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DOI: 10.4230/LIPIcs.COSIT.2024.4

Qualitative Formalization of a Curve on a Two-Dimensional Plane

Authors: Kazuko Takahashi

Published in: LIPIcs, Volume 315, 16th International Conference on Spatial Information Theory (COSIT 2024)

Abstract

We propose a theoretical framework for qualitative spatial representation and reasoning about curves on a two-dimensional plane. We regard a curve as a sequence of segments, each of which has its own direction and convexity, and give a symbolic expression to it. We propose a reasoning method on this symbolic expression; when only a few segments of a curve are visible, we find missing segments by connecting them to create a global smooth continuous curve. In addition, we discuss whether the shape of the created curve can represent that of a real object; if the curve forms a spiral, such a curve is sometimes not appropriate as a border of an object. We show a method that judges the appropriateness of a curve, by considering the orientations of the segments.

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Kazuko Takahashi. Qualitative Formalization of a Curve on a Two-Dimensional Plane. In 16th International Conference on Spatial Information Theory (COSIT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 315, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{takahashi:LIPIcs.COSIT.2024.4,
  author =	{Takahashi, Kazuko},
  title =	{{Qualitative Formalization of a Curve on a Two-Dimensional Plane}},
  booktitle =	{16th International Conference on Spatial Information Theory (COSIT 2024)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-330-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{315},
  editor =	{Adams, Benjamin and Griffin, Amy L. and Scheider, Simon and McKenzie, Grant},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2024.4},
  URN =		{urn:nbn:de:0030-drops-208193},
  doi =		{10.4230/LIPIcs.COSIT.2024.4},
  annote =	{Keywords: qualitative spatial reasoning, knowledge representation, logical reasoning, shape information}
}

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DOI: 10.4230/LIPIcs.COSIT.2019.7

Towards a Qualitative Reasoning on Shape Change and Object Division

Authors: Momo Tosue and Kazuko Takahashi

Published in: LIPIcs, Volume 142, 14th International Conference on Spatial Information Theory (COSIT 2019)

Abstract

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.

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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)

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@InProceedings{tosue_et_al:LIPIcs.COSIT.2019.7,
  author =	{Tosue, Momo and Takahashi, Kazuko},
  title =	{{Towards a Qualitative Reasoning on Shape Change and Object Division}},
  booktitle =	{14th International Conference on Spatial Information Theory (COSIT 2019)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-115-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{142},
  editor =	{Timpf, Sabine and Schlieder, Christoph and Kattenbeck, Markus and Ludwig, Bernd and Stewart, Kathleen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2019.7},
  URN =		{urn:nbn:de:0030-drops-110998},
  doi =		{10.4230/LIPIcs.COSIT.2019.7},
  annote =	{Keywords: qualitative spatial representation, symbolic shape representation, Process-Grammar}
}

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Documents authored by Takahashi, Kazuko

Qualitative Formalization of a Curve on a Two-Dimensional Plane

Abstract

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Towards a Qualitative Reasoning on Shape Change and Object Division

Abstract

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