## Abstract

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. 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 combined two-stage 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.

Original language | English |
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Pages | 181-185 |

Number of pages | 5 |

State | Published - 1 Dec 1998 |

Event | Proceedings of the 1998 International Conference on Image Processing, ICIP. Part 2 (of 3) - Chicago, IL, USA Duration: 4 Oct 1998 → 7 Oct 1998 |

### Conference

Conference | Proceedings of the 1998 International Conference on Image Processing, ICIP. Part 2 (of 3) |
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City | Chicago, IL, USA |

Period | 4/10/98 → 7/10/98 |

## ASJC Scopus subject areas

- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering