Local and global geometric methods for analysis, interrogation, reconstruction, modification and design of shape

Wolter, Franz-Erich; Friese, Karl-Ingo

doi:10.1109/cgi.2000.852329

Cited by 22 publications

(17 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on the theory developed in [35] we will explain the techniques from the point of view of its application on images, although they can be used for more general shapes also. See [47] and [37,38] for an introduction to the theory of Laplace spectra in general shape matching.…”

Section: Introductionmentioning

confidence: 99%

Laplace spectra as fingerprints for image recognition

Peinecke

Wolter

Reuter

2007

Computer-Aided Design

View full text Add to dashboard Cite

In the area of image retrieval from data bases and for copyright protection of large image collections there is a growing demand for unique but easily computable fingerprints for images. These fingerprints can be used to quickly identify every image within a larger set of possibly similar images. This paper introduces a novel method to automatically obtain such fingerprints from an image. It is based on a reinterpretation of an image as a Riemannian manifold. This representation is feasible for gray value images and color images. We discuss the use of the spectrum of eigenvalues of different variants of the Laplace operator as a fingerprint and show the usability of this approach in several use cases. Contrary to existing works in this area we do not only use the discrete Laplacian, but also with a particular emphasis the underlying continuous operator. This allows better results in comparing the resulting spectra and deeper insights in the problems arising. We show how the well known discrete Laplacian is related to the continuous Laplace-Beltrami operator. Furthermore, we introduce the new concept of solid height functions to overcome some potential limitations of the method.

show abstract

Section: Introductionmentioning

confidence: 99%

Laplace spectra as fingerprints for image recognition

Peinecke

Wolter

Reuter

2007

Computer-Aided Design

View full text Add to dashboard Cite

show abstract

“…for relatively small wrinkles). In terms of computing geodesic curves on a surface [12], several researchers have studied this problem in other contexts earlier, for example, refer to [13,14,15,16]. We describe the basics and our algorithm for these computations next.…”

Section: Parametric Wrinkle Operatormentioning

confidence: 99%

“…While it is possible to solve this system of two equations numerically [13,16], we used a simple iterative algorithm to generate geodesics. The algorithm computes an approximate geodesic by starting to move orthogonal to the boundary curve C, taking tiny steps along the geodesic at each point.…”

Section: Parametric Wrinkle Operatormentioning

confidence: 99%

Modeling Wrinkles on Smooth Surfaces for Footwear Design

Fu¹,

Joneja²,

Tang³

2004

Computer-Aided Design and Applications

View full text Add to dashboard Cite

We describe two new shape operators that superimpose wrinkles on top of a smooth NURBS surface. Previous research studying wrinkles focused mostly on cloth modeling or in animations, which are driven more by visual realism, but allow large elastic deformations. Our operators generate wrinkle-shaped deformations in a region of a smooth surface along a given boundary based on a few basic parametric inputs such as wrinkle magnitude and extent (these terms will be defined in the paper). The essential geometric transformation to map the smooth surface to a wrinkled one will be defined purely in terms of the geometry of the surface and the input parameters. Our model is based on two surface properties: geodesic offsets and surface energy. Practical implementation of the operators is discussed, and examples presented. Finally, the motivation for the operators will be given through their application in the computer-aided design and manufacture of footwear.

show abstract

“…In Euclidean space, medial axis transformations [34], [66], [20] and generalized Euclidean distance transformations [19], [41], [46] are widely studied for digital images and volume data. For spaces with non-Euclidean metrics, the domain of Voronoi diagrams has also been extended to spheres [4], [50], polyhedral surfaces [49], [30], [67], parametric surfaces [33], hyperbolic spaces [53] and the general Riemannian manifolds [65], [36], [52]. For detailed surveys, the reader is referred to [5], [51] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces

Liu

Chen

Tang

2011

IEEE Trans. Pattern Anal. Mach. Intell.

View full text Add to dashboard Cite

Abstract-In the research of computer vision and machine perception, three-dimensional objects are usually represented by 2-manifold triangular meshes M. In this paper, we present practical and efficient algorithms to construct iso-contours, bisectors and Voronoi diagrams of point sites on M, based on an exact geodesic metric. Compared to Euclidean metric spaces, the Voronoi diagrams on M exhibit many special properties that fail all the existing Euclidean Voronoi algorithms. To provide practical algorithms for constructing geodesic-metric-based Voronoi diagrams on M, this paper studies the analytic structure of iso-contours, bisectors and Voronoi diagrams on M. After a necessary preprocessing of model M, practical algorithms are proposed for quickly obtaining full information about iso-contours, bisectors and Voronoi diagrams on M. The complexity of the construction algorithms is also analyzed. Finally three interesting applications, surface sampling and reconstruction, 3D skeleton extraction and point pattern analysis are presented that show the potential power of the proposed algorithms in pattern analysis.

show abstract

Local and global geometric methods for analysis, interrogation, reconstruction, modification and design of shape

Cited by 22 publications

References 6 publications

Laplace spectra as fingerprints for image recognition

Laplace spectra as fingerprints for image recognition

Modeling Wrinkles on Smooth Surfaces for Footwear Design

Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces

Contact Info

Product

Resources

About