Interpolation of stereo data using Lagrangian polynomials

Rafic A. Bachnak; Jihad S. Yamout

doi:10.1117/12.46291

1 August 1991 Interpolation of stereo data using Lagrangian polynomials

Rafic A. Bachnak, Jihad S. Yamout

Proceedings Volume 1457, Stereoscopic Displays and Applications II; (1991) https://doi.org/10.1117/12.46291
Event: Electronic Imaging '91, 1991, San Jose, CA, United States

Abstract

Surface reconstruction is an important problem within computer vision. This paper studies the application of the Lagrange polynomials to interpolating three-dimensional stereo data. The process consists of fitting a surface function to the given 3-D data. The value of the constructed surface at a point (x,y) is calculated locally in finite intervals based on the data at relatively nearby points. This produces a large number of polynomials; however, it requires less computational time than a global solution. This local interpolation is of interest when considering unusual shapes where the data points are irregularly scattered throughout the 3-D space. Overlapping is used when constructing the polynomials to ensure the continuity and smoothness of the surfaces from one scene point to the next. Because the data are generally sparse, the horizontal and vertical one-dimensional operations give different results. Final approximation is based on minimizing the error based on the least square criterion. Experiments show that the method produces good results.

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Rafic A. Bachnak and Jihad S. Yamout "Interpolation of stereo data using Lagrangian polynomials", Proc. SPIE 1457, Stereoscopic Displays and Applications II, (1 August 1991); https://doi.org/10.1117/12.46291

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KEYWORDS

Cameras

Stereoscopic displays

Imaging systems

3D image processing

Information operations

3D vision

Computer vision technology

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