Synthesis of Median Spectral Graph

Ferrer, Miquel; Serratosa, Francesc; Sanfeliu, Alberto

doi:10.1007/11492542_18

Cited by 16 publications

(23 citation statements)

References 13 publications

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“…Since this invariance is only partial, and alignment step is still needed. [30] Furthermore, spectral embedding is able to handle graphs of different sizes, by enlarging the smaller graph using dummy nodes. [31] Aside from the adjacency matrix, other matrices may be used for the spectral decomposition.…”

Section: Graph Classificationmentioning

confidence: 99%

3D Object Detection and Scene Optimization for Tangible Augmented Reality

Szemenyei

Vajda

2018

Period. Polytech. Elec. Eng. Comp. Sci.

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Object recognition in 3D scenes is one of the fundamental tasks in computer vision. It is used frequently in robotics or augmented reality applications [1]. In our work we intend to apply 3D shape recognition to create a Tangible Augmented Reality system that is able to pair virtual and real objects in natural indoors scenes. In this paper we present a method for arranging virtual objects in a real-world scene based on primitive shape graphs. For our scheme, we propose a graph node embedding algorithm for graphs with vectorial nodes and edges, and genetic operators designed to improve the quality of the global setup of virtual objects. We show that our methods improve the quality of the arrangement significantly.

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Section: Graph Classificationmentioning

confidence: 99%

3D Object Detection and Scene Optimization for Tangible Augmented Reality

Szemenyei

Vajda

2018

Period. Polytech. Elec. Eng. Comp. Sci.

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“…As a consequence, in real applications we are forced to use suboptimal methods in order to obtain approximate solutions for the generalized median graph in reasonable time. Such approximate methods [2,6,8,9,10] apply some heuristics in order to reduce the complexity of the graph distance computation and the size of the search space. Recent works [3,4] rely on graph embedding into vector spaces.…”

Section: Median Graphmentioning

confidence: 99%

“…Up to now, two exact algorithms have been presented [6,7]. As the computational cost of these algorithms is very high, a set of approximate algorithms have also been presented in the past based on different approaches such as genetic search [2,6], greedy algorithms [8] and spectral graph theory [9,10]. However, all these algorithms can only be applied to restricted sets of graphs, regarding either the type or the size of the graphs.…”

Section: Introductionmentioning

confidence: 99%

A generic framework for median graph computation based on a recursive embedding approach

Ferrer

Karatzas

Valveny

et al. 2011

Computer Vision and Image Understanding

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The median graph has been shown to be a good choice to obtain a representative of a set of graphs. However, its computation is a complex problem. Recently, graph embedding into vector spaces has been proposed to obtain approximations of the median graph. The problem with such an approach is how to go from a point in the vector space back to a graph in the graph space. The main contribution of this paper is the generalization of this previous method, proposing a generic recursive procedure that permits to recover the graph corresponding to a point in the vector space, introducing only the amount of approximation inherent to the use of graph matching algorithms. In order to evaluate the proposed method, we compare it with the set median and with the other state-of-the-art embedding-based methods for the median graph computation. The experiments are carried out using four different databases (one semi-artificial and three containing real-world data). Results show that with the proposed approach we can obtain better medians, in terms of the sum of distances to the training graphs, than with the previous existing methods.

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“…The existing exact algorithms can only be applied to small sets of graphs with a very small number of nodes. Approximate algorithms are therefore needed [6,9]. Thus, graph embedding techniques have been recently used to solve graph matching problems more efficiently.…”

Section: Median Graphmentioning

confidence: 99%

“…However, its computation is exponential both in the number of input graphs and their size [7]. A number of algorithms for the generalized median graph computation have been reported in the past [6,8,9], but in general they suffer from either a large complexity or are restricted to special types of graphs.…”

Section: Introductionmentioning

confidence: 99%

Graph-Based k-Means Clustering: A Comparison of the Set Median versus the Generalized Median Graph

Ferrer

Valveny

Serratosa

et al. 2009

Computer Analysis of Images and Patterns

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Abstract. In this paper we propose the application of the generalized median graph in a graph-based k -means clustering algorithm. In the graph-based k -means algorithm, the centers of the clusters have been traditionally represented using the set median graph. We propose an approximate method for the generalized median graph computation that allows to use it to represent the centers of the clusters. Experiments on three databases show that using the generalized median graph as the clusters representative yields better results than the set median graph.

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Synthesis of Median Spectral Graph

Cited by 16 publications

References 13 publications

3D Object Detection and Scene Optimization for Tangible Augmented Reality

3D Object Detection and Scene Optimization for Tangible Augmented Reality

A generic framework for median graph computation based on a recursive embedding approach

Graph-Based k-Means Clustering: A Comparison of the Set Median versus the Generalized Median Graph

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