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Anjan Dutta, Josep Llados, Horst Bunke, & Umapada Pal. (2018). Product graph-based higher order contextual similarities for inexact subgraph matching. PR - Pattern Recognition, 76, 596–611.
Abstract: Many algorithms formulate graph matching as an optimization of an objective function of pairwise quantification of nodes and edges of two graphs to be matched. Pairwise measurements usually consider local attributes but disregard contextual information involved in graph structures. We address this issue by proposing contextual similarities between pairs of nodes. This is done by considering the tensor product graph (TPG) of two graphs to be matched, where each node is an ordered pair of nodes of the operand graphs. Contextual similarities between a pair of nodes are computed by accumulating weighted walks (normalized pairwise similarities) terminating at the corresponding paired node in TPG. Once the contextual similarities are obtained, we formulate subgraph matching as a node and edge selection problem in TPG. We use contextual similarities to construct an objective function and optimize it with a linear programming approach. Since random walk formulation through TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities and better discrimination among the nodes and edges. Experimental results shown on synthetic as well as real benchmarks illustrate that higher order contextual similarities increase discriminating power and allow one to find approximate solutions to the subgraph matching problem.
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Anjan Dutta, Josep Llados, Horst Bunke, & Umapada Pal. (2013). Near Convex Region Adjacency Graph and Approximate Neighborhood String Matching for Symbol Spotting in Graphical Documents. In 12th International Conference on Document Analysis and Recognition (pp. 1078–1082).
Abstract: This paper deals with a subgraph matching problem in Region Adjacency Graph (RAG) applied to symbol spotting in graphical documents. RAG is a very important, efficient and natural way of representing graphical information with a graph but this is limited to cases where the information is well defined with perfectly delineated regions. What if the information we are interested in is not confined within well defined regions? This paper addresses this particular problem and solves it by defining near convex grouping of oriented line segments which results in near convex regions. Pure convexity imposes hard constraints and can not handle all the cases efficiently. Hence to solve this problem we have defined a new type of convexity of regions, which allows convex regions to have concavity to some extend. We call this kind of regions Near Convex Regions (NCRs). These NCRs are then used to create the Near Convex Region Adjacency Graph (NCRAG) and with this representation we have formulated the problem of symbol spotting in graphical documents as a subgraph matching problem. For subgraph matching we have used the Approximate Edit Distance Algorithm (AEDA) on the neighborhood string, which starts working after finding a key node in the input or target graph and iteratively identifies similar nodes of the query graph in the neighborhood of the key node. The experiments are performed on artificial, real and distorted datasets.
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Anjan Dutta, Josep Llados, Horst Bunke, & Umapada Pal. (2014). A Product Graph Based Method for Dual Subgraph Matching Applied to Symbol Spotting. In Bart Lamiroy, & Jean-Marc Ogier (Eds.), Graphics Recognition. Current Trends and Challenges (Vol. 8746, pp. 7–11). LNCS. Springer Berlin Heidelberg.
Abstract: Product graph has been shown as a way for matching subgraphs. This paper reports the extension of the product graph methodology for subgraph matching applied to symbol spotting in graphical documents. Here we focus on the two major limitations of the previous version of the algorithm: (1) spurious nodes and edges in the graph representation and (2) inefficient node and edge attributes. To deal with noisy information of vectorized graphical documents, we consider a dual edge graph representation on the original graph representing the graphical information and the product graph is computed between the dual edge graphs of the pattern graph and the target graph. The dual edge graph with redundant edges is helpful for efficient and tolerating encoding of the structural information of the graphical documents. The adjacency matrix of the product graph locates the pair of similar edges of two operand graphs and exponentiating the adjacency matrix finds similar random walks of greater lengths. Nodes joining similar random walks between two graphs are found by combining different weighted exponentials of adjacency matrices. An experimental investigation reveals that the recall obtained by this approach is quite encouraging.
Keywords: Product graph; Dual edge graph; Subgraph matching; Random walks; Graph kernel
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Anjan Dutta, Josep Llados, Horst Bunke, & Umapada Pal. (2013). A Product graph based method for dual subgraph matching applied to symbol spotting. In 10th IAPR International Workshop on Graphics Recognition.
Abstract: Product graph has been shown to be an efficient way for matching subgraphs. This paper reports the extension of the product graph methodology for subgraph matching applied to symbol spotting in graphical documents. This paper focuses on the two major limitations of the previous version of product graph: (1) Spurious nodes and edges in the graph representation and (2) Inefficient node and edge attributes. To deal with noisy information of vectorized graphical documents, we consider a dual graph representation on the original graph representing the graphical information and the product graph is computed between the dual graphs of the query graphs and the input graph.
The dual graph with redundant edges is helpful for efficient and tolerating encoding of the structural information of the graphical documents. The adjacency matrix of the product graph locates similar path information of two graphs and exponentiating the adjacency matrix finds similar paths of greater lengths. Nodes joining similar paths between two graphs are found by combining different exponentials of adjacency matrices. An experimental investigation reveals that the recall obtained by this approach is quite encouraging.
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