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An Extended Qualitative Model for Reasoning About 3D Objects Using Depth and Different Perspectives

Authors Martí Ejarque , Zoe Falomir

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Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Automated reasoning
  • Theory of computation → Programming logic
  • Computing methodologies → Knowledge representation and reasoning
  • Computing methodologies → Spatial and physical reasoning
Keywords
  • qualitative spatial reasoning
  • spatial cognition
  • first order logics
  • three-dimensional information
  • perspectives
  • object perception
  • SWI-Prolog

Metrics

Abstract

Reconstructing a three-dimensional structure from partial two-dimensional views requires spatial reasoning. This paper presents the EQ3D, a dimension-agnostic extension of the Qualitative 3D (Q3D) model that generalises qualitative volumetric reasoning to arbitrary H× W× L configurations. EQ3D preserves symbolic depth representations while incorporating adjacent-view propagation rules that increase cross-view inference opportunities. Implemented in SWI-Prolog as a fully declarative pipeline, EQ3D infers hidden views from three orthographic Front-Right-Up views, producing correct inferred cells for the Q3D-Dataset which includes 24 objects of varying size and shape, while ambiguous cells remain explicitly undetermined. Coverage of hidden structure ranges from 26.85% to 82.67%, demonstrating that while inference remains logically sound, the proportion of determinable volume is inherently configuration-dependent. EQ3D provides an interpretable symbolic framework for qualitative 3D reasoning that scales across resolutions without size-specific adaptation.

Cite As Get BibTex

Martí Ejarque and Zoe Falomir. An Extended Qualitative Model for Reasoning About 3D Objects Using Depth and Different Perspectives. In 17th International Conference on Spatial Information Theory (COSIT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 393, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.COSIT.2026.5

Author Details

Martí Ejarque
  • Computing Science Department, Umeå Universitet, Sweden
Zoe Falomir
  • Computing Science Department, Umeå Universitet, Sweden

Funding

We acknowledge the funding by the Wallenberg AI, Autonomous Systems and Software Program (WASP) awarded by the Knut and Alice Wallenberg Foundation, Sweden.

Supplementary Materials

References

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