Marco Attene

Mesh Segmentation - A Comparative Study

Mesh segmentation has become an important component in many applications in computer graphics. In the last several years, many algorithms have been proposed in this growing area, offering a diversity of methods and various evaluation criteria. This paper provides a comparative study of some of the latest algorithms and results, along several axes. We evaluate only algorithms whose code is available to us, and thus it is not a comprehensive study. Yet, it sheds some light on the vital properties of the methods and on the challenges that future algorithms should face

ReMESH: An Interactive Environment to Edit and Repair Triangle Meshes

Polygonal meshes obtained from acquisition of real-world objects may easily exhibit topological or geometrical defects, which often prevent subsequent processing and analysis to provide satisfactory results. This paper describes the foundations of ReMESH, a user-friendly graphical tool which incorporates several mesh-repairing features, and allows to perform a kind of low-level editing which is often missing in most existing software packages. We show how state-of-the-art techniques have been adapted and extended to form an intuitive and integrated environment, and introduce some optimizations and novel ideas that make ReMESH particularly efficient. The main application in which the tool proves to be extremely useful is the post-processing of scanned surface models. In this context, ReMESH represents a valid support for the production of certified quality meshes

Automatic Surface Reconstruction from Point Sets in Space

In this paper an algorithm is proposed that takes as input a generic set of unorganized points, sampled on a real object, and returns a closed interpolating surface. Specifically, this method generates a closed 2‐manifold surface made of triangular faces, without limitations on the shape or genus of the original solid. The reconstruction method is based on generation of the Delaunay tetrahedralization of the point set, followed by a sculpturing process constrained to particular criteria. The main applications of this tool are in medical analysis and in reverse engineering areas. It is possible, for example, to reconstruct anatomical parts starting from surveys based on TACs or magnetic resonance.

Shape understanding by contour-driven retiling

Given a triangle mesh representing a closed manifold surface of arbitrary genus, a method is proposed to automatically extract the Reeb graph of the manifold with respect to the height function. The method is based on a slicing strategy that traces contours while inserting them directly in the mesh as constraints. Critical areas, which identify isolated and non-isolated critical points of the surface, are recognized and coded in the extended Reeb graph (ERG). The remeshing strategy guarantees that topological features are correctly maintained in the graph, and the tiling of ERG nodes reproduces the original shape at a minimal, but topologically correct, geometric level.

Sharpen&Bend: recovering curved sharp edges in triangle meshes produced by feature-insensitive sampling

Various acquisition, analysis, visualization, and compression approaches sample surfaces of 3D shapes in a uniform fashion without any attempt to align the samples with sharp edges or to adapt the sampling density to the surface curvature. Consequently, triangle meshes that interpolate these samples usually chamfer sharp features and exhibit a relatively large error in their vicinity. We present two new filters that improve the quality of these resampled models. EdgeSharpener restores the sharp edges by splitting the chamfer edges and forcing the new vertices to lie on intersections of planes extending the smooth surfaces incident upon these chamfers. Bender refines the resulting triangle mesh using an interpolating subdivision scheme that preserves the sharpness of the recovered sharp edges while bending their polyline approximations into smooth curves. A combined Sharpen&Bend postprocessing significantly reduces the error produced by feature-insensitive sampling processes. For example, we have observed that the mean-squared distortion introduced by the SwingWrapper remeshing-based compressor can often be reduced by 80 percent executing EdgeSharpener alone after decompression. For models with curved regions, this error may be further reduced by an additional 60 percent if we follow the EdgeSharpening phase by Bender.

Semantic annotation of 3D surface meshes based on feature characterization

In this paper we describe the main aspects of a system to perform non-trivial segmentations of 3D surface meshes and to annotate the detected parts through concepts expressed by an ontology. Each part is connected to an instance in a knowledge base to ease the retrieval process in a semantics-based context. Through an intuitive interface, users create such instances by simply selecting proper classes in the ontology; attributes and relations with other instances can be computed automatically based on a customizable analysis of the underlying topology and geometry of the parts.

Edge-sharpener: recovering sharp features in triangulations of non-adaptively re-meshed surfaces

3D scanners, iso-surface extraction procedures, and several recent geometric compression schemes sample surfaces of 3D shapes in a regular fashion, without any attempt to align the samples with the sharp edges and corners of the original shape. Consequently, the interpolating triangle meshes chamfer these sharp features and thus exhibit significant errors. The new Edge-Sharpener filter introduced here identifies the chamfer edges and subdivides them and their incident triangles by inserting new vertices and by forcing these vertices to lie on intersections of planes that locally approximate the smooth surfaces that meet at these sharp features. This post-processing significantly reduces the error produced by the initial sampling process. For example, we have observed that the L2 error introduced by the Swing Wrapper9 remeshing-based compressor can be reduced down to a fifth by executing Edge-Sharpener after decompression, with no additional information.

SwingWrapper: Retiling triangle meshes for better edgebreaker compression

We focus on the lossy compression of manifold triangle meshes. Our SwingWrapper approach partitions the surface of an original mesh <i>M</i> into simply connected regions, called <i>triangloids</i>. From these, we generate a new mesh <i>M</i>^′. Each triangle of <i>M</i>^′ is an approximation of a triangloid of <i>M</i>. By construction, the connectivity of <i>M</i>^′ is fairly regular and can be compressed to less than a bit per triangle using EdgeBreaker or one of the other recently developed schemes. The locations of the vertices of <i>M</i>^′ 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. For a variety of popular models, a rate of 0.4 bits/triangle yields an <i>L</i>² distortion of about 0.01% of the bounding box diagonal. The proposed solution may also be used to encode crude meshes for adaptive transmission or for controlling subdivision surfaces.

Thesaurus-based 3D Object Retrieval with Part-in-Whole Matching

Research in content-based 3D retrieval has already started, and several approaches have been proposed which use in different manner a similarity assessment to match the shape of the query against the shape of the objects in the database. However, the success of these solutions are far from the success obtained by their textual counterparts.A major drawback of most existing 3D retrieval solutions is their inability to support partial queries, that is, a query which does not need to be formulated by specifying a whole query shape, but just a part of it, for example a detail of its overall shape, just like documents are retrieved by specifying words and not whole texts. Recently, researchers have focused their investigation on 3D retrieval which is solved by partial shape matching. However, at the extent of our knowledge, there is still no 3D search engine that provides an indexing of the 3D models based on all the interesting subparts of the models.In this paper we present a novel approach to 3D shape retrieval that uses a collection-aware shape decomposition combined with a shape thesaurus and inverted indexes to describe and retrieve 3D models using part-in-whole matching. The proposed method clusters similar segments obtained trough a multilevel decomposition of models, constructing from such partition the shape thesaurus. Then, to retrieve a model containing a sub-part similar to a given query, instead of looking on a large set of subparts or executing partial matching between the query and all models in the collection, we just perform a fast global matching between the query and the few entries in the thesaurus. With this technique we overcame the time complexity problems associated with partial queries in large collections.

Hierarchical convex approximation of 3D shapes for fast region selection

Given a 3D solid model S represented by a tetrahedral mesh, we describe a novel algorithm to compute a hierarchy of convex polyhedra that tightly enclose S. The hierarchy can be browsed at interactive speed on a modern PC and it is useful for implementing an intuitive feature selection paradigm for 3D editing environments. Convex parts often coincide with perceptually relevant shape components and, for their identification, existing methods rely on the boundary surface only. In contrast, we show that the notion of part concavity can be expressed and implemented more intuitively and efficiently by exploiting a tetrahedrization of the shape volume. The method proposed is completely automatic, and generates a tree of convex polyhedra in which the root is the convex hull of the whole shape, and the leaves are the tetrahedra of the input mesh. The algorithm proceeds bottom‐up by hierarchically clustering tetrahedra into nearly convex aggregations, and the whole process is significantly fast. We prove that, in the average case, for a mesh of n tetrahedra O(n log2 n) operations are sufficient to compute the whole tree.