Indexing through laplacian spectra

Demirci, M. Fatih; Leuken, Reinier H. van; Veltkamp, Remco C.

doi:10.1016/j.cviu.2007.09.012

Cited by 24 publications

(29 citation statements)

References 49 publications

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“…The problem that remains, is to find subgraphs that are appropriate for this purpose. One proposed approach is extracting all possible subgraphs of all possible sizes, and match only subgraphs of the same size [8]. This is, however, a time consuming approach, and requires calculation of distances between many subgraphs that are not meaningful or irrelevant to the original graph.…”

Section: Subgraph Decompositionmentioning

confidence: 99%

“…The spectrum of the Laplacian matrix can be used as a signature representation for the graph, and thus for efficient retrieval purposes (indexing) [8]. One of the main reasons for this is that many graph properties and invariants are reflected by the Laplacian spectrum [16].…”

Section: Graph Property Matricesmentioning

confidence: 99%

“…bipartite graph matching through minimizing the distance between node labels [6], matching based on graph hierarchy [4,7] and maximum common subgraph computation based on the node attributes [5]. An alternative approach to reduce the complexity of graph matching is to use the spectrum or eigenvectors of an associated matrix [8,9,10,11,12]. Unfortunately, the descriptiveness of the used matrices is limited, and it's often unclear how to handle graphs of different sizes.…”

Section: Introductionmentioning

confidence: 99%

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Complex Fiedler Vectors for Shape Retrieval

Leuken

Symonova

Veltkamp

et al. 2008

Lecture Notes in Computer Science

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Abstract. Adjacency and Laplacian matrices are popular structures to use as representations of shape graphs, because their sorted sets of eigenvalues (spectra) can be used as signatures for shape retrieval. Unfortunately, the descriptiveness of these spectra is limited, and handling graphs of different size remains a challenge. In this work, we propose a new framework in which the shapes (3D models in our test corpus) are represented by multi-labeled graphs. A Hermitian matrix is associated to each graph, in which the entries are defined such that they contain all information stored in the graph edges. Additional constraints ensure that this Hermitian matrix mimics the well-studied spectral behaviour of the Laplcian matrix. We therefore use the Hermitian Fiedler vector as shape signature during retrieval. To deal with graphs of different size, we efficiently reuse the calculated Fiedler vector to decompose the graph into a limited number of non-overlapping, meaningful subgraphs. Retrieval results are based on both complete matching and subgraph matching.

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Section: Subgraph Decompositionmentioning

confidence: 99%

Section: Graph Property Matricesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Complex Fiedler Vectors for Shape Retrieval

Leuken

Symonova

Veltkamp

et al. 2008

Lecture Notes in Computer Science

Self Cite

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“…Various shape matching methods exist (Tangelder and Veltkamp, 2008;Cardone et al, 2003;Iyer et al, 2005;Li et al, 2010;Brière-Côté et al, 2012;Demirci et al, 2008;Zhu et al, 2012;Ohbuchi et al, 2005) and can be classified in three main categories: feature-based methods, graph-based methods and geometry-based methods (Figure 2). These methods have been implemented and tested and the results are more or less efficient but only when trying to retrieve a shape which is similar to the one of the query from the point of view of form and structure.…”

Section: Related Workmentioning

confidence: 99%

Thin part identification for CAD model classification

Pernot

Giannini

Petton

2015

Engineering Computations

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Purpose -The purpose of this paper is to focus on the characterization and classification of parts with respect to the meshing issue, and notably the meshing of thin parts difficulty handled automatically and which often requires adaptation steps. The objective is to distinguish the so-called thin parts and parts with thin features from the other parts. Design/methodology/approach -The concepts of thin part and part with thin features are introduced together with the mechanisms and criteria used for their identification in a CAD models database. The criteria are built on top of a set of shape descriptors and notably the distance distribution which is used to characterize the thickness of the object. To speed up the identification process, shape descriptors are computed from tessellated parts. Findings -A complete modular approach has been designed. It computes shape descriptors over parts stored in a directory and it uses criteria to distinguish three categories: thin parts, parts with thin features and other parts. Being the three categories identified, the user can spend more time on the parts that are considered as more difficulty meshable.Research limitations/implications -The approach is limited to the three above mentioned categories. However, it has been designed so that the values corresponding to the shape descriptors and associated meshing qualities can easily be inserted within a machining learning tool later on. Practical implications -The use of the developed tool can be seen as a pre-processing step during the preparation of finite element (FE) simulation models. It is automatic and can be run in batch and in parallel. Originality/value -The approach is modular, it is simple and easy to implement. Categories are built on top of several shape descriptors and not on a unique signature. It is independent of the CAD modeler. This approach is integrated within a FE simulation model preparation framework and help engineers anticipating difficulties when meshing CAD models.

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“…Some methods have been proposed to speed up the matching process. In [22], [23], the matching process is separated into two steps. The first step makes use of graph spectrum to encode structure for fast pruning.…”

Section: Articulated Geometry Model Retrievalmentioning

confidence: 99%

Embedding Retrieval of Articulated Geometry Models

Tam

Lau

2012

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-Due to the popularity of computer games and animation, research on 3D articulated geometry model retrieval is attracting a lot of attention in recent years. However, most existing works extract high dimensional features to represent models and suffer from practical limitations. First, misalignment in high dimensional features may produce unreliable Euclidean distances and affect retrieval accuracy. Second, the curse of dimensionality also degrades efficiency. In this paper, we propose an embedding retrieval framework to improve the practicability of these methods. It is based on a manifold learning technique, the Diffusion Map (DM). We project all pairwise distances onto a low dimensional space. This improves retrieval accuracy because inter-cluster distances are exaggerated. Then we adapt the Density-Weighted Nyström extension and further propose a novel step to locally align the Nyström embedding to the eigensolver embedding so as to reduce extension error and preserve retrieval accuracy. Finally, we propose a heuristic to handle disconnected manifolds by augmenting the kernel matrix with multiple similarity measures and shortcut edges, and further discuss the choice of DM parameters. We have incorporated two existing matching algorithms for testing. Our experimental results show improvement in precision at high recalls and in speed. Our work provides a robust retrieval framework for the matching of multimedia data that lie on manifolds.

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Indexing through laplacian spectra

Cited by 24 publications

References 49 publications

Complex Fiedler Vectors for Shape Retrieval

Complex Fiedler Vectors for Shape Retrieval

Thin part identification for CAD model classification

Embedding Retrieval of Articulated Geometry Models

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