978
    Pages: 565-574
    Series: Lecture Notes in Computer Science
    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.
    Digital Object Identifier (DOI): 10.1007/978-3-642-24085-0_58

  • Title: A Geometric Approach to Curvature Estimation on Triangulated 3D Shapes
    Authors: M.M.Mesmoudi; L.De Floriani; P.Magillo
    Year: 2010
    Conference: International Conference on Computer Graphics Theory and Applications (GRAPP)
    Place: Angers, France
    Dates: May 17, 2010
    Book title: Proceedings International Conference on Computer Graphics Theory and Applications (GRAPP)
    Pages: 90-95
    Abstract: We present a geometric approach to define discrete normal, principal, Gaussian and mean curvatures, that we call Ccurvature. Our approach is based on the notion of concentrated curvature of a polygonal line and a simulation of rotation of the normal plane of the surface at a point. The advantages of our approach is its simplicity and its natural meaning. A comparison with widely-used discrete methods is presented.
    Digital Object Identifier (DOI): 10.5220/0002825900900095

  • Title: Multiresolution Morse Triangulations
    Authors: E.Danovaro; L.De Floriani; P.Magillo; M.Vitali
    Year: 2010
    Conference: Symposium of Solid and Phisical Modeling (SPM)
    Place: Haifa, Israel
    Book title: Proceedings Symposium of Solid and Phisical Modeling (SPM)
    Pages: 183-188
    Abstract: We address the problem of representing the geometry and the morphology of a triangulated surface endowed with a scalar field in a combined geometric and topological multiresolution model. The model, called a Multiresolution Morse Triangulation (MMT), is composed of a multiresolution triangle mesh, and of a multiresolution Morse complex describing the morphology of the field. The MMT is built through a combined morphological and geometrical generalization, and supports queries to extract consistent geometrical and morphological representations of the field at both uniform and variable resolutions.
    Digital Object Identifier (DOI): 10.1145/1839778.1839806

  • Title: Spatial indexing on tetrahedral meshes
    Authors: L.De Floriani; R.Fellegara; P.Magillo
    Year: 2010
    Conference: International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2010)
    Place: San Jose, California, USA, Dates: November 2-5, 2010
    Book title: Proceedings 18th International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2010)
    Pages: 506-509
    Abstract: We address the problem of performing spatial queries on tetrahedral meshes. These latter arise in several application domains including 3D GIS, scientific visualization, finite element analysis. We have defined and implemented a family of spatial indexes, that we call tetrahedral trees. Tetrahedral trees subdivide a cubic domain containing the mesh in an octree or 3D kd-tree fashion, with three different subdivision criteria. Here, we present and compare such indexes, their memory usage, and spatial queries on them.
    Digital Object Identifier (DOI): 10.1145/1869790.1869873

  • Title: Modeling and Generalization of Discrete Morse Terrain Decompositions
    Authors: L. De Floriani; P. Magillo; M. Vitali
    Year: 2010
    Conference: 20th International Conference on Pattern Recognition
    Place: Istanbul, Turkey, Dates: August 23-26, 2010
    Book title: Proceedings 20th International Conference on Pattern Recognition (ICPR)
    Pages: 999-1002
    Abstract: We address the problem of morphological analysis of real terrains. We describe a morphological model for a terrain by considering extensions of Morse theory to the discrete case. We propose a two-level model of the morphology of a terrain based on a graph joining the critical points of the terrain through integral lines. We present a new set of generalization operators specific for discrete piece-wise linear terrain models, which are used to reduce noise and the size of the morphological representation. We show results of our approach on real terrains.
    Digital Object Identifier (DOI): 10.1109/ICPR.2010.250

  • Title: Concentrated Curvature for Mean Curvature Estimation
    Authors: M.M.Mesmoudi; L.De Floriani; P.Magillo
    Year: 2010
    Book title: Proceedings Workshop on Applications of Discrete Geometry and Mathematical Morphology (WADGMM)
    Pages: 32-36
    Conference: Workshop on Applications of Discrete Geometry and Mathematical Morphology (WADGMM)
    Place: Istanbul, Turkey
    Abstract: We present a mathematical result that allows computing the discrete mean curvature of a polygonal surface from the so-called concentrated curvature generally used for Gaussian curvature estimation. Our result adds important value to concentrated curvature as a geometric and metric tool to study accurately the morphology of a surface.

Years 2000 - 2009

  • Title: Digital Elevation Models
    Authors: L.De Floriani; P.Magillo
    Year: 2009
    Book title: Encyclopedia of Database Systems
    Pages: 817-821
    Publisher: Springer, US
    Digital Object Identifier (DOI): 10.1007/978-0-387-39940-9_129

  • Title: Discrete Distortion for Surface Meshes
    Authors: M.M.Mesmoudi; L.De Floriani; P.Magillo
    Year: 2009
    Book title: Image Analysis and Processing - ICIAP 2009
    Volume: 5716
    Pages: 652-661
    Abstract: Discrete distortion for two- and three-dimensional combinatorial manifolds is a discrete alternative to Ricci curvature known for differentiable manifolds. Here, we show that distortion can be successfully used to estimate mean curvature at any point of a surface. We compare our approach with the continuous case and with a common discrete approximation of mean curvature, which depends on the area of the star of each vertex in the triangulated surface. This provides a new, area-independent, tool for curvature estimation and for morphological shape analysis. We illustrate our approach through experimental results showing the behavior of discrete distortion.
    Digital Object Identifier (DOI): 10.1007/978-3-642-04146-4_70

  • Title: Morphology Analysis of 3D Scalar Fields Based on Morse Theory and Discrete Distortion
    Authors: M.M.Mesmoudi; L.De Floriani; P.Magillo
    Year: 2009
    Conference: ACM Int. Conf. on Advances in Geographic Information Systems
    Place: Seattle, WA, USA, Dates: November 4-6, 2009
    Book title: Proceedings 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
    Pages: 187-196
    Abstract: We investigate a morphological approach to the analysis and understanding of 3D scalar fields defined by volume data sets. We consider a discrete model of the 3D field obtained by discretizing its domain into a tetrahedral mesh. We use Morse theory as the basic mathematical tool which provides a segmentation of the graph of the scalar field based on relevant morphological features (such as critical points). Since the graph of a discrete 3D field is a tetrahedral hypersurface in 4D space, we measure the distortion of the transformation which maps the tetrahedral decomposition of the domain of the scalar field into the tetrahedral mesh representing its graph in R4, and we call it discrete distortion. We develop a segmentation algorithm to produce a Morse decompositions associated with the scalar field and its discrete distortion. We use a merging procedure to control the number of 3D regions in the segmentation output. Experimental results show the validity of our approach.
    Digital Object Identifier (DOI): 10.1145/1653771.1653799

  • Title: Morphological analysis of terrains based on curvature and discrete distortion
    Authors: Mesmoudi M.M.; De Floriani L.; Magillo P.
    Year: 2008
    Conference: ACM International Conference on Geographic Information Systems (ACM-GIS)
    Place: Irvine, California, USA, Dates: 5-7 Novembre 2008
    Book title: Proceedings 16th ACM International Conference on Geographic Information Systems (ACM-GIS).
    Pages: 415-418
    Abstract: In order to characterize the morphology of a triangulated terrain, we define several discrete estimators that mimic mean and Gaussian curvatures in the discrete case. We start from concentrated curvature, a discrete notion of Gaussian curvature for polyhedral surfaces, defined by Troyanov [7]. Since concentrated curvature does not depend on the local geometric shape of the terrain, we introduce Ccurvature that allows us to obtain discrete counterparts of both Gaussian and mean curvature. Finally, we define distortion, which behaves as an approximation of mean curvature. We apply all such measures to the analysis of the morphology of triangulated terrains.
    Digital Object Identifier (DOI): 10.1145/1463434.1463498

  • Title: Visualizing Multiple Scalar Fields on a Surface
    Authors: Mesmoudi M.M.; De Floriani L.; Magillo P.
    Year: 2008
    Conference: 3rd International Conference on Computer Graphics Theory and Applications, Place: Funchal, Madeira, Portugal, Dates: January 22-25, 2008
    Book title: Proceedings 3rd International Conference on Computer Graphics Theory and Applications (GRAPP)
    Pages: 138-142
    Abstract: We present a new technique for the simultaneous visualization of an arbitrary number of scalar fields defined on a surface. The technique is called Generalized Atmosphere Upper Bound Level (GAUBL), since it is an evolution of our previous AUBL technique, that allowed for the visualization of a single scalar field. The generalized AUBL can highlight the dependencies and interactions between many scalar fields, and can handle a multi-valued scalar field as a special case. We have implemented the GAUBL into a visualization tool that handles triangle-based surface models, and we show here some experimental results.
    Digital Object Identifier (DOI): 10.5220/0001097201380142

  • Title: A Hierarchical spatial index for triangulated surfaces
    Authors: De Floriani L.; Facinoli M.; Magillo P.; Dimitri D.
    Year: 2008
    Conference: 3rd International Conference on Computer Graphics Theory and Applications
    Place: Funchal, Madeira (Portugal), Dates: January 22-25, 2008
    Book title: Proceedings 3rd International Conference on Computer Graphics Theory and Applications (GRAPP)
    Pages: 86-91
    Abstract: We present the PM2-Triangle quadtree (PM2T-quadtree), a new hierarchical spatial index for triangle meshes which has been designed for performing spatial queries on triangle-based terrain models. The PM2T-quadtree is based on a recursive space decomposition into square blocks. Here, we propose a highly compact data structure encoding a PM2T-quadtree, which decouples the spatial indexing structure from the combinatorial description of the mesh. We compare the PM2T-quadtree against other spatial indexes by considering the structure of the underlying domain subdivision, the storage costs of their data structures and the performance in geometric queries.
    Digital Object Identifier (DOI): 10.5220/0001097300860091

  • Title: A Discrete Approach to Compute Terrain Morphology
    Authors: P. Magillo; E.Danovaro; L.De Floriani; L.Papaleo; M.Vitali
    Year: 2008
    Book title: Computer Vision and Computer Graphics. Theory and Applications, International Conference VISIGRAPH 2007, Barcelona, Spain, March 8-11, 2007. Revised Selected Papers
    Book Series: "Communications in Computer and Information Science"
    Volume: 21
    Pages: 13-26
    Abstract: We consider the problem of extracting morphology of a terrain represented as a Triangulated Irregular Network (TIN). We propose a new algorithm and compare it with representative algorithms of the main approaches existing in the literature to this problem. The new algorithm has the advantage of being simple, using only comparisons (and no floating-point computations), and of being suitable for an extension to higher dimensions. Our experiments consider both real data and artificial test data. We evaluate the difference in the results produced on the same terrain data, as well as the impact of resolution level on such a difference, by considering representations of the same terrain at different resolutions.
    Digital Object Identifier (DOI): 10.1007/978-3-540-89682-1_2

  • Title: Multi-Scale Dual Morse Complexes for Representing Terrain Morphology
    Authors: Danovaro E; L. De Floriani; Vitali M; Magillo P
    Year: 2007
    Conference: ACM International Conference on Geographic Information Systems (ACM-GIS)
    Place: Seattle, Washington, USA, Dates: November 7-9, 2007
    Book title: Proceedings 15th ACM International Symposium on Advances in Geographic Information Systems
    Pages: 29-36
    Abstract: We propose a new multi-scale terrain model, based on a hierarchical representation for the morphology of a terrain. The basis of our morphological model is a dual Morse decomposition of the terrain, composed by the stable and unstable manifolds defined by its critical points and its integral lines. We propose a two-level representation of the dual Morse decomposition and we define new simplification operators for the Morse decomposition which act on such representation. Based on these operators, we define a hierarchical morphology-based representation, that we call a Multi-scale Morse Complex (MMC). Results from our implementation of the MMC are presented.
    Digital Object Identifier (DOI): 10.1145/1341012.1341050

  • Title: Extracting Terrain Morphology: A New Algorithm and a Comparative Evaluation
    Authors: Magillo P.; Danovaro E.; De Floriani L.; Papaleo L.; Vitali M.
    Year: 2007
    Conference: Second International Conference on Computer Graphics Theory and Applications
    Place: Barcelona (Spain)
    Book title: 2nd International Conference on Computer Graphics Theory and Applications (GRAPP'07)
    Pages: 13-20
    Abstract: We consider the problem of extracting morphology of a terrain represented as a Triangulated Irregular Network (TIN). We propose a new algorithm and compare it with representative algorithms of the main approaches existing in the literature to this problem.
    Digital Object Identifier (DOI): 10.5220/0002076200130020

  • Title: Multi-VMap: a Multi-Scale Model for Vector Maps
    Authors: R. Viania; P. Magillo; E. Puppo; P.A. Ramos
    Year: 2006
    Journal: GeoInformatica, Volume: 10(3), Pages: 359-394
    Abstract: Multi-VMap is a compact framework from which plane graphs representing geographic maps at different levels of detail can be extracted. Its main feature is that the scale of the extracted map can be variable through its domain, while each entity maintains consistent combinatorial relations with the rest of entities represented in the map. The model is based on a set of operators, called updates, which modify the level of detail in a small portion of a map. The set of updates is partially ordered, and can therefore be represented as a Directed Acyclic Graph, which defines our multi-scale structure. An algorithm to extract a map at the required resolution is proposed, and a lower bound for the number of different maps which can be extracted from the model is given. The model supports map data processing operations (e.g., querying), as well as progressive and selective transmission of maps over a network.
    Digital Object Identifier (DOI): 10.1007/s10707-006-9832-y

  • Title: Level-of-Detail for Data Analysis and Exploration: a historical overview and some new perspectives
    Authors: E.Danovaro; L.De Floriani; P. Magillo; E.Puppo; D.Sobrero
    Year: 2006
    Journal: Computers & Graphics, Volume: 30(3), Pages: 334-344
    Abstract: Level-of-detail (LOD) techniques have been studied for many years in computer graphics. Research in this area has reached maturity and several effective tools in LOD modeling are now available. However, most models and tools proposed in the literature are oriented to rendering. This is just one among many tasks that LOD should support in the context of applications involving geometric meshes of large size. Our approach to the research on LOD has always been to develop models and data structures that can support a range of spatial queries, rather than being optimized for rendering. Here, we present a historical overview, by highlighting the impact of this approach in the design of LOD models and data structures, and we briefly describe our current research, outlining new challenges in which LOD finds important applications.
    Digital Object Identifier (DOI): 10.1016/j.cag.2006.02.006

  • Title: Multi-Scale Geographic Maps
    Authors: R. Viania; P. Magillo; E. Puppo
    Year: 2005
    Book title: Advances in Multiresolution for Geometric Modelling
    Pages: 101-115
    Abstract: We consider geographic maps represented as plane graphs, which undergo a process of generalisation performed through sequences of local updates. Generalisation transforms a highly detailed map into one with fewer details, spanning many different scales of representation through the sequence of updates. We study intrinsic dependency relations among updates in the sequence and, on this basis, we derive a multi-scale model that supports efficient retrieval of maps at different scales, possibly variable through the domain.
    Digital Object Identifier (DOI): 10.1007/3-540-26808-1_6

  • Title: Encoding Level-Of-Detail Tetrahedral Meshes
    Authors: N.Sokolovky; E.Danovaro; L.De Floriani; P. Magillo
    Year: 2005
    Book title: Advances in Multiresolution for Geometric Modelling
    Pages: 89-100
    Abstract: Level-Of-Detail (LOD) techniques can be a valid support to the analysis and visualisation of volume data sets of large size. In our previous work, we have defined a general LOD model for d-dimensional simplicial meshes, called a Multi-Tessellation (MT), which consists of a partially ordered set of mesh updates. Here, we consider an instance of the MT for tetrahedral meshes, called a Half-Edge MT, which is built through a common simplification operation, half-edge collapse. We discuss two compact encodings for a Half-Edge MT, based on alternative ways to represent the partial order.
    Digital Object Identifier (DOI): 10.1007/3-540-26808-1_5

  • Title: The Half-Edge Tree: A Compact Data Structure for Level-of-Detail Tetrahedral Meshes
    Authors: E. Danovaro; L. De Floriani; P. Magillo; E. Puppo; D. Sobrero; N. Sokolovsky
    Year: 2005
    Conference: SMI 2005 - International Conference on Shape Modeling and Applications
    Place: Cambridge (MA), USA, Dates: June 13-17, 2005
    Book title: Proceedings of SMI 2005 - International Conference on Shape Modeling and Applications
    Pages: 334-339
    Abstract: We propose a new data structure for the compact encoding of a level-of detail (LOD) model of a three-dimensional scalar field based on unstructured tetrahedral meshes. Such data structure, called a half-edge tree (HET), is built through the iterative application of a half-edge collapse, i.e. by contracting an edge to one of its endpoints. We also show that selective refined meshes extracted from an HET contain on average about 34% and up to 75% less tetrahedra than those extracted from an LOD model built through a general edge collapse.
    Digital Object Identifier (DOI): 10.1109/SMI.2005.47

  • Title: A multi-resolution topological representation for non-manifold meshes
    Authors: L. De Floriani; P. Magillo; E. Puppo; D. Sobrero
    Year: 2004
    Journal: Computer-Aided Design, Volume: 36 (2), Pages: 141-159
    Abstract: We address the problem of representing and processing 3D objects, described through simplicial meshes, which consist of parts of mixed dimensions, and with a non-manifold topology, at different levels of detail. First, we describe a multi-resolution model, that we call a non-manifold multi-tessellation (NMT), and we consider the selective refinement query, which is at the heart of several analysis operations on multi-resolution meshes. Next, we focus on a specific instance of a NMT, generated by simplifying simplicial meshes based on vertex-pair contraction, and we describe a compact data structure for encoding such a model. We also propose a new data structure for two-dimensional simplicial meshes, capable of representing both connectivity and adjacency information with a small memory overhead, which is used to describe the mesh extracted from an NMT through selective refinement. Finally, we present algorithms to efficiently perform updates on such a data structure.
    Digital Object Identifier (DOI): 10.1016/S0010-4485(03)00058-7

  • Title: Encoding Level-Of-Detail Tetrahedral Meshes through the Half-Edge Tree
    Authors: E.Danovaro; L. De Floriani; P.Magillo; E.Puppo; D.Sobrero; N.Sokolovky
    Year: 2004
    Conference: Second Convention of the Italian Group of Researchers in Pattern Recognition (GIRPR)
    Place: Perugia, Italy
    Dates: September 15-17, 2004.
    Book title: Proceedings of Second Convention of the Italian Group of Researchers in Pattern Recognition (GIRPR)

  • Title: Selective refinement queries for volume visualization of unstructured tetrahedral meshes
    Authors: Cignoni P.; De Floriani L.; Magillo P.; Puppo E.; Scopigno R.
    Year: 2004
    Journal: IEEE Transactions on Visualization and Computer Graphics
    Volume: 10 (1), Pages: 29-45
    Abstract: In this paper, we address the problem of the efficient visualization of large irregular volume data sets by exploiting a multiresolution model based on tetrahedral meshes. Multiresolution models, also called Level-Of-Detail (LOD) models, allow encoding the whole data set at a virtually continuous range of different resolutions. We have identified a set of queries for extracting meshes at variable resolution from a multiresolution model, based on field values, domain location, or opacity of the transfer function. Such queries allow trading off between resolution and speed in visualization. We define a new compact data structure for encoding a multiresolution tetrahedral mesh built through edge collapses to support selective refinement efficiently and show that such a structure has a storage cost from 3 to 5.5 times lower than standard data structures used for tetrahedral meshes. The data structures and variable resolution queries have been implemented together with state-of-the art visualization techniques in a system for the interactive visualization of three-dimensional scalar fields defined on tetrahedral meshes. Experimental results show that selective refinement queries can support interactive visualization of large data sets.
    Digital Object Identifier (DOI): 10.1109/TVCG.2004.1260756

  • Title: Triangle-based Multiresolution Models for Height Fields
    Authors: L. De Floriani; P. Magillo
    Year: 2003
    Book title: Curve and Surface Fitting: Saint-Malo 2002
    Pages: 97-106
    Abstract: Large-size data sets describing height elds (e.g., terrains) can be handled with multi-resolution models. We analyze and compare two multi-resolution models for height elds based on regular and irregular triangle meshes, respectively. Our comparison takes into account the space required by the data structures and the effectiveness in extracting variable-resolution surface representations.
    Digital Object Identifier (DOI): 10.1.1.8.4836

  • Title: Algorithms for visibility computation on terrains: a survey
    Authors: L. De Floriani; P. Magillo
    Year: 2003
    Journal: Environment and Planning B
    Volume: 30(5), Pages: 709-728
    Abstract: Several environment applications require the computation of visibility information on a terrain. Examples are optimal placement of observation points, line-of-sight communication, and computation of hidden as well as scenic paths. Visibility computations on a terrain may involve either one or many viewpoints, and range from visibility queries (for example, testing whether a given query point is visible), to the computation of structures that encode the visible portions of the surface. In this paper, the authors consider a number of visibility problems on terrains and present an overview of algorithms to tackle such problems on triangulated irregular networks and regular square grids.
    Digital Object Identifier (DOI): 10.1068/b12979

  • Title: Level-Of-Detail (LOD) modeling of scalar fields through topology-driven simplification
    Authors: E. Danovaro; P. Magillo; M.M. Mesmoudi
    Year: 2003
    Conference: 2th Eurographics Italian Chapter
    Place: Milano
    Book title: Proceedings 2th Eurographics Italian Chapter

  • Title: Data structures for 3D multi-tessellations: an overview
    Authors: E. Danovaro; L. De Floriani; P. Magillo; E. Puppo
    Year: 2003
    Book title: Data visualization: the state of the art - Part IV
    Pages: 239-256
    Series: The Springer International Series in Engineering and Computer Science
    Series Volume: 713
    Abstract: Multiresolution models support the interactive visualization of large volumetric data through selective refinement, an operation which permits to focus resolution only on the most relevant portions of the domain, or in the proximity of interesting field values. A 3D Multi-Tessellation (MT) is a multiresolution model, consisting of a coarse tetrahedral mesh at low resolution, and of a set of updates refining such a mesh, arranged as a partial order. In this paper, we describe and compare different data structures which permit to encode a 3D MT and to support selective refinement.
    DOI: 10.1007/978-1-4615-1177-9_17

  • Title: Morphology-driven simplification and multiresolution modeling of terrains
    Authors: E. Danovaro; L. De Floriani; P. Magillo; M.M. Mesmoudi; E. Puppo
    Year: 2003
    Conference: ACM Workshop on Advances in Geographic Information Systems - ACMGIS03
    Place: New Orleans Louisiana, USA, Dates: November 7-8, 2003
    Book title: Proceedings 11th ACM Workshop on Advances in Geographic Information Systems - ACMGIS03
    Pages: 63-70
    Abstract: We propose a technique for simplification and
    multiresolution modeling of a terrain represented as a TIN. Our goal is to maintain the morphological structure of the terrain in the resulting multiresolution model. To this aim, we extend Morse theory, developed for continuous and differentiable functions, to the case of piecewise linear functions. We decompose a TIN into areas with uniform morphological properties (such as valleys, basins, etc.) separated by a network of critical lines and points. We describe an algorithm to compute the above decomposition and the critical net, and a TIN simplification algorithm that preserves them. On this basis, we build a multiresolution terrain model, which provides a representation of critical features at any level of detail.

    Digital Object Identifier (DOI): 10.1145/956676.956685

  • Title: Multiresolution mesh representation: Models and data structures
    Authors: L. De Floriani; P. Magillo
    Year: 2002
    Book title: Tutorials on Multiresolution in Geometric Modelling
    Pages: 363-417
    Publisher: Springer, Berlin, Heidelberg
    Series: Mathematics and Visualization
    Abstract: Multiresolution meshes are a common basis for building representations of a geometric shape at different levels of detail. The use of the term multiresolution depends on the remark that the accuracy (or, level of detail) of a mesh in approximating a shape is related to the mesh resolution, i.e., to the density (size and number) of its cells. A multiresolution mesh provides several alternative mesh-based approximations of a spatial object (e.g., a surface describing the boundary of a solid object, or the graph of a scalar field).
    A multiresolution mesh is a collection of mesh fragments, describing usually small portions of a spatial object with different accuracies, plus suitable relations that allow selecting a subset of fragments (according to user-defined accuracy criteria), and combining them into a mesh covering the whole object, or an object part. Existing multiresolution models differ in the type of mesh fragments they consider and in the way they define relations among such fragments.
    In this chapter, we introduce a framework for multiresolution meshes in order to analyze and compare existing models proposed in the literature on a common basis. We have identified two sets of basic queries on a multiresolution meshes, that we call selective refinement and spatial selection. We describe two approaches for answering such queries, and discuss the primitives involved in them, which must be efficiently supported by any data structure implementing a multiresolution mesh. We then describe and analyze data structures proposed in the literature for encoding multiresolution meshes.

    Digital Object Identifier (DOI): 10.1007/978-3-662-04388-2 of book, and 10.1007/978-3-662-04388-2_13 of this chapter.

  • Title: Regular and Irregular Multi-Resolution Terrain Models: a Comparison
    Authors: De Floriani L.; Magillo P.
    Year: 2002
    Conference: 10th ACM International Symposium on Advances in Geographic Information Systems (ACM-GIS'02)
    Place: McLean, Virginia, USA, Dates: November 8-9, 2002
    Book title: Proceedings 10th ACM International Symposium on Advances in Geographic Information Systems (ACM-GIS'02)
    Pages: 143-148
    Abstract: The paper deals with the problem of modeling large-size terrain data sets. To this aim, we consider multi-resolution models based on triangle meshes. We analyze and compare two multi-resolution terrain models based on regular and irregular meshes. The two models are viewed as instances of a common multi-resolution model, that we call a multi-resolution triangle mesh. Our comparison takes into account the space requirements of the data structures implementing the two models as well their effectiveness in supporting the extraction of variable-resolution terrain representations.
    Digital Object Identifier (DOI): 10.1145/585147.585178

  • Title: A multi-resolution topological representation for non-manifold meshes
    Authors: De Floriani L.; Magillo P.; Puppo E.; Sobrero D.
    Year: 2002
    Conference: 7th ACM Symposium on Solid Modeling and Applications
    Place: Saarbrucken, Germany. Dates: June 17-21, 2002
    Book title: Proceedings 7th ACM Symposium on Solid Modeling and Applications (SMA '02).
    Pages: 159-170
    Abstract: We address the problem of representing and processing non-regular, non-manifold two-dimensional simplicial meshes, that we call triangle-segment meshes, at different levels of detail. Such meshes are used to describe spatial objects consisting of parts of mixed dimensions, and with a non-manifold topology. First, we describe a multi-resolution model for non-regular, non-manifold meshes, that we call a Non-manifold Multi-Tessellation (NMT). We consider the selective refinement query, which is at the heart of several analysis operations on multiresolution meshes. Next, we focus on a specific instance of a NMT, generated by a simplification process based on vertex-pair contraction, and we describe a compact data structure for encoding it. We also propose a new data structure for triangle-segment meshes, capable of representing both connectivity and adjacency information with a small memory overhead, that we use to describe the mesh extracted with selective refinement. To this aim, we define algorithms to efficiently perform mesh updates on such a data structure.
    Digital Object Identifier (DOI): 10.1145/566282.566307

  • Title: Representing vertex-based multiresolution simplicial complexes
    Authors: E. Danovaro; L. De Floriani; P. Magillo; E. Puppo
    Year: 2001
    Book title: Digital and Image Geometry
    Series: Lecture Notes in Computer Science
    Volume: 2243, Pages: 129-149
    Abstract: In this paper, we consider the problem of representing a multiresolution geometric model, called a Simplicial Multi-Complex (SMC), in a compact way. We present encoding schemes for both two-an d threedimensional SMCs built through a vertex insertion (removal) simplification strategy.We show that a good compression ratio is achieved not only with respect to a general-purpose data structure for a SMC, but also with respect to just encoding the complex at the maximum resolution.
    Digital Object Identifier (DOI): 10.1007/3-540-45576-0_8

  • Title: Non-Manifold Multi-Tessellation: from Meshes to Iconic
    Representations of 3D Objects

    Authors: L. De Floriani; P. Magillo; Morando F.; E. Puppo
    Year: 2001
    Book title: Visual Form 2001
    Series: Lecture Notes in Computer Science
    Volume: 2059, Pages: 654-664
    Abstract: This paper describes preliminary research work aimed at obtaining a multi-level iconic representation of 3D objects from geometric meshes. A single-level iconic model describes an object through parts of different dimensions connected to form a hypergraph. The multi-level iconic model, called Non-manifold Multi-Tessellation, incorporates decompositions of an object into parts at different levels of abstraction, and permits to refine an iconic representation selectively.
    Digital Object Identifier (DOI): 10.1007/3-540-45129-3_60

  • Title: Multiresolution Modeling of Three-Dimensional Shapes
    Authors: L. De Floriani; P. Magillo
    Year: 2001
    Book title: 3D Synthetic Environment Reconstruction
    Chapter 2.
    Pages: 35-59
    Series: The Springer International Series in Engineering and Computer Science, Volume: 611
    Abstract: Multiresolution models can provide representations of a geometric shape at different degrees of accuracy and complexity, based on user requirements. They have an impact in many applications, which require the manipulation of complex three-dimensional objects. In this chapter, we present a survey of existing multiresolution techniques. A comprehensive framework for multiresolution modeling is introduced, and existing models are presented, interpreted and compared by referring to such framework.
    Digital Object Identifier (DOI): 10.1007/978-1-4419-8756-3_2

  • Title: Compressing Multiresolution Triangle Meshes
    Authors: E. Danovaro; L. De Floriani; P. Magillo; E. Puppo
    Year: 2001
    Book title: Advances in Spatial and Temporal Databases. SSTD 2001
    Series: Lecture Notes in Computer Science
    Volume: 2121
    Pages: 345-364
    Abstract: In this paper, we consider triangle-based two-dimensional multiresolution complexes, called Multi-Triangulations (MTs), constructed based on a vertex-removal simplification strategy, which is the most common strategy used to build simplified representations of surfaces, e.g., terrains. We describe and compare compact encoding structures for such MTs. We show that these structures provide good compression ratios not only with respect to an economical data structure for general MTs, but also with respect to encoding the original mesh (i.e., the mesh at the full resolution). We also analyze the basic atomic operations needed for performing selective refinement on an MT, and we show that such operations are efficiently supported by the data structures described.
    DOI: 10.1007/3-540-47724-1_18

Before year 2000

  • Title: On-line Space Sculpturing for 3D Shape Manipulation
    Authors: De Floriani L.; Magillo P.; E. Puppo
    Year: 2000
    Conference: 15th International Conference on Pattern Recognition (ICPR)
    Place: Barcelona, Spain, Dates: September 3-7
    Book title: Proceedings 15th International Conference on Pattern Recognition (ICPR)
    Pages: 105-108
    Abstract: We present a new data structure, called the Multi-Sculpture to represent 3D shapes at multiple levels of detail. The input shape at high resolution is described as a mesh of triangles. A coarse approximation of this shape is provided by the convex hull of the mesh, while intermediate approximations are obtained by sculpturing the space that separates the convex hull from the mesh. A higher level of detail corresponds to a higher degree of concavity in the shape approximation. The data structure supports on-line extraction of a shape representation at a user-defined level of detail, possibly varying over different parts of the shape. This mechanism allows speeding up recognition, classification, collision detection, and planning of manipulation tasks.
    Digital Object Identifier (DOI): 10.1109/ICPR.2000.905285

  • Title: Compressing triangulated irregular networks
    Authors: De Floriani L.; Magillo P.; Puppo E.
    Year: 2000
    Journal: GeoInformatica
    Volume: 4(1), Pages: 67-88
    Abstract: We address the problem of designing compact data structures for encoding a Triangulated Irregular Network (TIN). In particular, we study the problem of compressing connectivity, i.e., the information describing the topological structure of the TIN, and we propose two new compression methods which have different purposes. The goal of the first method is to minimize the number of bits needed to encode connectivity information: it encodes each vertex once, and at most two bits of connectivity information for each edge of a TIN; algorithms for coding and decoding the corresponding bitstream are simple and efficient. A practical evaluation shows compression rates of about 4.2 bits per vertex, which are comparable with those achieved by more complex methods. The second method compresses a TIN at progressive levels of detail and it is based on a strategy which iteratively removes a vertex from a TIN according to an error-based criterion. Encoding and decoding algorithms are presented and compared with other approaches to progressive compression. Our method can encode more general types of triangulations, such as those constrained by topographic features, at the cost of a slightly longer bitstream.
    Digital Object Identifier (DOI): 10.1023/A:1009880409451

  • Title: VARIANT: A System for Terrain Modeling at Variable Resolution
    Authors: De Floriani L.; Magillo P.; Puppo E.
    Year: 2000
    Journal: GeoInformatica
    Volume: 4(3), Pages: 287-315
    Abstract: We describe VARIANT (VAriable Resolution Interactive ANalysis of Terrain), an extensible system for processing and visualizing terrains represented through Triangulated Irregular Networks (TINs), featuring the accuracy of the representation, possibly variable over the terrain domain, as a further parameter in computation.
    VARIANT is based on a multiresolution terrain model, which we developed in our earlier research. Its architecture is made of a kernel, which provides primitive operations for building and querying the multiresolution model; and of application programs, which access a terrain model based on the primitives in the kernel.
    VARIANT directly supports basic queries (e.g., windowing, buffering, computation of elevation at a given point, or along a given line) as well as high-level operations (e.g., fly-over visualization, contour map extraction, viewshed analysis). However, the true power of VARIANT lies in the possibility of extending it with new applications that can exploit its multiresolution features in a transparent way.

    Digital Object Identifier (DOI): 10.1023/A:1009805426595

  • Title: Dynamic view-dependent multiresolution on a client-server architecture
    Authors: De Floriani L.; Magillo P.; Morando F.; Puppo E.
    Year: 2000
    Journal: Computer-Aided Design
    Volume: 32(13)
    Special Issue on Multiresolution Geometric Models
    Pages: 805-823
    Abstract: We consider the problem of transmitting huge triangle meshes in the context of a Web-like client-server architecture. Approximations of the original mesh are transmitted by applying selective refinement. A multiresolution geometric model is maintained by the server. A client may query the server for a mesh at an arbitrary, continuously variable, level of detail. The client makes repeated queries over time with different query parameters. The server answers to queries by traversing the multiresolution model and transmitting updates to the client, which uses them to progressively modify a current mesh.
    We study this problem in the context of a vertex-based multiresolution model, which is a special instance of the Multi-Triangulation (a model that was developed in an earlier work), based on vertex insertion and removal. We define a compact data structure for such a model that exploits the specific update rule. We propose a dynamic algorithm for selective refinement and we discuss in detail its implementation as a client–server application. In order to reduce memory requirements and channel traffic, we develop a compressed representation which allows us to express mesh updates with a code of small size. We also address client caching to further limit bandwidth occupancy. Experimental results show that the Multi-Triangulation can be a key Web technology for triangle mesh manipulation.

    Digital Object Identifier (DOI): 10.1016/S0010-4485(00)00070-1

  • Title: Volume Visualization of Large Tetrahedral Meshes on Low Cost Platforms
    Authors: P. Cignoni; L. De Floriani; P. Magillo; E. Puppo; R. Scopigno
    Year: 2000
    Conference: NSF/DoE Lake Tahoe Workshop on Hierarchical Approximation and Geometrical Methods for Scientific Visualization
    Place: Tahoe City, California
    Dates: 15-17 October 2000
    Book title: Proceedings NSF/DoE Lake Tahoe Workshop on Hierarchical Approximation and Geometrical Methods for Scientific Visualization

  • Title: A Library for Multiresolution Modeling of Field Data in GIS
    Authors: P. Magillo; L. De Floriani; E. Puppo
    Year: 2000
    Conference: Int. Workshop on Emerging Technologies for Geo-Based Applications, Place: Ascona, Switzerland
    Dates: May 22-26, 2000
    Book title: Proc. Int. Workshop on Emerging Technologies for Geo-Based Applications
    Pages: 133-151

  • Title: Triangle-Based Surface Models
    Authors: L. De Floriani; S. Bussi; P. Magillo
    Year: 2000
    Book title: Intelligent Systems and Robotics
    Pages: 340-373
    Chapter 9.

  • Title: Managing Large Terrain Data Sets with a Multiresolution Structure
    Authors: P. Magillo; V. BERTOCCI
    Year: 2000
    Conference: 11th International Workshop on Database and Expert Systems and Applications
    Place: Greenwich, London, UK
    Dates: 4-8 September 2000
    Book title: Proceedings 11th International Workshop on Database and Expert Systems and Applications
    Pages: 894-898
    Abstract: We propose an algorithm to build a modular multiresolution terrain model consisting of a collection of patches that can be loaned and combined together in order to cover a portion of the domain. This method allows the management of huge data sets that would not fit in main memory as a whole.
    Digital Object Identifier (DOI): 10.1109/DEXA.2000.874995

  • Title: Data structures for simplicial multi-complexes
    Authors: L. De Floriani; P. Magillo; E. Puppo
    Year: 1999
    Book title: Advances in spatial databases
    Series: Lecture Notes in Computer science
    Volume: 1651
    Pages: 33-51
    Abstract: The Simplicial Multi-Complex (SMC) is a general multiresolution model for representing k-dimensional spatial objects through simplicial complexes. An SMC integrates several alternative representations of an object and offers simple methods for handling representations at variable resolution effciently, thus providing a basis for the development of applications that need to manage the level-of-detail of complex objects. In this paper, we present general query operations on such models, we describe and classify alternative data structures for encoding an SMC, and we discuss the cost and performance of such structures.
    Digital Object Identifier (DOI): 10.1007/3-540-48482-5_5

  • Title: Intervisibility on Terrains
    Authors: L. De Floriani; P. Magillo
    Year: 1999
    Book title: Geographic Information Systems: Principles Techniques, Managament and Applications
    Volume: 1
    Chapter 38, Pages: 543-556

  • Title: Applications of Computational Geometry to Geographical Information Systems
    Authors: De Floriani L.; Puppo E.; Magillo P.
    Year: 1999
    Book title: Handbook of Computational Geometry
    Chapter 7, Pages: 333-388
    Publisher: Elsevier Science - North Holland
    Digital Object Identifier (DOI): 10.1016/B978-044482537-7/50008-5

  • Title: Multiresolution Representation of Shapes Based on Cell Complexes
    Authors: L. De Floriani; P. Magillo; E. Puppo
    Year: 1999
    Book title: Discrete Geometry for Computer Imagery - DGCI 1999
    Series: Lecture Notes in Computer Science
    Volume: 1568
    Pages: 3-18
    Abstract: This paper introduces a dimension-independent multiresolution model of a shape, called the Multi-Complex (MC), which is based on decomposition into cells. An MC describes a shape as an initial cell complex approximating it, plus a collection of generic modification patterns to such complex arranged according to a partial order. The partial order is essential to extract variable-resolution shape descriptions in real time. We show how existing multiresolution models reduce to special cases of MCs characterized by specific modification patterns. The MC acts as a unifying framework that is also useful for comparing and evaluating the expressive power of different approaches.
    Digital Object Identifier (DOI): 10.1007/3-540-49126-0_1

 

  • Title: Compressing TINs
    Authors: L. De Floriani, P. Magillo, E. Puppo
    Booktitle: GIS'98 Proceedings of the 6th ACM international symposium on Advances in geographic information systems
    Place: Washington, DC, USA,
    Dates: November 6-7,
    Year: 1998
    Pages: 145-150
    Abstract:
    DOI: 10.1145/288692.288718

 

 

  • Title: Efficient implementation of Multi-Triangulations
    Authors: L. De Floriani, P. Magillo, E. Puppo
    Year: 1998
    Booktitle: Proceedings IEEE Visualization '98
    Place: Research Triangle Park, NC, USA, Dates: October 18-23,
    Pages: 43-50.
    Abstract: Multi-triangulation (MT) is a general framework for managing the level-of-detail in large triangle meshes, which we have introduced in our previous work. In this paper, we describe an efficient implementation of an MT based on vertex decimation. We present general techniques for querying an MT, which are independent of a specific application, and which can be applied for solving problems, such as selective refinement, windowing, point location, and other spatial interference queries. We describe alternative data structures for encoding an MT, which achieve different trade-offs between space and performance. Experimental results are discussed.
    DOI: 10.1109/VISUAL.1998.745283

 

 

  • Title: Managing the level of detail in 3D shape reconstruction and representation
    Authors: L. De Floriani, P. Magillo, E. Puppo
    Year: 1998
    Booktitle: Proceedings 14th International Conference on Pattern Recognition (ICPR'98),
    Place: Brisbane, Queensland, Australia, Dates: August 16-20,
    Pages: 389-391
    Abstract: We address the problem of reconstructing the shape of a solid object from sparse data, and of representing it at multiple levels of detail. We provide a multiresolution model, based on a set of local sculpturing updates on an initial tetrahedral mesh, which supports extraction of representations at an arbitrary level of detail. We present a new sculpturing algorithm that we use to build the multiresolution model.
    DOI: 10.1109/ICPR.1998.711162

 

 

  • Title: Algorithms for Parallel Terrain Modelling and Visualisation
    Authors: P. Magillo, E. Puppo
    Booktitle: Parallel Processing Algorithms for GIS, Chapter 16
    Pages: 351-386
    Taylor and Francis,
    Year: 1998

 

 

  • Title: VARIANT - Processing and visualizing terrains at variable resolution
    Authors: L. De Floriani, P. Magillo, E. Puppo,
    Year: 1997
    Booktitle: Proceedings 5th ACM Workshop on Advances in Geographic Information Systems
    Place: Las Vegas, Nevada
    Dates: November 13-14
    Pages: 15-19
    Publisher: ACM Press

 

 

  • Title: Visibility computations on hierarchical triangulated terrain models
    Authors: L. De Floriani, P. Magillo,
    Year: 1997
    Journal: Geoinformatica
    Volume: 1(3), Pages: 219-250
    Abstract: Hierarchical terrain models provide a multiresolution description of a topographic surface based on a nested partition of the domain. The tree-like structure of these models is an effective support to processing spatial operations. In this paper, we consider visibility computations on hierarchical terrain models based on triangular subdivisions, called Hierarchical Triangulated Irregular Networks (HTINs). We address two basic problems in visibility computation, namely determining the visibility of a query object, and computing the viewshed of a given viewpoint. We propose algorithms for performing such operations on an HTIN at variable resolution. A general drawback of hierarchical models is in the inconsistency of representations at variable resolution obtained from them, since vertical gaps may occur at edges where different resolutions meet. The algorithms proposed here avoid this undesired effect. A related, but independent, contribution of this paper is also a new algorithm for extracting a consistent terrain representation at variable resolution from an HTIN.
    DOI: 10.1023/A:1009708413602

 

 

  • Title: A formal approach to multiresolution modeling
    Authors: L. De Floriani, E. Puppo, P. Magillo
    Year: 1997
    Booktitle: Geometric Modeling: Theory and Practice
    Pages: 302-323
    Publisher: Springer, Berlin, Heidelberg
    Abstract: Multiresolutio
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