TY - JOUR

T1 - Parametric estimation of the orientation of textured planar surfaces

AU - Francos, Joseph M.

AU - Permuter, Haim H.

N1 - Funding Information:
Manuscript received November 19, 1998; revised August 18, 2000. This work was supported in part by the Israel Ministry of Science, Eshkol Fellowship Program in Applied Mathematics under Grant 0616196, in part by the Israel Ministry of Science and the French Ministry of Research and Technology under Grant 8814196, and in part by the Israel Ministry of Science under Grant 8635297. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Patrick Bouthemy.

PY - 2001/3/1

Y1 - 2001/3/1

N2 - This paper presents a parametric solution to the problem of estimating the orientation in space of a planar textured surface, from a single, noisy, 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. The functional dependence of the sinusoid phase in location is uniquely determined by the tilt and slant angles of the surface. Using the phase differencing algorithm we fit a polynomial phase model to a sinusoidal component of the observed texture. Assuming the estimated polynomial coefficients are the coefficients of a Taylor series expansion of the phase, we establish a linear recursive relation between the model parameters and the unknown slant and tilt. A linear least squares solution of the resulting system provides the slant and tilt estimates. To improve accuracy, an iterative refinement procedure is applied in a small neighborhood of these estimates. The performance of the proposed algorithms is evaluated by applying them to images of different planar surfaces, and by comparing their statistical performance with the Cramer-Rao bound. The combined two-stage algorithm is shown to produce estimates that are close to the bound.

AB - This paper presents a parametric solution to the problem of estimating the orientation in space of a planar textured surface, from a single, noisy, 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. The functional dependence of the sinusoid phase in location is uniquely determined by the tilt and slant angles of the surface. Using the phase differencing algorithm we fit a polynomial phase model to a sinusoidal component of the observed texture. Assuming the estimated polynomial coefficients are the coefficients of a Taylor series expansion of the phase, we establish a linear recursive relation between the model parameters and the unknown slant and tilt. A linear least squares solution of the resulting system provides the slant and tilt estimates. To improve accuracy, an iterative refinement procedure is applied in a small neighborhood of these estimates. The performance of the proposed algorithms is evaluated by applying them to images of different planar surfaces, and by comparing their statistical performance with the Cramer-Rao bound. The combined two-stage algorithm is shown to produce estimates that are close to the bound.

KW - Nonhomogeneous two-dimensional signals

KW - Parametric texture modeling

KW - Perspective estimation

KW - Two-dimensional polynomial phase models.

UR - http://www.scopus.com/inward/record.url?scp=0035280208&partnerID=8YFLogxK

U2 - 10.1109/83.908513

DO - 10.1109/83.908513

M3 - Article

C2 - 18249630

AN - SCOPUS:0035280208

VL - 10

SP - 403

EP - 418

JO - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

SN - 1057-7149

IS - 3

ER -