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Shape and motion reconstruction of non rigid objects from their 2D projections under uniform expansion conditions

Rekonstruktion der Bewegung und Form von beweglichen Objekten aus zweidimensionalen Projektionen unter gleichförmigen Expansionsbedingungen

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Abstract

This paper deals with the 3D-motion and structure reconstruction of a particular class of nonrigid objects based on a sequence of their 2D orthographic projections (images). The investigation focuses on the case where it is known a-pri-ori that the object deforms continuously in a uniform manner performing either expansion or contraction at a constant but, at the same time, unknown rate. Epipolar equations are properly extended to meet the requirements of this particular problem. It is shown that four point correspondences over four views yield a unique solution to motion and structure reconstruction. The theory is supported by a numerical result.

Zusammenfassung

In dieser Arbeit wird die Rekonstruktion von Bewegung und Form einer bestimmetn Sorte von beweglichen Objekten auf der Basis von 2D orthografischen Projektionen behandelt. Die Untersuchung ist auf Fälle konzentriert, in denen a priori bekannt ist, dass das Objekt auf gleichmäßige Weise deformiert wird und dabei einer Kontraktion oder Ausweitung in einem konstanten, aber unbekanntem Tempo unterliegt. Epipolar-geometrische Gleichungen werden erweitert, um den Anforderungen dieses partikulären Problems zu genügen. Es wird gezeigt, dass vier-Punkte-Korrespondenzen über vier Ansichten eine eindeutige Lösung für die Bestimmung von Bewegung und Form liefern. Die Theorie wird mittels eines numerischen Ergebnisses untermauert.

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Authors and Affiliations

  1. School of Mechanical Engineering, National Technical University of Athens, 9 Iroon Polytechniou Str., 15773, Athens, Greece

    C. G. Provatidis & D. T. Venetsanos

Authors
  1. C. G. Provatidis
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  2. D. T. Venetsanos
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Correspondence to C. G. Provatidis.

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Provatidis, C.G., Venetsanos, D.T. Shape and motion reconstruction of non rigid objects from their 2D projections under uniform expansion conditions . Forsch Ingenieurwes 70, 187–197 (2006). https://doi.org/10.1007/s10010-006-0031-7

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  • DOI: https://doi.org/10.1007/s10010-006-0031-7

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