Invariant reconstruction of 3-D curves and surfaces

Robert L. Stevenson; Edward J. Delp III

doi:10.1117/12.25229

1 February 1991 Invariant reconstruction of 3-D curves and surfaces

Proceedings Volume 1382, Intelligent Robots and Computer Vision IX: Neural, Biological, and 3D Methods; (1991) https://doi.org/10.1117/12.25229
Event: Advances in Intelligent Robotics Systems, 1990, Boston, MA, United States

Abstract

The reconstruction of curves and surfaces from sparse data is an important task in many applications. In computer vision problems the reconstructed curves and surfaces generally represent some physical property of a real object in a scene. Thus the characteristics of the reconstruction process differs from straight forward fitting of smooth curves and surfaces to a set of data. Since the collected data is represented in an arbitrarily chosen coordinate system the reconstruction process should be invariant to the choice of the coordinate system (except for the transformation between the two coordinate systems). In this paper reconstruction algorithms are presented for reconstructing invariant estimates of both curves and surfaces. The reconstruction problem will be cast as an illposed inverse problem which must be stablized using a priori information about the constraint formation. Tikhonov regularization is used to form a wellposed mathematical problem statement. Examples of typical reconstructed objects are also given. 1.

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Robert L. Stevenson and Edward J. Delp III "Invariant reconstruction of 3-D curves and surfaces", Proc. SPIE 1382, Intelligent Robots and Computer Vision IX: Neural, Biological, and 3D Methods, (1 February 1991); https://doi.org/10.1117/12.25229

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