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Polynomial Methods for Structure from Motion
December 1990 (vol. 12 no. 12)
pp. 1150-1166

The authors analyze the limitations of structure from motion (SFM) methods presented in the literature and propose the use of a polynomial system of equations, with the unit quaternions representing rotation, to recover SFM under perspective projection. The authors combine the equations by the method of resultants with the MAXIMA symbolic algebra system, reducing the system to a single polynomial. Its real roots are then found with Sturm sequences. Since this system has multiple solutions, a hypothesize-and-verify scheme is used to eliminate incorrect ones. The scheme diminishes the sensitivity of using polynomial equations. The authors examine the effect of different rotation axes and angles on SFM accuracy and compare the performance of the algorithm to a few earlier approaches. Generally, it is found that a large amount of motion is the most important factor in getting good SFM accuracy.

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Index Terms:
3D structure recovery; 2D image frames; picture processing; pattern recognition; structure from motion; polynomial; MAXIMA; symbolic algebra system; Sturm sequences; pattern recognition; picture processing; polynomials
Citation:
C. Jerian, R. Jain, "Polynomial Methods for Structure from Motion," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 12, pp. 1150-1166, Dec. 1990, doi:10.1109/34.62604
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