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Least-squares Matching with Advanced Geometric Transformation Models Kleinste-Quadrate-Zuordnung mit erweiterten geometrischen Transformationen

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Least-squares matching (LSM) for area-based image matching is a well known technique in photogrammetry and computer vision since more than two decades. Differences between two or more images can be modelled by estimating geometric and radiometric transformation functions within the functional model. Commonly the affine transformation is used as geometric transformation. Since this approach is not strict in terms of the projective imaging model, it is worthwhile to investigate alternative transformation models. Based on special close-range applications this paper presents an advanced least-squares matching algorithm that uses the projective transformation model and polynomial transformations to handle geometric distortions between the images. In the first part a detailed description of the functional model is given for both approaches. In the second part the results of different tests are presented. The first test uses synthetic image data to investigate the 2D accuracy of the matching results (image coordinates). Within the second test a calibrated 3D reference body is used to investigate the 3D accuracy of point clouds that have been created with the PISA software for 3D free-form measurements by using the different matching approaches. All tests have shown that the polynomial transformation model yields to results with highest accuracy. The affine and the projective model yield to distinct systematic deviations, especially for the non-plane surface of the 3D reference body.

Die photogrammetrische Bildzuordnung durch Kleinste-Quadrate-Zuordnung hat sich in den letzten zwei Jahrzehnten als praktikable Methode zur subpixelgenauen Lösung des Korrespondenzproblems in den Bereichen Photogrammetrie und Computer Vision etabliert. Veröffentlichungen zum Thema basieren in der Regel auf der vereinfachten Annahme, dass sich die geometrische Beziehung zwischen einem Referenz- und n Suchfenstern durch die Affintransformation ausreichend gut beschreiben lässt. Motiviert durch spezielle Anwendungen mit einer kalibrierten Stereokamera in der Nahbereichsphotogrammetrie stellt der vorliegende Beitrag zwei Erweiterungen des Ansatzes hinsichtlich der zu verwendenden Geometrietransformationen vor: anstelle der Affintransformation werden die Projektivtransformation und die Polynomtransformation eingesetzt. Das funktionale Modell wird für beide Ansätze umfassend beschrieben. Die verschiedenen Ansätze werden anhand von synthetisch erzeugten Bilddaten sowie unter Verwendung eines kalibrierten Referenzkörpers untersucht. Die Tests zeigen, dass bei der hier gegebenen speziellen Aufgabenstellung mit je zwei konvergenten Messbildern höchste Zuordnungsgenauigkeiten mit dem Ansatz der Polynomtransformation erreicht werden und bei Verwendung der Affin- und Projektivtransformation z. T. deutliche systematische Abweichungen auftreten.


Language: German

Document Type: Research Article


Publication date: March 1, 2011

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  • Photogrammetrie - Fernerkundung - Geoinformation (PFG) is an international scholarly journal covering the progress and application of photogrammetric methods, remote sensing technology and the intricately connected field of geoinformation processing.

    Papers published in PFG highlight new developments and applications of these technologies in practice. The journal hence addresses both researchers and student of these disciplines at academic institutions and universities and the downstream users in both the private sector and public administration.

    PFG places special editorial emphasis on the communication of new methodologies in data acquisition, new approaches to optimized processing and interpretation of all types of data which were acquired by photogrammetric methods, remote sensing, image processing and the computer-aided interpretation of such data in general.

    PFG is the official journal of the German Society of Photogrammetry and Remote Sensing.
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