Z. Les and M. Les (Australia)

Shape understanding, visual concept, visual inference.

This paper presents the method of understanding visual objects that can be considered as mathematical objects. The proposed method of understanding of the mathematical objects is part of the shape understanding method. The main novelty of the proposed method is that it relates the concept of the visual object to the sub-symbolic representation given in the form of the symbolic names of possible classes of shape. Interpretation of the visual object as a mathematical object is interpreted based on the visual inference. In this research the visual inference is applied to solve the problem of a curve identification, graphical investigation of the characteristic points of the curve, interpreting of the model of the visual processes and visual diagnosis, graphical explanation, visual tests and identification of statistical visual objects. Visual tests containing mathematical concepts and mathematical objects are formulated as the tasks given to the system. The research has shown that the system of shape understanding is able to understand non-trivial mathematical concepts and solve tasks that are part of the students’ examination.

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