Abstract: In this paper we propose a symbol spotting technique in graphical documents. Graphs are used to represent the documents and a (sub)graph matching technique is used to detect the symbols in them. We propose a graph serialization to reduce the usual computational complexity of graph matching. Serialization of graphs is performed by computing acyclic graph paths between each pair of connected nodes. Graph paths are one-dimensional structures of graphs which are less expensive in terms of computation. At the same time they enable robust localization even in the presence of noise and distortion. Indexing in large graph databases involves a computational burden as well. We propose a graph factorization approach to tackle this problem. Factorization is intended to create a unified indexed structure over the database of graphical documents. Once graph paths are extracted, the entire database of graphical documents is indexed in hash tables by locality sensitive hashing (LSH) of shape descriptors of the paths. The hashing data structure aims to execute an approximate k-NN search in a sub-linear time. We have performed detailed experiments with various datasets of line drawings and compared our method with the state-of-the-art works. The results demonstrate the effectiveness and efficiency of our technique.

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.

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.

Abstract: Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments,
etc.) and edges characterize the relationships between these primitives. However, these non-vectorial graph data cannot be straightforwardly plugged into off-the-shelf machine learning algorithms without a preliminary step of – explicit/implicit –graph vectorization and embedding. This embedding process
should be resilient to intra-class graph variations while being highly discriminant. In this paper, we propose a novel high-order stochastic graphlet embedding (SGE) that maps graphs into vector spaces. Our main contribution includes a new stochastic search procedure that efficiently parses a given graph and extracts/samples unlimitedly high-order graphlets. We consider
these graphlets, with increasing orders, to model local primitives as well as their increasingly complex interactions. In order to build our graph representation, we measure the distribution of these graphlets into a given graph, using particular hash functions that efficiently assign sampled graphlets into isomorphic sets with a very low probability of collision. When
combined with maximum margin classifiers, these graphlet-based representations have positive impact on the performance of pattern comparison and recognition as corroborated through extensive experiments using standard benchmark databases.

Abstract: There is a resurgence in the use of structural approaches in the usual object recognition and retrieval problem. Graph theory, in particular, graph matching plays a relevant role in that. Specifically, the detection of an object (or a part of that) in an image in terms of structural features can be formulated as a subgraph matching. Subgraph matching is a challenging task. Specially due to the presence of outliers most of the graph matching algorithms do not perform well in subgraph matching scenario. Also exact subgraph isomorphism has proven to be an NP-complete problem. So naturally, in graph matching community, there are lot of efforts addressing the problem of subgraph matching within suboptimal bound. Most of them work with approximate algorithms that try to get an inexact solution in estimated way. In addition, usual recognition must cope with distortion. Inexact graph matching consists in finding the best isomorphism under a similarity measure. Theoretically this thesis proposes algorithms for solving subgraph matching in an approximate and inexact way.
We consider the symbol spotting problem on graphical documents or line drawings from application point of view. This is a well known problem in the graphics recognition community. It can be further applied for indexing and classification of documents based on their contents. The structural nature of this kind of documents easily motivates one for giving a graph based representation. So the symbol spotting problem on graphical documents can be considered as a subgraph matching problem. The main challenges in this application domain is the noise and distortions that might come during the usage, digitalization and raster to vector conversion of those documents. Apart from that computer vision nowadays is not any more confined within a limited number of images. So dealing a huge number of images with graph based method is a further challenge.
In this thesis, on one hand, we have worked on efficient and robust graph representation to cope with the noise and distortions coming from documents. On the other hand, we have worked on different graph based methods and framework to solve the subgraph matching problem in a better approximated way, which can also deal with considerable number of images. Firstly, we propose a symbol spotting method by hashing serialized subgraphs. Graph serialization allows to create factorized substructures such as graph paths, which can be organized in hash tables depending on the structural similarities of the serialized subgraphs. The involvement of hashing techniques helps to reduce the search space substantially and speeds up the spotting procedure. Secondly, we introduce contextual similarities based on the walk based propagation on tensor product graph. These contextual similarities involve higher order information and more reliable than pairwise similarities. We use these higher order similarities to formulate subgraph matching as a node and edge selection problem in the tensor product graph. Thirdly, we propose near convex grouping to form near convex region adjacency graph which eliminates the limitations of traditional region adjacency graph representation for graphic recognition. Fourthly, we propose a hierarchical graph representation by simplifying/correcting the structural errors to create a hierarchical graph of the base graph. Later these hierarchical graph structures are matched with some graph matching methods. Apart from that, in this thesis we have provided an overall experimental comparison of all the methods and some of the state-of-the-art methods. Furthermore, some dataset models have also been proposed.