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Similarity Graph Comparison Polygon Morphing Character Evaluation Curvature Evaluation Tailor Plumber Computational Topology Reeb Graphs Apparent Contours Dual Meshes Skeletal Structures Reeb Graphs Medial Axis Curvature-based Skeleton Meshing/Remeshing Compression Reconstruction Sharp Feature Enhancement Feature Line Extraction Parameterization of Meshes Computer Aided Design Feature Extraction Feature Recognition&Mapping Free-Form Modelling Product Modelling Distributed Design Past Research Fuzzy Geometry Modelling Parallel Computing for Fuzzy Geometry Parallel Computing for Feature Extraction Others	Graph Comparison A skeletal structure is a one-dimensional representation, which encodes the decomposition of a shape into relevant parts that may have either a geometric or an application-dependent meaning. The shape comparison approach based on a graph matching technique allows a structured process for identifying matched areas on the input objects so that the matching results are intuitive and visually meaningful. View list of related publications Polygon Morphing The first step in polygon morphing consists in automatically finding on the source and target polygons couples of corresponding vertices to guide the blend. We tried to solve this problem through a morphological characterization of the shape. An approximated skeleton is suggested for coding the shape as a graph of meaningful areas, and the correspondence problem is therefore reduced to a skeleton matching process. The correspondences are found taking into account the global structure of the shapes and also local similarity criteria are used to further refine the matching. View list of related publications Tailor Shape analysis and coding are challenging problems in Computer Vision and Graphics. To characterize a shape we have used the paradigm of Blowing Bubbles: a set of spheres of increasing radius is drawn, whose centers are at each vertex of the mesh, and whose radius represent the scale at which the shape is analyzed. The number of connected components of the intersection curve between each bubble and the mesh gives a first qualitative characterization of the shape in a 3D neighborhood of each vertex. Then geometric properties, such as an approximated curvature estimation, are used to refine the classification and detect specific features like sharp protrusions or wells, mounts or dips, blends or branching parts. View list of related publications Plumber The Plumber algorithm is finalized at the identification of tubular features of 3D objects represented by triangular meshes. Plumber is developed on the basis of the multiscale morphological characterization produced by "Tailor". For each tubular part found at a given scale, its approximated axis and cross sections are determined. The final goal is to segment a 3D model into main bodies and tubular parts and to encode the tube/body connectivity and the spatial arrangement of the tube attachments onto the body. View list of related publications Reeb Graphs The main features of a shape and their configuration are important to devise a surface understanding mechanism that discards irrelevant details without loosing the overall surface structure. Our approach is based on the classical Morse theory and would seem to be suitable for analysing any data that can be modelled as a surface. Through the analysis of the evolution of the contour levels of a surface, we obtain a discrete description which effectively represents the shape. Such a description can be encoded into a topological graph, called a Reeb graph. In particular, the notion of Extended Reeb Graph (ERG), we have introduced, is based on a characterisation strategy that recognizes critical points and areas by evaluating the behaviour of the contour levels on a shape, including also the so-called degenerate configurations. Finally, we have proposed an algorithm for the construction of the ERG extraction both for terrain models and 3D closed surfaces. View list of related publications Apparent Contours An important visibility feature of a smooth object with respect to a direction is its outline (or profile or contour generator), that is the curve on the surface that separates front face regions from the back ones. This curve is correlated both to the view direction and the object embedding; furthermore, it may reflect some of the shape properties. Instead, the apparent contour of a shape is the projection of the outline onto a plane perpendicular to the view direction. By their properties, apparent contours have been extensively studied in computer vision and computer graphics; in particular, they are used for non-photo-realistic and silhouette rendering, camera motion estimation and partial reconstruction of surfaces. Moreover, it has been demonstrated that the knowledge of the apparent contour and its singularities is enough for estimating the genus of the surface. Currently our research efforts are in the direction of adapting to discrete context some theoretical results and studying the evolution of the apparent contour of a shape when the view direction changes with time. View list of related publications Dual Meshes This research focus on duality considering basic relationships between a 2-manifold triangle mesh M and its dual representation M'. The achieved combinatorial properties define a discrete homeomorphism between M and M', and the "dual Laplacian smoothing" which combines the application to the dual mesh M' of well-known smoothing algorithms with an inverse transformation for reconstructing the regularized triangle mesh. The use of M' instead of M exploits a topological mask different from the 1-neighborhood one, related to Laplacian-based algorithms, guaranteeing good results and optimizing storage and computational requirements. View list of related publications Medial Axis An intuitive definition of the skeleton in the continuum was given by Blum in 1967, who described the skeleton by analogy with a fire front which starts at the boundary of the shape and propagates isotropically towards the interior. The medial axis is defined by the locations at which the fire fronts collide. The medial axis, together with the radius function, i.e. the distance from each point on the axis to the nearest point on the boundary, define the medial axis transformation (MAT). The power of this representation is that the shape's boundary and its MAT are equivalent and one can be computed from the other, therefore a two-dimensional object is effectively transformed into a one-dimensional graph-like structure. We have investigated the MAT properties and drawbacks, and developed an approximated MAT for planar shapes for use in matching for polygon blending and surface reconstruction. View list of related publications Curvature-based Skeleton The Multiscale Curvature Evaluation proposed exploited in Tailor, also paved the way to the extraction of a skeletal structure of a triangle mesh starting from high-curvature regions of its surface. Since a high curvature region is usually located at the end of a protrusion, the achieved skeleton strictly reseambles the object shape and, beeing curvature an intrinsic characteristic of the surface, the skeleton is indeed an affine-invariant representation of the object. View list of related publications Compression Here we focus on the lossy compression of manifold triangle meshes. Our approach, called SwingWrapper, performs a retiling of the mesh to be compressed. In the retiled mesh, all the triangles are isosceles and the locations of the vertices are compactly encoded with our new prediction technique, which uses a single correction parameter per vertex. SwingWrapper strives to reach a user-defined output file size rather than to guarantee a given error bound. This makes it particularly useful when transmitting meshes over networks with time and band constraints. View list of related publications Reconstruction This research tackles the problem of creating a triangle mesh out of a data source, which may be in the form of an unorganized point cloud, but also a parametric definition of a manifold. Our contribution in the surface reconstruction context is a sculpturing algorithm which is able to produce boundary representations of solids with through holes. When approximating parametric surfaces, we show how to design a tessellation primitive that is independent of the particular mapping used to describe the surface. Moreover, we show how to create both isotropic and anisotropic meshes through our triangulation approach endowed with a remeshing strategy. View list of related publications Sharp Feature Enhancement This research studies the 3D "aliasing" of triangle meshes obtained by feature-insensitive samplings. Our contribution is a new Edge-Sharpener filter which identifies the aliased regions and performs a local refinement. Information in the neighborhood is used to sharpen the alised regions, so that the processed mesh better reflects the sharp features of the original model. Experiments shown that the distortion introduced by the SwingWrapper remeshing-based compressor can be reduced down to a fifth by executing Edge-Sharpener after decompression, with no additional information. View list of related publications Feature Line Extraction Given an object digitized as sequences of scan lines, we propose an approach to the extraction of feature lines and object segmentation based on a multi-resolution representation and analysis of the scan data. First, the scan lines are represented using a multi-resolution model which provides a flexible and useful reorganization of the data for simplification purposes and especially for the classification of points according to their level of detail, or scale. Then, scan lines are analyzed from a geometrical point of view in order to decompose each profile into basic patterns which identify 2D features of the profile. Merging the scale and geometric classification, 3D feature lines of the digitized object are reconstructed tracking patterns of similar shape across profiles. Finally, a segmentation is achieved which gives a form-feature oriented view of the digitized data. The proposed approach provides a computationally light solution to the simplification of large models and to the segmentation of object digitized as sequences of scan lines, but it can be applied to a wider range of digitized data. View list of related publications FreeForm Modelling Free-form modelling is investigated with respect to some CAD application fields, from the traditional mechanical engineering one to the aesthetic design. In particular, the research focuses on the extension of the feature-concept to the free-form domain, where the freedom of the possible defined shapes and alternatives makes hard to define a proper classification and the insertion of a feature consists in a deformation of the surface. Whereas in the mechanical domain few numerical parameters are sufficient to instantiate a specific feature element; in free-form modelling parameters must be higher geometric level entities (e.g. curves) in order to allow for the feature shape specification. A taxonomy of free-form features in the aesthetic design has been proposed and prototypes are under development. The feature-based approach is a high semantic level methodology which is independent of the underlying geometry. Together with an application to the de-facto standard representation by NURBS, the subdivision surface technique is also explored as an alternative. When NURBS surfaces are adopted to represent the geometry, the deformation process defined by the feature curvilinear parameters has been obtained through a mechanical model based on the Density Force Method. In case of subdivision surface, an algorithm to perform generalised sweep operations (Sweep-like Features), lead by a profile section propagating along a directrix, has been implemented. View list of related publications
	Developed by M.Mortara and F.Robbiano ( smg@ge.imati.cnr.it )