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Applying soft computing in defining spatial relations
... While cognitive aspects of static spatial relations have been researched in the spatial sciences with a special focus on requirements of spatial information technology such as the formal characterization of spatial relations and their constituents (Mark & Egenhofer, 1994b;Xu, 2007;Nedas, Egenhofer, & Wilmsen, 2007;Riedemann, 2005;Matsakis & Sztandera, 2002), movement patterns have not yet been given the same attention, at least not from a cognitive behavioral perspective. We do not lack suggestions for conceptual temporal models (Peuquet, 1994;Mennis, Peuquet, & Qian, 2000;Galton, 2004;Hornsby & Egenhofer, 2000). ...
In this paper, we discuss the role of topology as a predictor for the conceptualization of dynamically changing spatial configurations (referred to as movement patterns). We define meaningful units of movement patterns as paths through a topologically defined conceptual neighborhood graph. Topology plays a central role in formal approaches to human cognition and in predicting cognitive similarity ratings—although primarily for static spatial configurations. Formal specifications of the role of topology for characterizing movement patterns do exist, yet there is paucity of behavioral validation. To bridge this gap, we conducted an experiment based on the grouping paradigm to assess factors that underlie conceptualizations of movement patterns. The experiment was designed such that paths through the conceptual neighborhood graph were distinguished by topologically differentiated ending relations. We believe topology can make an important contribution in explaining movement conceptualizations. One recently formulated topology-based contribution is the endpoint hypothesis, asserting that a cognitive focus is placed on event ending relations. We discuss the results of our experiment in relation to previous experiments targeted toward a framework for modeling the cognitive conceptualization of dynamically changing spatial relations.
... ), it is clear that these concepts are not precise by nature, and that they require a flexible modeling supporting reasoning under imprecision and dealing with ambiguity. Actually, applying soft computing concepts for modeling spatial relations is a widely accepted idea, and many methods have been proposed in this direction (see for example the books [MS02,JPPS10]). In the context of hand-drawn patterns processing, it seems natural to make use of these concepts for handling objects that are by nature noisy, imprecise, and subject to a strong variability according to the numerous input conditions (writer identity, nature of the input material, environment, space and time. . . ). ...
It is widely admitted that modeling of spatial information is very important for interpretation and recognition of handwritten expressions. Two distinct tasks have to be addressed by spatial models in this context. Evaluation task consists in measuring the correspondence between the relationship of two objects and a predefined model of spatial relation. Localization task consists in retrieving objects that are related to a reference object according to a predefined model of spatial relation. In this work, we introduce a new modeling of relative spatial positioning that handles the two tasks under a unified framework and a training scheme for learning spatial models from data. The use of fuzzy mathematical morphology allows to deal with imprecision of positioning and to adapt to varying shapes of handwritten objects. Experimentations of the evaluation task over two datasets of online handwritten patterns prove that the proposed modeling outperforms commonly used relative positioning features.
The rise of pen-enabled interfaces is supported by the development of automatic methods for interpretation of more and more rich and complex input data: handwritten text, mathematical equations, sketches, free handwritten notes... For efficiently recognizing these handwritten documents, one has to consider jointly the shapes of their components and the relative positioning between them. Our research focuses on the modeling of relative positioning between handwritten objects, considering that the potential of this part of the information is not fully exploited in the current methods. We introduce spatial meta-templates, a generic modeling for describing spatial relations between objects of diverse nature, complexity, and shape. These models can be trained from data and provide richer and more accurate descriptions because they authorize to reason about spatial information directly in the image space. Relying on fuzzy sets theory and mathematical morphology allows dealing with imprecision and offers intuitive description of spatial relations. A meta-template is endowed with a prediction capacity: it provides the description of modeled spatial relations with respect to a reference object in the image, as a spatial template. This enables to conduct segmentation of objects depending on their spatial context. By exploiting these models, we present a new representation for structured handwritten objects. It relies only on modeling of the spatial information so as to demonstrate the importance of spatial information for interpretation of these objects. The segmentation of handwritten strokes into structural primitives is driven by positioning models, making use of their prediction ability. Experimental results, obtained with objects of diverse nature and complexity (Chinese characters, editing gestures, mathematical symbols, letters), validate the quality of positioning description offered by our models. The performance on the task of recognizing symbols with a spatial-based representation further attests the importance of this information and confirms the ability of meta-templates to model it properly and accurately. These results both show the richness of spatial information and give an insight on the potential of meta-templates for improving methods for handwritten document interpretation.
We introduce in this work a new approach for learn-ing spatial relationships between elements of hand-drawn patterns with the help of fuzzy mathematical morphology operators. Relying on mathematical morphology allows to take into account the actual shapes of hand-drawn patterns when modeling their spatial relationships, and thus to cope with the variability of handwriting signal. Extension of mathematical morphology to the fuzzy set framework further allows to handle imprecision of handwriting and to deal with the ambiguity of spatial relationships. The novelty lies in the generative aspect of the models we propose, in the sense that they can exhibit the region of space where the learnt relation is satisfied with respect to a reference object, and can thus be used for driving structural analysis of complex patterns. Experiments over on-line handwritten data show their performance, and prove their ability to deal with variability of handwriting and reasoning under imprecision.
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