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: 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: 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: In this paper we propose an error tolerant subgraph matching algorithm based on bag-of-paths for solving the problem of symbol spotting in line drawings. Bag-of-paths 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.

Abstract: Despite being very successful within the pattern recognition and machine learning community, graph-based methods are often unusable because of the lack of mathematical operations defined in graph domain. Graph embedding, which maps graphs to a vectorial space, has been proposed as a way to tackle these difficulties enabling the use of standard machine learning techniques. However, it is well known that graph embedding functions usually suffer from the loss of structural information. In this paper, we consider the hierarchical structure of a graph as a way to mitigate this loss of information. The hierarchical structure is constructed by topologically clustering the graph nodes and considering each cluster as a node in the upper hierarchical level. Once this hierarchical structure is constructed, we consider several configurations to define the mapping into a vector space given a classical graph embedding, in particular, we propose to make use of the stochastic graphlet embedding (SGE). Broadly speaking, SGE produces a distribution of uniformly sampled low-to-high-order graphlets as a way to embed graphs into the vector space. In what follows, the coarse-to-fine structure of a graph hierarchy and the statistics fetched by the SGE complements each other and includes important structural information with varied contexts. Altogether, these two techniques substantially cope with the usual information loss involved in graph embedding techniques, obtaining a more robust graph representation. This fact has been corroborated through a detailed experimental evaluation on various benchmark graph datasets, where we outperform the state-of-the-art methods.

Abstract: Staff removal is an important preprocessing step of the Optical Music Recognition (OMR). The process aims to remove the stafflines from a musical document and retain only the musical symbols, later these symbols are used effectively to identify the music information. This paper proposes a simple but robust method to remove stafflines from printed musical scores. In the proposed methodology we have considered a staffline segment as a horizontal linkage of vertical black runs with uniform height. We have used the neighbouring properties of a staffline segment to validate it as a true segment. We have considered the dataset along with the deformations described in for evaluation purpose. From experimentation we have got encouraging results.

Abstract: Zero-shot sketch-based image retrieval (SBIR) is an emerging task in computer vision, allowing to retrieve natural images relevant to sketch queries that might not been seen in the training phase. Existing works either require aligned sketch-image pairs or inefficient memory fusion layer for mapping the visual information to a semantic space. In this work, we propose a semantically aligned paired cycle-consistent generative (SEM-PCYC) model for zero-shot SBIR, where each branch maps the visual information to a common semantic space via an adversarial training. Each of these branches maintains a cycle consistency that only requires supervision at category levels, and avoids the need of highly-priced aligned sketch-image pairs. A classification criteria on the generators' outputs ensures the visual to semantic space mapping to be discriminating. Furthermore, we propose to combine textual and hierarchical side information via a feature selection auto-encoder that selects discriminating side information within a same end-to-end model. Our results demonstrate a significant boost in zero-shot SBIR performance over the state-of-the-art on the challenging Sketchy and TU-Berlin datasets.