Riccardo Scateni

A modified look-up table for implicit disambiguation of Marching Cubes

A new triangulation scheme for the Marching Cubes algorithm is proposed. The scheme allows the extraction of continuous isosurfaces from volumetric data without the need to use disamgiguation techniques.

Discretized Marching Cubes

Since the introduction of standard techniques for isosurface extraction from volumetric datasets, one of the hardest problems has been to reduce the number of triangles (or polygons) generated. The paper presents an algorithm that considerably reduces the number of polygons generated by a Marching Cubes-like scheme (W. Lorensen and H. Cline, 1987) without excessively increasing the overall computational complexity. The algorithm assumes discretization of the dataset space and replaces cell edge interpolation by midpoint selection. Under these assumptions, the extracted surfaces are composed of polygons lying within a finite number of incidences, thus allowing simple merging of the output facets into large coplanar polygons. An experimental evaluation of the proposed approach on datasets related to biomedical imaging and chemical modelling is reported.<<ETX>>

PolyCut: monotone graph-cuts for PolyCube base-complex construction

PolyCubes, or orthogonal polyhedra, are useful as parameterization base-complexes for various operations in computer graphics. However, computing quality PolyCube base-complexes for general shapes, providing a good trade-off between mapping distortion and singularity counts, remains a challenge. Our work improves on the state-of-the-art in PolyCube computation by adopting a graph-cut inspired approach. We observe that, given an arbitrary input mesh, the computation of a suitable PolyCube base-complex can be formulated as associating, or labeling, each input mesh triangle with one of six signed principal axis directions. Most of the criteria for a desirable PolyCube labeling can be satisfied using a multi-label graph-cut optimization with suitable local unary and pairwise terms. However, the highly constrained nature of PolyCubes, imposed by the need to align each chart with one of the principal axes, enforces additional global constraints that the labeling must satisfy. To enforce these constraints, we develop a constrained discrete optimization technique, PolyCut, which embeds a graph-cut multi-label optimization within a hill-climbing local search framework that looks for solutions that minimize the cut energy while satisfying the global constraints. We further optimize our generated PolyCube base-complexes through a combination of distortion-minimizing deformation, followed by a labeling update and a final PolyCube parameterization step. Our PolyCut formulation captures the desired properties of a PolyCube base-complex, balancing parameterization distortion against singularity count, and produces demonstrably better PolyCube base-complexes then previous work.

Extraction of the Quad Layout of a Triangle Mesh Guided by Its Curve Skeleton

Starting from the triangle mesh of a digital shape, that is, mainly an articulated object, we produce a coarse quad layout that can be used in character modeling and animation. Our quad layout follows the intrinsic object structure described by its curve skeleton; it contains few irregular vertices of low degree; it can be immediately refined into a semiregular quad mesh; it provides a structured domain for UV mapping and parametrization. Our method is fast, one-click, and does not require any parameter setting. The user can steer and refine the process through simple interactive tools during the construction of the quad layout.

Reconstructing the Curve-Skeletons of 3D Shapes Using the Visual Hull

Curve-skeletons are the most important descriptors for shapes, capable of capturing in a synthetic manner the most relevant features. They are useful for many different applications: from shape matching and retrieval, to medical imaging, to animation. This has led, over the years, to the development of several different techniques for extraction, each trying to comply with specific goals. We propose a novel technique which stems from the intuition of reproducing what a human being does to deduce the shape of an object holding it in his or her hand and rotating. To accomplish this, we use the formal definitions of epipolar geometry and visual hull. We show how it is possible to infer the curve-skeleton of a broad class of 3D shapes, along with an estimation of the radii of the maximal inscribed balls, by gathering information about the medial axes of their projections on the image planes of the stereographic vision. It is definitely worth to point out that our method works indifferently on (even unoriented) polygonal meshes, voxel models, and point clouds. Moreover, it is insensitive to noise, pose-invariant, resolution-invariant, and robust when applied to incomplete data sets.

Decreasing isosurface complexity via discrete fitting

Since the introduction of techniques for isosurface extraction from volumetric datasets, one of the hardest problems has been to reduce the number of generated triangles (or polygons). This paper presents an algorithm that considerably reduces the number of triangles generated by a Marching Cubes algorithm, while presenting very close or shorter running times. The algorithm first assumes discretization of the dataset space and replaces cell edge interpolation by midpoint selection. Under these assumptions the extracted surfaces are composed of polygons lying within a finite number of incidences, thus allowing simple merging of the output facets into large coplanar triangular facets. Lastly, the vertices which survived the decimation process are located on their exact positions and normals are computed. An experimental evaluation of the proposed approach on datasets relevant to biomedical imaging and chemical modeling is reported. TEL:: +39 050 593451 EMAIL:: montani@iei.pi.cnr.it

An Iterative Stripification Algorithm Based on Dual Graph Operations

This paper describes the preliminary results obtained using an iterative method for generating a set of triangle strips from a mesh of triangles. The algorithm uses a simple topological operation on the dual graph of the mesh, to generate an initial stripification and iteratively rearrange and decrease the number of strips. Our method is a major improvement of a proposed one originally devised for both static and continuous level-of-detail (CLOD) meshes and retains this feature. The usage of a dynamical identification strategy for the strips allows us to drastically reduce the length of the searching paths in the graph needed for the rearrangement and produce loop-free triangle strips without any further controls and post-processing.

Extracting curve-skeletons from digital shapes using occluding contours

Curve-skeletons are compact and semantically relevant shape descriptors, able to summarise both topology and pose of a wide range of digital objects. Most of the state-of-the-art algorithms for their computation rely on the type of geometric primitives used and sampling frequency. In this paper, we introduce a formally sound and intuitive definition of a curve-skeleton, then we propose a novel method for skeleton extraction that relies on the visual appearance of the shapes. To achieve this result, we inspect the properties of occluding contours, showing how information about the symmetry axes of a 3D shape can be inferred from a small set of its planar projections. The proposed method is fast, insensitive to noise and resolution, capable of working with different shape representations, and easy to implement.

Polycube simplification for coarse layouts of surfaces and volumes

Representing digital objects with structured meshes that embed a coarse block decomposition is a relevant problem in applications like computer animation, physically‐based simulation and Computer Aided Design (CAD). One of the key ingredients to produce coarse block structures is to achieve a good alignment between the mesh singularities (i.e., the corners of each block). In this paper we improve on the polycube‐based meshing pipeline to produce both surface and volumetric coarse block‐structured meshes of general shapes. To this aim we add a new step in the pipeline. Our goal is to optimize the positions of the polycube corners to produce as coarse as possible base complexes. We rely on re‐mapping the positions of the corners on an integer grid and then using integer numerical programming to reach the optimal. To the best of our knowledge this is the first attempt to solve the singularity misalignment problem directly in polycube space. Previous methods for polycube generation did not specifically address this issue. Our corner optimization strategy is efficient and requires a negligible extra running time for the meshing pipeline. In the paper we show that our optimized polycubes produce coarser block structured surface and volumetric meshes if compared with previous approaches. They also induce higher quality hexahedral meshes and are better suited for spline fitting because they reduce the number of splines necessary to cover the domain, thus improving both the efficiency and the overall level of smoothness throughout the volume.

Skeleton-driven adaptive hexahedral meshing of tubular shapes

We propose a novel method for the automatic generation of structured hexahedral meshes of articulated 3D shapes. We recast the complex problem of generating the connectivity of a hexahedral mesh of a general shape into the simpler problem of generating the connectivity of a tubular structure derived from its curve‐skeleton. We also provide volumetric subdivision schemes to nicely adapt the topology of the mesh to the local thickness of tubes, while regularizing per‐element size. Our method is fast, one‐click, easy to reproduce, and it generates structured meshes that better align to the branching structure of the input shape if compared to previous methods for hexa mesh generation.