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Automatic Projector Calibration for Curved Surfaces Using an Omnidirectional Camera
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2017 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Automatiserad projektorkalibrering för krökta ytor med en rundstrålande kamera (Swedish)
Abstract [en]

This master’s thesis presents one approach to remove distortions generated by projecting onto non flat surfaces. By using an omnidirectional camera a full 360 dome could be calibrated and the corresponding angles between multiple projections could be calculated. The camera was modelled with the Unified Projection Model allowing any omnidirectional camera system to be used. Surface geometry was captured by using Gray code patterns, the optimal image centre was calculated as an quadratic optimisation problem and in the end a Spline surface countering the distortions was generated by using the FAST-LTS regression algorithm. The developed system used a RICOH THETA S camera calibrated by the omnidir module in openCV. A desirable result was achieved and during use of overlapping projectors a maximum error of 0.5° was measured. Testing indicates part of the error could have been introduced in the evaluation measurements. The resulting application is seen as a success and will be used by ÅF Technology AB during calibration of flight simulators.

Abstract [sv]

Denna rapport presenterar en metod för att motverka de distorsioner som uppkommer när en bild projeseras på en icke plan yta. Genom att använda en omnidirectional kamera kan en omslutande dome upplyst av flertalet projektorer bli kalibrerad. Kameran modellerades med The Unified Projection Model då modellen går att anpassa för ett stort antal kamerasystem. Projektorernas bild på ytan lästes av genom att använda Gray kod och sedan beräknades den optimala mittpunkten för den kalibrerade bilden genom att numeriskt lösa ett kvadratiskt NLP problem. Till slut skapas en Spline yta som motvärkar projektionsförvrängningen genom FAST-LTS regression. I den experimentella uppställningen användes en RICOH THETA S kamera som kalibrerades men omnidir modulen i openCV. Ett enligt författarna lyckat resultat uppnåddes och vid överlappning av flertalet projektorer så mättes ett maximalt fel på 0.5° upp. Vidare mätningar antyder att delar av detta fel uppkommit på grund av saknad noggrannhet i utrustningen under evalueringsfasen. Resultatet ses som lyckat och den utvecklade applikationen kommer att användas av ÅF Technology AB vid deras calibrering av flygsimulatorer.

Place, publisher, year, edition, pages
2017.
Series
TRITA-MAT-E ; 2017:42
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-209675OAI: oai:DiVA.org:kth-209675DiVA, id: diva2:1113509
External cooperation
ÅF Technology AB
Subject / course
Optimization and Systems Theory
Educational program
Master of Science - Applied and Computational Mathematics
Supervisors
Examiners
Available from: 2017-06-21 Created: 2017-06-21 Last updated: 2017-06-21Bibliographically approved

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CiteExportLink to record
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