Article Dans Une Revue Surface Topography: Metrology and Properties Année : 2025

Modelling of the influence of measurement uncertainties on the algorithmic complexity of 3D topography stitching

Résumé

Observation of physical phenomena and their expression on solids is a challenge, especially considering their coupling. As a privileged place of interaction between solids and the external environment, surface should be studied. Roughness analysis often relies on optical profilometers to provide detailed topographic maps of the solid. To facilitate the analysis of physical phenomena, multiscale analysis is used to separate each phenomenon at their scale of application. However, optical profilometers natively propose a limited scale range to observe. Stitching is an assembling technique of topographic map solving this problem, by generating high resolution over a large field of measurement. Stitching can be summed up as an optimization problem of the alignment of elementary maps, i.e., registration. Yet, the stitching optimization problem is not trivial to solve. This paper proposes a theoretical analysis of the algorithmic complexity of the stitching problem and provides an estimation of the stitching problem complexity, considering measurement uncertainties, which is lacking from literature. First, a simplified stitching problem is presented, based on the assumption that stitching in standard conditions is at least as algorithmically complex. Simulations of local stitching displacements are performed based on the simplified stitching problem. Modelling of stitching reveals that the stitching problem is in exponential time problem class. The complexity of the simplified stitching problem is then estimated to follow an evolution similar to 2^n by a theoretical analysis of the stitching problem complexity.

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mardi 12 mai 2026
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Complète hal-05231882 Article Robin Guibert, Frederic Robache, Julie Lemesle, Saïd Hanafi, Christopher Brown, et al.. Review of 3D topography stitching and registration algorithms: procedure, error evaluation and mathematical modelling. Surface Topography: Metrology and Properties, 2025, 13 (1), pp.013001. ⟨10.1088/2051-672X/adabfd⟩. ⟨hal-05231882⟩

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Complète hal-04122323 Article Julie Lemesle, Robin Guibert, Maxence Bigerelle. A Novel 3D Topography Stitching Algorithm Based on Reflectance and Multimap. Applied Sciences, 2023, 13 (2), pp.857. ⟨10.3390/app13020857⟩. ⟨hal-04122323⟩

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Complète tel-03575253 Thèse de doctorat Robin Guibert. Stitching of 3D Elementary Topographies for Roughness Multiscale Analysis. Computer Science [cs]. Université Polytechnique Hauts-de-France; Institut national des sciences appliquées Hauts-de-France, 2021. English. ⟨NNT : 2021UPHF0034⟩. ⟨tel-03575253⟩

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mardi 12 mai 2026
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Dates et versions

hal-05367414 , version 1 (15-11-2025)

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Maxence Bigerelle, Robin Guibert. Modelling of the influence of measurement uncertainties on the algorithmic complexity of 3D topography stitching. Surface Topography: Metrology and Properties, 2025, 13 (4), pp.045008. ⟨10.1088/2051-672X/ae198e⟩. ⟨hal-05367414⟩
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