
Anguelos Nicolaou, Sounak Dey, V.Christlein, A.Maier and Dimosthenis Karatzas. 2018. Nondeterministic Behavior of Rankingbased Metrics when Evaluating Embeddings. International Workshop on Reproducible Research in Pattern Recognition.71–82. (LNCS.)
Abstract: Embedding data into vector spaces is a very popular strategy of pattern recognition methods. When distances between embeddings are quantized, performance metrics become ambiguous. In this paper, we present an analysis of the ambiguity quantized distances introduce and provide bounds on the effect. We demonstrate that it can have a measurable effect in empirical data in stateoftheart systems. We also approach the phenomenon from a computer security perspective and demonstrate how someone being evaluated by a third party can exploit this ambiguity and greatly outperform a random predictor without even access to the input data. We also suggest a simple solution making the performance metrics, which rely on ranking, totally deterministic and impervious to such exploits.



Anjan Dutta. 2010. Symbol Spotting in Graphical Documents by Serialized Subgraph Matching. (Master's thesis, .)



Anjan Dutta. 2014. Inexact Subgraph Matching Applied to Symbol Spotting in Graphical Documents. (Ph.D. thesis, Ediciones Graficas Rey.)
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 NPcomplete 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 stateoftheart methods. Furthermore, some dataset models have also been proposed.



Anjan Dutta and Hichem Sahbi. 2018. Stochastic Graphlet Embedding. TNNLS, 1–14.
Abstract: Graphbased methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semistructured data as graphs where nodes correspond to primitives (parts, interest points, segments,
etc.) and edges characterize the relationships between these primitives. However, these nonvectorial graph data cannot be straightforwardly plugged into offtheshelf machine learning algorithms without a preliminary step of – explicit/implicit –graph vectorization and embedding. This embedding process
should be resilient to intraclass graph variations while being highly discriminant. In this paper, we propose a novel highorder 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 highorder 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 graphletbased representations have positive impact on the performance of pattern comparison and recognition as corroborated through extensive experiments using standard benchmark databases.
Keywords: Stochastic graphlets; Graph embedding; Graph classification; Graph hashing; Betweenness centrality



Anjan Dutta, Jaume Gibert, Josep Llados, Horst Bunke and Umapada Pal. 2012. Combination of Product Graph and Random Walk Kernel for Symbol Spotting in Graphical Documents. 21st International Conference on Pattern Recognition.1663–1666.
Abstract: This paper explores the utilization of product graph for spotting symbols on graphical documents. Product graph is intended to find the candidate subgraphs or components in the input graph containing the paths similar to the query graph. The acute angle between two edges and their length ratio are considered as the node labels. In a second step, each of the candidate subgraphs in the input graph is assigned with a distance measure computed by a random walk kernel. Actually it is the minimum of the distances of the component to all the components of the model graph. This distance measure is then used to eliminate dissimilar components. The remaining neighboring components are grouped and the grouped zone is considered as a retrieval zone of a symbol similar to the queried one. The entire method works online, i.e., it doesn't need any preprocessing step. The present paper reports the initial results of the method, which are very encouraging.



Anjan Dutta, Josep Llados, Horst Bunke and Umapada Pal. 2013. Near Convex Region Adjacency Graph and Approximate Neighborhood String Matching for Symbol Spotting in Graphical Documents. 12th International Conference on Document Analysis and Recognition.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.



Anjan Dutta, Josep Llados, Horst Bunke and Umapada Pal. 2013. A Product graph based method for dual subgraph matching applied to symbol spotting. 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.



Anjan Dutta, Josep Llados, Horst Bunke and Umapada Pal. 2014. A Product Graph Based Method for Dual Subgraph Matching Applied to Symbol Spotting. In Bart Lamiroy and JeanMarc Ogier, eds. Graphics Recognition. Current Trends and Challenges. Springer Berlin Heidelberg, 7–11. (LNCS.)
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



Anjan Dutta, Josep Llados, Horst Bunke and Umapada Pal. 2018. Product graphbased higher order contextual similarities for inexact subgraph matching. PR, 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.



Anjan Dutta, Josep Llados and Umapada Pal. 2011. A BagofPaths Based Serialized Subgraph Matching for Symbol Spotting in Line Drawings. In Jordi Vitria, Joao Miguel Raposo and Mario Hernandez, eds. 5th Iberian Conference on Pattern Recognition and Image Analysis. Berlin, Springer Berlin Heidelberg, 620–627. (LNCS.)
Abstract: In this paper we propose an error tolerant subgraph matching algorithm based on bagofpaths for solving the problem of symbol spotting in line drawings. Bagofpaths is a factorized representation of graphs where the factorization is done by considering all the acyclic paths between each pair of connected nodes. Similar paths within the whole collection of documents are clustered and organized in a lookup table for efficient indexing. The lookup table contains the index key of each cluster and the corresponding list of locations as a single entry. The mean path of each of the clusters serves as the index key for each table entry. The spotting method is then formulated by a spatial voting scheme to the list of locations of the paths that are decided in terms of search of similar paths that compose the query symbol. Efficient indexing of common substructures helps to reduce the computational burden of usual graph based methods. The proposed method can also be seen as a way to serialize graphs which allows to reduce the complexity of the subgraph isomorphism. We have encoded the paths in terms of both attributed strings and turning functions, and presented a comparative results between them within the symbol spotting framework. Experimentations for matching different shape silhouettes are also reported and the method has been proved to work in noisy environment also.

