Towards a Qualitative Reasoning on Shape Change and Object Division

Authors Momo Tosue, Kazuko Takahashi

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Author Details

Momo Tosue
  • School of Science and Technology, Kwansei Gakuin University, 2-1, Gakuen, Sanda, 669-1337, Japan
Kazuko Takahashi
  • School of Science and Technology, Kwansei Gakuin University, 2-1, Gakuen, Sanda, 669-1337, Japan


The authors would like to thank Professor Christian Freksa for his comments on shape transformation, and anonymous reviewers for valuable comments.

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Momo Tosue and Kazuko Takahashi. Towards a Qualitative Reasoning on Shape Change and Object Division. In 14th International Conference on Spatial Information Theory (COSIT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 142, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We propose a qualitative representation for handling shape change and object division. We model the shape of a smooth curve in a two-dimensional plane together with its temporal change, using curvature extrema. The representation is based on Process-Grammar, which gives a causal account for each shape change. We introduce several rewriting rules to handle object division, that consist of making a tangent point, reconstruction, and separation. On the treatment of the division process, the expression can clarify the relative locations of multiple objects. We show formalization and application to represent a sequence of shape changes frequently observed in an organogenesis process.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Knowledge representation and reasoning
  • qualitative spatial representation
  • symbolic shape representation
  • Process-Grammar


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