Approaches to symbol recognition and spotting

Abstract

The problem of symbol recognition and symbol spotting have been addressed in this thesis. First of all we reviewed the literature of the symbol recognition problem from three aspects: 1) how to represent a symbol, 2) how to matching the symbols based on their representations, and 3) how to solve the symbol alignment problem during symbol matching. As the main contributions, we then propose two different approaches for symbol recognition and symbol spotting. The first contribution is a statistical approach to symbol recognition. In the approach, a symbol is measured and represented in 2-dimensional kernel densities around the sampling points on its skeleton. The Kullback-Leibler (KL) divergence is then exploited to measure the similarity between the densities of two symbols. Compared to the results of the same test sets reported in (Yang, 2005), the best overall results in the 2003 GREC Contest, our method achieves the better overall performance except in two subsets with combination of deformation and degradation. On the hand-drawn drawings generated with the 50 models also from the 2003 GREC Contest, our recognition results are 96% and 94% for the two generated sets respectively. It is much better than those of Su’s method, which are 72% and 74% correspondingly. We propose two methods to eliminate the rotation effect. One is to adjust the rotation angel by minimizing the KL divergence between the test symbol and the model symbol with the gradient-based method. The other is to exploit the independent component analysis (ICA) technique, which considers the higher-order statistical information of the data and whose outputs are generally invariant to any invertible linear transformation. The first method gives quite accurate results, as shown in the experiment section, and the second method reduces the computation greatly with the performance degraded just around 5%. By introducing ICA, it only takes about 80ms to match a pair of symbols, which is only 1 30 of that for the gradient-based algorithm. The second approach is a hybrid approach to symbol recognition or spotting of symbols in vectorial forms. We calculate all primitivepair relationships in a symbol and generate the signature of the symbol with those relationships. Finally, the symbol is represented as a feature set containing all the primitive-pair relationships. Matching between two symbols/drawings is then reduced to the problem of matching two feature sets. We apply the approach on the GREC2003 test sets with symbols in vectorial forms. Since all the best matching models for the test symbols are correctly retrieved, the recognition accuracies are all 100%. Note that, the retrieved most similar models for a test symbol may not be unique. If the recognition standard is that the recognition result must be unique, the accuracy of the approach drops. However, all of the recognition accuracy are still above 92%. For this database, at most two best matching models are retrieved for each test symbol. Under such situation, the approach can be applied to filter out the impossible similar symbols and further accurate recognition can be performed based on those results. The approach preserves high recognition accuracy, while speeding up the matching procedure. Since all the models can be processed in advance, the important factor to reveal the efficiency of the approach in the symbol recognition task is the average time to create a signature for a test symbol and the time for matching a pair of symbol. Averagely, a signature of a symbol in the proposed approach can be created in 0.025 seconds. Moreover, matching a pair of symbols only costs 0.01 seconds. Compared with the time cost used in the proposed statistical method, which costs about 2.4 seconds for matching a pair of symbols with rotation estimation, the proposed approach improves the matching speed by two hundred times. Moreover, we generate a general framework for the performance evaluation of certain recognition approaches. All the preprocessing steps are the same for the to-be-evaluated approaches. Both symbol databases and shape databases are applied to do evaluation. In symbol databases, a symbol is unique and people target to find the exact matching symbol for the testing symbol. However, shape databases usually include shapes in various categories or classes and people aim at finding the characteristics of a class and retrieving the top similar shapes for the testing symbol. Different traditional measures, e.g. recognition accuracy and top matching rates, are applied to evaluate the performance of the methods. Generally, the symbol recognition approaches perform well on the symbol databases and have strong competitive performance in retrieving the top similar shapes. Furthermore, new measures, namely homogeneity and separability, are proposed to explore more characteristics of the methods so that they can be better understood. High homogeneity means that a descriptor can represent the symbols in the same class in a highly similar way. High separability means that a descriptor can distinct symbols in different classes well. These two measures are expected to evaluate how well distributed are the symbols in the space of representation provided by the symbol descriptor. Experimental results show that the proposed statistical method in Chapter 3 describes a relatively sparse inner-class structure, that if we regard the representations of the shapes in one class as points in one class, sparse inner-class structure means that their distribution is relatively sparse. It is also an explanation to the question why the proposed statistical method is robust to noisy and distorted symbols.