3,424 research outputs found
Pattern vectors from algebraic graph theory
Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs
Many-to-Many Graph Matching: a Continuous Relaxation Approach
Graphs provide an efficient tool for object representation in various
computer vision applications. Once graph-based representations are constructed,
an important question is how to compare graphs. This problem is often
formulated as a graph matching problem where one seeks a mapping between
vertices of two graphs which optimally aligns their structure. In the classical
formulation of graph matching, only one-to-one correspondences between vertices
are considered. However, in many applications, graphs cannot be matched
perfectly and it is more interesting to consider many-to-many correspondences
where clusters of vertices in one graph are matched to clusters of vertices in
the other graph. In this paper, we formulate the many-to-many graph matching
problem as a discrete optimization problem and propose an approximate algorithm
based on a continuous relaxation of the combinatorial problem. We compare our
method with other existing methods on several benchmark computer vision
datasets.Comment: 1
Disconnected Skeleton: Shape at its Absolute Scale
We present a new skeletal representation along with a matching framework to
address the deformable shape recognition problem. The disconnectedness arises
as a result of excessive regularization that we use to describe a shape at an
attainably coarse scale. Our motivation is to rely on the stable properties of
the shape instead of inaccurately measured secondary details. The new
representation does not suffer from the common instability problems of
traditional connected skeletons, and the matching process gives quite
successful results on a diverse database of 2D shapes. An important difference
of our approach from the conventional use of the skeleton is that we replace
the local coordinate frame with a global Euclidean frame supported by
additional mechanisms to handle articulations and local boundary deformations.
As a result, we can produce descriptions that are sensitive to any combination
of changes in scale, position, orientation and articulation, as well as
invariant ones.Comment: The work excluding {\S}V and {\S}VI has first appeared in 2005 ICCV:
Aslan, C., Tari, S.: An Axis-Based Representation for Recognition. In
ICCV(2005) 1339- 1346.; Aslan, C., : Disconnected Skeletons for Shape
Recognition. Masters thesis, Department of Computer Engineering, Middle East
Technical University, May 200
Multiple graph matching and applications
En aplicaciones de reconocimiento de patrones, los grafos con atributos son en gran medida apropiados. Normalmente, los vértices de los grafos representan partes locales de los objetos i las aristas relaciones entre estas partes locales. No obstante, estas ventajas vienen juntas con un severo inconveniente, la distancia entre dos grafos no puede ser calculada en un tiempo polinómico. Considerando estas caracterÃsticas especiales el uso de los prototipos de grafos es necesariamente omnipresente. Las aplicaciones de los prototipos de grafos son extensas, siendo las más habituales clustering, clasificación, reconocimiento de objetos, caracterización de objetos i bases de datos de grafos entre otras. A pesar de la diversidad de aplicaciones de los prototipos de grafos, el objetivo del mismo es equivalente en todas ellas, la representación de un conjunto de grafos. Para construir un prototipo de un grafo todos los elementos del conjunto de enteramiento tienen que ser etiquetados comúnmente. Este etiquetado común consiste en identificar que nodos de que grafos representan el mismo tipo de información en el conjunto de entrenamiento. Una vez este etiquetaje común esta hecho, los atributos locales pueden ser combinados i el prototipo construido. Hasta ahora los algoritmos del estado del arte para calcular este etiquetaje común mancan de efectividad o bases teóricas. En esta tesis, describimos formalmente el problema del etiquetaje global i mostramos una taxonomÃa de los tipos de algoritmos existentes. Además, proponemos seis nuevos algoritmos para calcular soluciones aproximadas al problema del etiquetaje común. La eficiencia de los algoritmos propuestos es evaluada en diversas bases de datos reales i sintéticas. En la mayorÃa de experimentos realizados los algoritmos propuestos dan mejores resultados que los existentes en el estado del arte.In pattern recognition, the use of graphs is, to a great extend, appropriate and advantageous. Usually, vertices of the graph represent local parts of an object while edges represent relations between these local parts. However, its advantages come together with a sever drawback, the distance between two graph cannot be optimally computed in polynomial time. Taking into account this special characteristic the use of graph prototypes becomes ubiquitous. The applicability of graphs prototypes is extensive, being the most common applications clustering, classification, object characterization and graph databases to name some. However, the objective of a graph prototype is equivalent to all applications, the representation of a set of graph. To synthesize a prototype all elements of the set must be mutually labeled. This mutual labeling consists in identifying which nodes of which graphs represent the same information in the training set. Once this mutual labeling is done the set can be characterized and combined to create a graph prototype. We call this initial labeling a common labeling. Up to now, all state of the art algorithms to compute a common labeling lack on either performance or theoretical basis. In this thesis, we formally describe the common labeling problem and we give a clear taxonomy of the types of algorithms. Six new algorithms that rely on different techniques are described to compute a suboptimal solution to the common labeling problem. The performance of the proposed algorithms is evaluated using an artificial and several real datasets. In addition, the algorithms have been evaluated on several real applications. These applications include graph databases and group-wise image registration. In most of the tests and applications evaluated the presented algorithms have showed a great improvement in comparison to state of the art applications
Matching hierarchical structures for shape recognition
In this thesis we aim to develop a framework for clustering trees and rep- resenting and learning a generative model of graph structures from a set of training samples. The approach is applied to the problem of the recognition and classification of shape abstracted in terms of its morphological skeleton. We make five contributions. The first is an algorithm to approximate tree edit-distance using relaxation labeling. The second is the introduction of the tree union, a representation capable of representing the modes of structural variation present in a set of trees. The third is an information theoretic approach to learning a generative model of tree structures from a training set.
While the skeletal abstraction of shape was chosen mainly as a exper- imental vehicle, we, nonetheless, make some contributions to the fields of skeleton extraction and its graph representation. In particular, our fourth contribution is the development of a skeletonization method that corrects curvature effects in the Hamilton-Jacobi framework, improving its localiza- tion and noise sensitivity. Finally, we propose a shape-measure capable of characterizing shapes abstracted in terms of their skeleton. This measure has a number of interesting properties. In particular, it varies smoothly as the shape is deformed and can be easily computed using the presented skeleton extraction algorithm.
Each chapter presents an experimental analysis of the proposed approaches applied to shape recognition problems
Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering
This paper describes work aimed at the unsupervised learning of shape-classes from shock trees. We commence by considering how to compute the edit distance between weighted trees. We show how to transform the tree edit distance problem into a series of maximum weight clique problems, and show how to use relaxation labeling to find an approximate solution. This allows us to compute a set of pairwise distances between graph-structures. We show how the edit distances can be used to compute a matrix of pairwise affinities using χ² statistics. We present a maximum likelihood method for clustering the graphs by iteratively updating the elements of the affinity matrix. This involves interleaved steps for updating the affinity matrix using an eigendecomposition method and updating the cluster membership indicators. We illustrate the new tree clustering framework on shock-graphs extracted from the silhouettes of 2D shapes
Fast Contour Matching Using Approximate Earth Mover's Distance
Weighted graph matching is a good way to align a pair of shapes represented by a set of descriptive local features; the set of correspondences produced by the minimum cost of matching features from one shape to the features of the other often reveals how similar the two shapes are. However, due to the complexity of computing the exact minimum cost matching, previous algorithms could only run efficiently when using a limited number of features per shape, and could not scale to perform retrievals from large databases. We present a contour matching algorithm that quickly computes the minimum weight matching between sets of descriptive local features using a recently introduced low-distortion embedding of the Earth Mover's Distance (EMD) into a normed space. Given a novel embedded contour, the nearest neighbors in a database of embedded contours are retrieved in sublinear time via approximate nearest neighbors search. We demonstrate our shape matching method on databases of 10,000 images of human figures and 60,000 images of handwritten digits
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