Results 1  10
of
22
Hierarchical mesh segmentation based on fitting primitives
 THE VISUAL COMPUTER
, 2006
"... In this paper we describe a hierarchical face clustering algorithm for triangle meshes based on fitting primitives belonging to an arbitrary set. The method proposed is completely automatic, and generates a binary tree of clusters, each of which fitted by one of the primitives employed. Initially, e ..."
Abstract

Cited by 70 (11 self)
 Add to MetaCart
In this paper we describe a hierarchical face clustering algorithm for triangle meshes based on fitting primitives belonging to an arbitrary set. The method proposed is completely automatic, and generates a binary tree of clusters, each of which fitted by one of the primitives employed. Initially, each triangle represents a single cluster; at every iteration, all the pairs of adjacent clusters are considered, and the one that can be better approximated by one of the primitives forms a new single cluster. The approximation error is evaluated using the same metric for all the primitives, so that it makes sense to choose which is the most suitable primitive to approximate the set of triangles in a cluster. Based on this approach, we implemented a prototype which uses planes, spheres and cylinders, and have experimented that for meshes made of 100k faces, the whole binary tree of clusters can be built in about 8 seconds on a standard PC. The framework here described has natural application in reverse engineering processes, but it has been also tested for surface denosing, feature recovery and character skinning.
Curveskeleton properties, applications, and algorithms
 IEEE Transactions on Visualization and Computer Graphics
, 2007
"... Curveskeletons are thinned 1D representations of 3D objects useful for many visualization tasks including virtual navigation, reducedmodel formulation, visualization improvement, animation, etc. There are many algorithms in the literature describing extraction methodologies for different applicati ..."
Abstract

Cited by 69 (3 self)
 Add to MetaCart
Curveskeletons are thinned 1D representations of 3D objects useful for many visualization tasks including virtual navigation, reducedmodel formulation, visualization improvement, animation, etc. There are many algorithms in the literature describing extraction methodologies for different applications; however, it is unclear how general and robust they are. In this paper, we provide an overview of many curveskeleton applications and compile a set of desired properties of such representations. We also give a taxonomy of methods and analyze the advantages and drawbacks of each class of algorithms.
Computational Methods for Understanding 3D Shapes
, 2005
"... Understanding shapes has been a challenging issue for many years, firstly motivated by computer vision and more recently by many complex applications in diverse fields, such as medical imaging, animation, or product modeling. Moreover, the results achieved so far prompted a significant amount of wor ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
Understanding shapes has been a challenging issue for many years, firstly motivated by computer vision and more recently by many complex applications in diverse fields, such as medical imaging, animation, or product modeling. Moreover, the results achieved so far prompted a significant amount of work in very innovative research fields such as semanticbased knowledge systems dealing with multidimensional media. This paper describes the historical evolvement of the research done at IMATIGE / CNR in the field of shape understanding. The most significant methods developed are classified and described along with some results, and discussed with respect to applications. Open issues are outlined along with future research plans.
Point cloud skeletons via laplacianbased contraction
 In Proc. Conf. on Shape Modeling and Appl
, 2010
"... Abstract—We present an algorithm for curve skeleton extraction via Laplacianbased contraction. Our algorithm can be applied to surfaces with boundaries, polygon soups, and point clouds. We develop a contraction operation that is designed to work on generalized discrete geometry data, particularly p ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
Abstract—We present an algorithm for curve skeleton extraction via Laplacianbased contraction. Our algorithm can be applied to surfaces with boundaries, polygon soups, and point clouds. We develop a contraction operation that is designed to work on generalized discrete geometry data, particularly point clouds, via local Delaunay triangulation and topological thinning. Our approach is robust to noise and can handle moderate amounts of missing data, allowing skeletonbased manipulation of point clouds without explicit surface reconstruction. By avoiding explicit reconstruction, we are able to perform skeletondriven topology repair of acquired point clouds in the presence of large amounts of missing data. In such cases, automatic surface reconstruction schemes tend to produce incorrect surface topology. We show that the curve skeletons we extract provide an intuitive and easytomanipulate structure for effective topology modification, leading to more faithful surface reconstruction. Keywordscurve skeleton; point cloud; Laplacian; contraction; topology repair; surface reconstruction I.
3D mesh decomposition using reeb graphs
 IMAGE VISION COMPUT
, 2009
"... Decomposition of complex 3D objects into simpler subparts is a challenging research subject with relevant outcomes for several application contexts. In this paper, an approach is proposed for decomposition of 3D objects based on Reebgraphs. The approach is motivated by perceptual principles and su ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Decomposition of complex 3D objects into simpler subparts is a challenging research subject with relevant outcomes for several application contexts. In this paper, an approach is proposed for decomposition of 3D objects based on Reebgraphs. The approach is motivated by perceptual principles and supports identification of salient object protrusions. Experimental results are presented to demonstrate the effectiveness of the proposed approach with respect to different solutions appeared in the literature, and with reference to groundtruth data obtained by manual decomposition of 3D objects.
A Randomized O(m log m) Time Algorithm for Computing Reeb Graphs of Arbitrary Simplicial Complexes
"... Given a continuous scalar field f: X → IR where X is a topological space, a level set of f is a set {x ∈ X: f(x) = α} for some value α ∈ IR. The level sets of f can be subdivided into connected components. As α changes continuously, the connected components in the level sets appear, disappear, spli ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Given a continuous scalar field f: X → IR where X is a topological space, a level set of f is a set {x ∈ X: f(x) = α} for some value α ∈ IR. The level sets of f can be subdivided into connected components. As α changes continuously, the connected components in the level sets appear, disappear, split and merge. The Reeb graph of f encodes these changes in connected components of level sets. It provides a simple yet meaningful abstraction of the input domain. As such, it has been used in a range of applications in fields such as graphics and scientific visualization. In this paper, we present the first subquadratic algorithm to compute the Reeb graph for a function on an arbitrary simplicial complex K. Our algorithm is randomized with an expected running time O(m log n), where m is the size of the 2skeleton of K (i.e, total number of vertices, edges and triangles), and n is the number of vertices. This presents a significant improvement over the previous Θ(mn) time complexity for arbitrary complex, matches (although in expectation only) the best known result for the special case of 2manifolds, and is faster than current algorithms for any other special cases (e.g, 3manifolds). Our algorithm is also very simple to implement. Preliminary experimental results show that it performs well in practice.
Horizontal Decomposition of Triangulated Solids for the Simulation of Dipcoating Processes
"... In dipcoating processes a threedimensional object, e.g. an entire car body, is dipped into a liquid bath. In order to simulate such processes, the space surrounding the object is decomposed into the socalled flow volumes, for which each intersection with a horizontal plane is connected. At any ti ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
In dipcoating processes a threedimensional object, e.g. an entire car body, is dipped into a liquid bath. In order to simulate such processes, the space surrounding the object is decomposed into the socalled flow volumes, for which each intersection with a horizontal plane is connected. At any time the liquid’s surface then has a unique level within such a flow volume, which greatly simplifies the simulation of the liquid. The decomposition into flow volumes corresponds to the Reeb graph of the object’s exterior (considered as 3manifold with boundary) with respect to the height function. This article presents an algorithm which computes this decomposition for an object represented as oriented triangular boundary mesh. First critical vertices of the surface are identified, which include the upper and lower ends of flow volumes. Using local information about horizontal intersection planes near the critical points, a sweep plane algorithm then constructs the volume decomposition in a second step. It is shown that the method can deal with realistic data. 1
Topologically enhanced slicing of MLS surfaces
 ASME Journal of Computing and Information Science in Engineering
, 2011
"... Growing use of massive scan data in various engineering applications has necessitated research on pointset surfaces. A pointset surface is a continuous surface defined directly with a set of discrete points. This paper presents a new approach that extends our earlier work on slicing pointset surf ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Growing use of massive scan data in various engineering applications has necessitated research on pointset surfaces. A pointset surface is a continuous surface defined directly with a set of discrete points. This paper presents a new approach that extends our earlier work on slicing pointset surfaces into planar contours for rapid prototyping usage. This extended approach can decompose a pointset surface into slices with guaranteed topology. Such topological guarantee stems from the use of Morse theory based topological analysis of the slicing operation. The Morse function for slicing is a height function restricted to the pointset surface, an implicitly defined moving leastsquares (MLS) surface. We introduce a Lagrangian multiplier formulation for critical point identification from the restricted surface. Integral lines are constructed to form MorseSmale complex and the enhanced Reeb graph. This graph is then used to provide seed points for forming slicing contours, with the guarantee that the sliced model has the same topology as the input pointset surface. The extension of this approach to degenerate functions on pointset surface is also discussed.
Structural descriptors for 3d shapes
 ContentBased Retrieval, number 06171 in Dagstuhl Seminar Proceedings. Internationales Begegnungs und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl
, 2006
"... Assessing the similarity among 3D shapes is a challenging research topic, and effective shape descriptions have to be devised in order to support the matching process. There is a growing consensus that shapes are recognized and coded mentally in terms of relevant parts and their spatial configuratio ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Assessing the similarity among 3D shapes is a challenging research topic, and effective shape descriptions have to be devised in order to support the matching process. There is a growing consensus that shapes are recognized and coded mentally in terms of relevant parts and their spatial configuration, or structure. The presentation will discuss the definition and use of structural descriptions for assessing shape similarity. The idea is to define a shape description framework based on results of differential topology which deal with the description of shapes by means of the properties of one, or more, realvalued functions defined over the shape. Studying these properties, several topological descriptions of the shape can be defined, which may also encode different geometric and morphological attributes that globally and locally describe the shape. Examples and results will be discussed and ongoing work outlined. 1