Topology matching for fully automatic similarity estimation of 3D shapes

Hilaga, Masaki; Shinagawa, Yoshihisa; Kohmura, Taku; Kunii, Tosiyasu L.

doi:10.1145/383259.383282

Cited by 1,128 publications

(811 citation statements)

References 38 publications

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“…In these experiments, the 2-dimensional measuring function is ϕ = (ϕ 1 , ϕ 2 ), with ϕ 1 the integral geodesic distance [21] and ϕ 2 the distance from the principal vector defined in [1,Section 6.2]. The values of ϕ are normalized so that they range in the interval [0,1].…”

Section: Methodsmentioning

confidence: 99%

A new algorithm for computing the 2-dimensional matching distance between size functions

Biasotti

Cerri

Frosini

et al. 2011

Pattern Recognition Letters

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Size Theory has proven to be a useful geometrical/topological approach to shape analysis and comparison. Originally introduced by considering 1-dimensional properties of shapes, described by means of real-valued functions, it has been subsequently generalized to take into account multidimensional properties coded by functions valued in R k .In the context of Size Theory, this generalization has led to introduce a shape descriptor called k-dimensional size function, and a distance to compare size functions, namely the k-dimensional matching distance. This paper proposes a novel computational framework to deal with the 2-dimensional case of Size Theory. More precisely, some new theoretical results about approximating the 2-dimensional matching distance are presented, leading to the formulation of an algorithm for its computation (up to an arbitrary error threshold).

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Section: Methodsmentioning

confidence: 99%

A new algorithm for computing the 2-dimensional matching distance between size functions

Biasotti

Cerri

Frosini

et al. 2011

Pattern Recognition Letters

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“…In general, shapes are recognized and coded mentally in terms of relevant parts and their spatial configuration or structure [131]. One idea to operationalize this concept was proposed, among others, by MASAKI HILAGA et al, who introduce the Multiresolution Reeb Graph, to represent the skeletal and topological structure of a 3D shape at various levels of resolution [132]. Structure recognition is a very active branch in the field of geometry processing.…”

Section: Semantic Enrichmentmentioning

confidence: 99%

A Survey of Algorithmic Shapes

2015

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In the context of computer-aided design, computer graphics and geometry processing, the idea of generative modeling is to allow the generation of highly complex objects based on a set of formal construction rules. Using these construction rules, a shape is described by a sequence of processing steps, rather than just by the result of all applied operations: shape design becomes rule design. Due to its very general nature, this approach can be applied to any domain and to any shape representation that provides a set of generating functions. The aim of this survey is to give an overview of the concepts and techniques of procedural and generative modeling, as well as their applications with a special focus on archeology and architecture.

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“…Hilaga et al [18] introduced the multiresolution Reeb graph, which represents a 3D model's topology and skeletal structure at various levels of detail. In [19] Zhang et al consider the use of medial surfaces to compute an equivalent directed acyclic graph of a voxelized model.…”

Section: Related Workmentioning

confidence: 99%

Efficient 3D shape matching and retrieval using a concrete radialized spherical projection representation

Papadakis

Pratikakis

Perantonis

et al. 2007

Pattern Recognition

166

105

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We present a 3D shape retrieval methodology based on the theory of spherical harmonics. Using properties of spherical harmonics, scaling and axial flipping invariance is achieved. Rotation normalization is performed by employing the continuous principal component analysis along with a novel approach which applies PCA on the face normals of the model. The 3D model is decomposed into a set of spherical functions which represents not only the intersections of the corresponding surface with rays emanating from the origin but also points in the direction of each ray which are closer to the origin than the furthest intersection point. The superior performance of the proposed methodology is demonstrated through a comparison against state-of-the-art approaches on standard databases. ᭧

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Topology matching for fully automatic similarity estimation of 3D shapes

Cited by 1,128 publications

References 38 publications

A new algorithm for computing the 2-dimensional matching distance between size functions

A new algorithm for computing the 2-dimensional matching distance between size functions

A Survey of Algorithmic Shapes

Efficient 3D shape matching and retrieval using a concrete radialized spherical projection representation

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