Bayesian graph edit distance

This paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of edit-distance originally introduced for graph-matching by Sanfeliu and Fu [1]. We show how the Levenshtein distance can be used to model the probability distribution for structural errors in the graph-matching problem. This probability distribution is used to locate matches using MAP label updates. We compare the resulting graph-matching algorithm with that recently reported by Wilson and Hancock. The use of edit-distance offers an elegant alternative to the exhaustive compilation of label dictionaries. Moreover, the method is polynomial rather than exponential in its worst-case complexity. We support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem. This demonstrates experimentally that the gain in efficiency is not at the expense of quality of match

Image Understanding by Hierarchical Symbolic Representation and Inexact Matching of Attributed Graphs

We study the symbolic representation of imagery information by a powerful global representation scheme in the form of Attributed Relational Graph (ARG), and propose new techniques for the extraction of such representation from spatial-domain images, and for performing the task of image understanding through the analysis of the extracted ARG representation. To achieve practical image understanding tasks, the system needs to comprehend the imagery information in a global form. Therefore, we propose a multi-layer hierarchical scheme for the extraction of global symbolic representation from spatial-domain images. The proposed scheme produces a symbolic mapping of the input data in terms of an output alphabet, whose elements are defined over global subimages. The proposed scheme uses a combination of model-driven and data-driven concepts. The model- driven principle is represented by a graph transducer, which is used to specify the alphabet at each layer in the scheme. A symbolic mapping is driven by the input data to map the input local alphabet into the output global alphabet. Through the iterative application of the symbolic transformational mapping at different levels of hierarchy, the system extracts a global representation from the image in the form of attributed relational graphs. Further processing and interpretation of the imagery information can, then, be performed on their ARG representation. We also propose an efficient approach for calculating a distance measure and finding the best inexact matching configuration between attributed relational graphs. For two ARGs, we define sequences of weighted error-transformations which when performed on one ARG (or a subgraph of it), will produce the other ARG. A distance measure between two ARGs is defined as the weight of the sequence which possesses minimum total-weight. Moreover, this minimum-total weight sequence defines the best inexact matching configuration between the two ARGs. The global minimization over the possible sequences is performed by a dynamic programming technique, the approach shows good results for ARGs of practical sizes. The proposed system possesses the capability to inference the alphabets of the ARG representation which it uses. In the inference phase, the hierarchical scheme is usually driven by the input data only, which normally consist of images of model objects. It extracts the global alphabet of the ARG representation of the models. The extracted model representation is then used in the operation phase of the system to: perform the mapping in the multi-layer scheme. We present our experimental results for utilizing the proposed system for locating objects in complex scenes

Structural matching by discrete relaxation

This paper describes a Bayesian framework for performing relational graph matching by discrete relaxation. Our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching. Broadly speaking there are two main aspects to this study. Firstly we locus on the issue of how relational inexactness may be quantified. We illustrate that several popular relational distance measures can be recovered as specific limiting cases of the Bayesian consistency measure. The second aspect of our comparison concerns the way in which structural inexactness is controlled. We investigate three different realizations ai the matching process which draw on contrasting control models. The main conclusion of our study is that the active process of graph-editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter

A Necessary and Sufficient Condition for Graph Matching to be equivalent to Clique Search

This paper formulates a necessary and sufficient condition for a generic graph matching problem to be equivalent to the maximum vertex and edge weight clique problem in a derived association graph. The consequences of this results are threefold: first, the condition is general enough to cover a broad range of practical graph matching problems; second, a proof to establish equivalence between graph matching and clique search reduces to showing that a given graph matching problem satisfies the proposed condition;\ud and third, the result sets the scene for generic continuous solutions for a broad range of graph matching problems. To illustrate the mathematical framework, we apply it to a number of graph matching problems, including the problem of determining the graph edit distance

Structural graph matching using the EM algorithm and singular value decomposition

This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding method

Determining Alpha-Helix Correspondence for Protein Structure Prediction from Cryo-EM Density Maps, Master\u27s Thesis, May 2007

Determining protein structure is an important problem for structural biologists, which has received a significant amount of attention in the recent years. In this thesis, we describe a novel, shape-modeling approach as an intermediate step towards recovering 3D protein structures from volumetric images. The input to our method is a sequence of alpha-helices that make up a protein, and a low-resolution volumetric image of the protein where possible locations of alpha-helices have been detected. Our task is to identify the correspondence between the two sets of helices, which will shed light on how the protein folds in space. The central theme of our approach is to cast the correspondence problem as that of shape matching between the 3D volume and the 1D sequence. We model both the shapes as attributed relational graphs, and formulate a constrained inexact graph matching problem. To compute the matching, we developed an optimal algorithm based on the A*-search with several choices of heuristic functions. As demonstrated in a suite of real protein data, the shape-modeling approach is capable of correctly identifying helix correspondences in noise-abundant volumes with minimal or no user intervention