Paola Magillo
Professore Associato
Indirizzo  Via Dodecaneso, 35  16146 Genova 

Ufficio  Valletta Puggia  305 
Telefono ufficio  (+39) 010353  6705 
Fax  (+39) 010353  6699 
Pagina personale  https://person.dibris.unige.it/magillopaola/ 
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 4valued combinatorial coordinate system
Authors: Comic, Lidija; Magillo, Paola
Year: 2018
Journal: Information Sciences
Abstract: A 3D binary image I is called wellcomposed if the set of points in the topological boundary of the cubes in I is a 2manifold. Repairing a 3D binary image is a process which produces a well composed image (or a polyhedral complex) from the nonwellcomposed image I.We propose here to repair 3D images by associating the BodyCentered 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 4valued 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: 4352
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: 761785
Abstract: Morse theory offers a natural and mathematicallysound 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): 10.1007/9781493921492 
Title: Morphologicallyaware 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 58, 2013
Book title: Proceedings 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Pages: 244253
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: 339348
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 wellknown 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 realworld 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 imanifolds and the topological structure of the two Morse complexes.
Digital Object Identifier (DOI): 10.1007/9783642411847_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: 7987
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 socalled 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): 10.1007/9783642302381_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: 2842
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): 10.1007/9783642323133_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: 325
Publisher: Springer, Berlin, Heidelberg
Series: MATHEMATICS AND VISUALIZATION
Abstract: We investigate a morphological approach to the analysis and understanding of threedimensional 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 multiresolution 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): 10.1007/9783642216084_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: 565574
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): 10.1007/9783642240850_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: 9095
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 widelyused 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: 183188
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 25, 2010
Book title: Proceedings 18th International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2010)
Pages: 506509
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 kdtree 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 2326, 2010
Book title: Proceedings 20th International Conference on Pattern Recognition (ICPR)
Pages: 9991002
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 twolevel 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 piecewise 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: 3236
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 socalled 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: 817821
Publisher: Springer, US
Digital Object Identifier (DOI): 10.1007/9780387399409_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: 652661
Abstract: Discrete distortion for two and threedimensional 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, areaindependent, 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): 10.1007/9783642041464_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 46, 2009
Book title: Proceedings 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Pages: 187196
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 (ACMGIS)
Place: Irvine, California, USA, Dates: 57 Novembre 2008
Book title: Proceedings 16th ACM International Conference on Geographic Information Systems (ACMGIS).
Pages: 415418
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 2225, 2008
Book title: Proceedings 3rd International Conference on Computer Graphics Theory and Applications (GRAPP)
Pages: 138142
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 multivalued scalar field as a special case. We have implemented the GAUBL into a visualization tool that handles trianglebased 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 2225, 2008
Book title: Proceedings 3rd International Conference on Computer Graphics Theory and Applications (GRAPP)
Pages: 8691
Abstract: We present the PM2Triangle quadtree (PM2Tquadtree), a new hierarchical spatial index for triangle meshes which has been designed for performing spatial queries on trianglebased terrain models. The PM2Tquadtree is based on a recursive space decomposition into square blocks. Here, we propose a highly compact data structure encoding a PM2Tquadtree, which decouples the spatial indexing structure from the combinatorial description of the mesh. We compare the PM2Tquadtree 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 811, 2007. Revised Selected Papers
Book Series: "Communications in Computer and Information Science"
Volume: 21
Pages: 1326
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 floatingpoint 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): 10.1007/9783540896821_2 
Title: MultiScale 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 (ACMGIS)
Place: Seattle, Washington, USA, Dates: November 79, 2007
Book title: Proceedings 15th ACM International Symposium on Advances in Geographic Information Systems
Pages: 2936
Abstract: We propose a new multiscale 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 twolevel 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 morphologybased representation, that we call a Multiscale 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: 1320
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: MultiVMap: a MultiScale Model for Vector Maps
Authors: R. Viania; P. Magillo; E. Puppo; P.A. Ramos
Year: 2006
Journal: GeoInformatica, Volume: 10(3), Pages: 359394
Abstract: MultiVMap 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 multiscale 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/s107070069832y 
Title: LevelofDetail 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: 334344
Abstract: Levelofdetail (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: MultiScale Geographic Maps
Authors: R. Viania; P. Magillo; E. Puppo
Year: 2005
Book title: Advances in Multiresolution for Geometric Modelling
Pages: 101115
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 multiscale model that supports efficient retrieval of maps at different scales, possibly variable through the domain.
Digital Object Identifier (DOI): 10.1007/3540268081_6 
Title: Encoding LevelOfDetail Tetrahedral Meshes
Authors: N.Sokolovky; E.Danovaro; L.De Floriani; P. Magillo
Year: 2005
Book title: Advances in Multiresolution for Geometric Modelling
Pages: 89100
Abstract: LevelOfDetail (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 ddimensional simplicial meshes, called a MultiTessellation (MT), which consists of a partially ordered set of mesh updates. Here, we consider an instance of the MT for tetrahedral meshes, called a HalfEdge MT, which is built through a common simplification operation, halfedge collapse. We discuss two compact encodings for a HalfEdge MT, based on alternative ways to represent the partial order.
Digital Object Identifier (DOI): 10.1007/3540268081_5 
Title: The HalfEdge Tree: A Compact Data Structure for LevelofDetail 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 1317, 2005
Book title: Proceedings of SMI 2005  International Conference on Shape Modeling and Applications
Pages: 334339
Abstract: We propose a new data structure for the compact encoding of a levelof detail (LOD) model of a threedimensional scalar field based on unstructured tetrahedral meshes. Such data structure, called a halfedge tree (HET), is built through the iterative application of a halfedge 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 multiresolution topological representation for nonmanifold meshes
Authors: L. De Floriani; P. Magillo; E. Puppo; D. Sobrero
Year: 2004
Journal: ComputerAided Design, Volume: 36 (2), Pages: 141159
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 nonmanifold topology, at different levels of detail. First, we describe a multiresolution model, that we call a nonmanifold multitessellation (NMT), and 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 simplifying simplicial meshes based on vertexpair contraction, and we describe a compact data structure for encoding such a model. We also propose a new data structure for twodimensional 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/S00104485(03)000587 
Title: Encoding LevelOfDetail Tetrahedral Meshes through the HalfEdge 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 1517, 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: 2945
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 LevelOfDetail (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 stateofthe art visualization techniques in a system for the interactive visualization of threedimensional 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: Trianglebased Multiresolution Models for Height Fields
Authors: L. De Floriani; P. Magillo
Year: 2003
Book title: Curve and Surface Fitting: SaintMalo 2002
Pages: 97106
Abstract: Largesize data sets describing height elds (e.g., terrains) can be handled with multiresolution models. We analyze and compare two multiresolution 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 variableresolution 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: 709728
Abstract: Several environment applications require the computation of visibility information on a terrain. Examples are optimal placement of observation points, lineofsight 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: LevelOfDetail (LOD) modeling of scalar fields through topologydriven 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 multitessellations: 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: 239256
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 MultiTessellation (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: 10.1007/9781461511779_17 
Title: Morphologydriven 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 78, 2003
Book title: Proceedings 11th ACM Workshop on Advances in Geographic Information Systems  ACMGIS03
Pages: 6370
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: 363417
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 meshbased 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 userdefined 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): 10.1007/9783662043882 of book, and 10.1007/9783662043882_13 of this chapter. 
Title: Regular and Irregular MultiResolution Terrain Models: a Comparison
Authors: De Floriani L.; Magillo P.
Year: 2002
Conference: 10th ACM International Symposium on Advances in Geographic Information Systems (ACMGIS'02)
Place: McLean, Virginia, USA, Dates: November 89, 2002
Book title: Proceedings 10th ACM International Symposium on Advances in Geographic Information Systems (ACMGIS'02)
Pages: 143148
Abstract: The paper deals with the problem of modeling largesize terrain data sets. To this aim, we consider multiresolution models based on triangle meshes. We analyze and compare two multiresolution terrain models based on regular and irregular meshes. The two models are viewed as instances of a common multiresolution model, that we call a multiresolution 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 variableresolution terrain representations.
Digital Object Identifier (DOI): 10.1145/585147.585178 
Title: A multiresolution topological representation for nonmanifold 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 1721, 2002
Book title: Proceedings 7th ACM Symposium on Solid Modeling and Applications (SMA '02).
Pages: 159170
Abstract: We address the problem of representing and processing nonregular, nonmanifold twodimensional simplicial meshes, that we call trianglesegment meshes, at different levels of detail. Such meshes are used to describe spatial objects consisting of parts of mixed dimensions, and with a nonmanifold topology. First, we describe a multiresolution model for nonregular, nonmanifold meshes, that we call a Nonmanifold MultiTessellation (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 vertexpair contraction, and we describe a compact data structure for encoding it. We also propose a new data structure for trianglesegment 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 vertexbased 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: 129149
Abstract: In this paper, we consider the problem of representing a multiresolution geometric model, called a Simplicial MultiComplex (SMC), in a compact way. We present encoding schemes for both twoan 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 generalpurpose data structure for a SMC, but also with respect to just encoding the complex at the maximum resolution.
Digital Object Identifier (DOI): 10.1007/3540455760_8 
Title: NonManifold MultiTessellation: 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: 654664
Abstract: This paper describes preliminary research work aimed at obtaining a multilevel iconic representation of 3D objects from geometric meshes. A singlelevel iconic model describes an object through parts of different dimensions connected to form a hypergraph. The multilevel iconic model, called Nonmanifold MultiTessellation, incorporates decompositions of an object into parts at different levels of abstraction, and permits to refine an iconic representation selectively.
Digital Object Identifier (DOI): 10.1007/3540451293_60 
Title: Multiresolution Modeling of ThreeDimensional Shapes
Authors: L. De Floriani; P. Magillo
Year: 2001
Book title: 3D Synthetic Environment Reconstruction
Chapter 2.
Pages: 3559
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 threedimensional 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): 10.1007/9781441987563_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: 345364
Abstract: In this paper, we consider trianglebased twodimensional multiresolution complexes, called MultiTriangulations (MTs), constructed based on a vertexremoval 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: 10.1007/3540477241_18
Before year 2000

Title: Online 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 37
Book title: Proceedings 15th International Conference on Pattern Recognition (ICPR)
Pages: 105108
Abstract: We present a new data structure, called the MultiSculpture 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 online extraction of a shape representation at a userdefined 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: 6788
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 errorbased 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: 287315
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 highlevel operations (e.g., flyover 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 viewdependent multiresolution on a clientserver architecture
Authors: De Floriani L.; Magillo P.; Morando F.; Puppo E.
Year: 2000
Journal: ComputerAided Design
Volume: 32(13)
Special Issue on Multiresolution Geometric Models
Pages: 805823
Abstract: We consider the problem of transmitting huge triangle meshes in the context of a Weblike clientserver 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 vertexbased multiresolution model, which is a special instance of the MultiTriangulation (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 MultiTriangulation can be a key Web technology for triangle mesh manipulation.
Digital Object Identifier (DOI): 10.1016/S00104485(00)000701 
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: 1517 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 GeoBased Applications, Place: Ascona, Switzerland
Dates: May 2226, 2000
Book title: Proc. Int. Workshop on Emerging Technologies for GeoBased Applications
Pages: 133151 
Title: TriangleBased Surface Models
Authors: L. De Floriani; S. Bussi; P. Magillo
Year: 2000
Book title: Intelligent Systems and Robotics
Pages: 340373
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: 48 September 2000
Book title: Proceedings 11th International Workshop on Database and Expert Systems and Applications
Pages: 894898
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 multicomplexes
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: 3351
Abstract: The Simplicial MultiComplex (SMC) is a general multiresolution model for representing kdimensional 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 levelofdetail 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): 10.1007/3540484825_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: 543556 
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: 333388
Publisher: Elsevier Science  North Holland
Digital Object Identifier (DOI): 10.1016/B9780444825377/500085 
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: 318
Abstract: This paper introduces a dimensionindependent multiresolution model of a shape, called the MultiComplex (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 variableresolution 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): 10.1007/3540491260_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 67,
Year: 1998
Pages: 145150
Abstract:
DOI: 10.1145/288692.288718
 Title: Efficient implementation of MultiTriangulations
Authors: L. De Floriani, P. Magillo, E. Puppo
Year: 1998
Booktitle: Proceedings IEEE Visualization '98
Place: Research Triangle Park, NC, USA, Dates: October 1823,
Pages: 4350.
Abstract: Multitriangulation (MT) is a general framework for managing the levelofdetail 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 tradeoffs 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 1620,
Pages: 389391
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: 351386
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 1314
Pages: 1519
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: 219250
Abstract: Hierarchical terrain models provide a multiresolution description of a topographic surface based on a nested partition of the domain. The treelike 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: 302323
Publisher: Springer, Berlin, Heidelberg
Abstract: Multiresolutio