TY - GEN

T1 - Estimating the orientation of planar surfaces using the phase differencing algorithm

AU - Permuter, Haim

AU - Francos, Joseph M.

N1 - Publisher Copyright:
© 1999 IEEE.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - This paper presents a parametric solution to the problem of estimating the orientation in space of a planar textured surface, from a single observed image of it. The coordinate transformation from surface to image coordinates, due to the perspective projection, transforms each homogeneous sinusoidal component of the surface texture into a sinusoid whose frequency is a function of location. It is shown in this paper that the phase of each of the sinusoids can be expressed as a linear function of some constants that are related, in a rather simple form, to the surface tilt and slant angles. Using the phase differencing algorithm we fit a polynomial phase model to a sinusoidal component of the observed texture. Substituting in the derived linear relation, the unknown phase with the one estimated using the phase differencing algorithm, we obtain a closed form, analytic, and computationally efficient solution to the problem of estimating the tilt and slant angles. The algorithm is shown to produce estimates that are close to the Cramer-Rao bound, at computational complexity which is considerably lower than that of any existing algorithm.

AB - This paper presents a parametric solution to the problem of estimating the orientation in space of a planar textured surface, from a single observed image of it. The coordinate transformation from surface to image coordinates, due to the perspective projection, transforms each homogeneous sinusoidal component of the surface texture into a sinusoid whose frequency is a function of location. It is shown in this paper that the phase of each of the sinusoids can be expressed as a linear function of some constants that are related, in a rather simple form, to the surface tilt and slant angles. Using the phase differencing algorithm we fit a polynomial phase model to a sinusoidal component of the observed texture. Substituting in the derived linear relation, the unknown phase with the one estimated using the phase differencing algorithm, we obtain a closed form, analytic, and computationally efficient solution to the problem of estimating the tilt and slant angles. The algorithm is shown to produce estimates that are close to the Cramer-Rao bound, at computational complexity which is considerably lower than that of any existing algorithm.

UR - http://www.scopus.com/inward/record.url?scp=85039951933&partnerID=8YFLogxK

U2 - 10.1109/HOST.1999.778720

DO - 10.1109/HOST.1999.778720

M3 - Conference contribution

AN - SCOPUS:85039951933

T3 - Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999

SP - 178

EP - 182

BT - Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999

PB - Institute of Electrical and Electronics Engineers

T2 - 1999 IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999

Y2 - 14 June 1999 through 16 June 1999

ER -