Abstract: In this paper, we propose a circular blurred shape model descriptor to deal with the problem of symbol detection and classification as a particular case of object recognition. The feature extraction is performed by capturing the spatial arrangement of significant object characteristics in a correlogram structure. The shape information from objects is shared among correlogram regions, where a prior blurring degree defines the level of distortion allowed in the symbol, making the descriptor tolerant to irregular deformations. Moreover, the descriptor is rotation invariant by definition. We validate the effectiveness of the proposed descriptor in both the multiclass symbol recognition and symbol detection domains. In order to perform the symbol detection, the descriptors are learned using a cascade of classifiers. In the case of multiclass categorization, the new feature space is learned using a set of binary classifiers which are embedded in an error-correcting output code design. The results over four symbol data sets show the significant improvements of the proposed descriptor compared to the state-of-the-art descriptors. In particular, the results are even more significant in those cases where the symbols suffer from elastic deformations.

Abstract: Many symbol recognition problems require the use of robust descriptors in order to obtain rich information of the data. However, the research of a good descriptor is still an open issue due to the high variability of symbols appearance. Rotation, partial occlusions, elastic deformations, intra-class and inter-class variations, or high variability among symbols due to different writing styles, are just a few problems. In this paper, we introduce a symbol shape description to deal with the changes in appearance that these types of symbols suffer. The shape of the symbol is aligned based on principal components to make the recognition invariant to rotation and reflection. Then, we present the Blurred Shape Model descriptor (BSM), where new features encode the probability of appearance of each pixel that outlines the symbols shape. Moreover, we include the new descriptor in a system to deal with multi-class symbol categorization problems. Adaboost is used to train the binary classifiers, learning the BSM features that better split symbol classes. Then, the binary problems are embedded in an Error-Correcting Output Codes framework (ECOC) to deal with the multi-class case. The methodology is evaluated on different synthetic and real data sets. State-of-the-art descriptors and classifiers are compared, showing the robustness and better performance of the present scheme to classify symbols with high variability of appearance.

Abstract: Symmetry is an important shape feature. In this paper, a simple and fast method to detect perfect and distorted rotational symmetries of 2D objects is described. The boundary of a shape is polygonally approximated and represented as a string. Rotational symmetries are found by cyclic string matching between two identical copies of the shape string. The set of minimum cost edit sequences that transform the shape string to a cyclically shifted version of itself define the rotational symmetry and its order. Finally, a modification of the algorithm is proposed to detect reflectional symmetries. Some experimental results are presented to show the reliability of the proposed algorithm