Estimating the orientation of planar surfaces: Algorithims and bounds
Estimating the orientation of planar surfaces: Algorithims and bounds
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DOI：
10.1109/18.857800
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发表时间：
2000-08
期刊：
影响因子：
--
通讯作者：
H. Permuter;J. Francos
中科院分区：
文献类型：
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作者：
H. Permuter;J. Francos
本文提出了一种计算和统计上有效的参数化解决方案，从一个单一的，嘈杂的，观察到的图像，它的平面纹理表面的空间方向估计的问题。从表面到图像坐标的坐标变换，由于透视投影，变换的每个均匀的正弦分量的表面纹理到一个正弦曲线的频率是一个函数的位置。正弦相位在位置上的函数依赖性唯一地由表面的倾斜和倾斜角确定。从透视投影的物理模型出发，推导了在观测噪声存在的情况下，观测面倾斜和倾斜估计误差方差的Cramer-Rao下界。它表明，在本文中，每个正弦曲线的相位可以表示为一个线性函数的一些变量，这些变量是有关的表面倾斜和倾斜角。使用相位差分算法，我们拟合多项式相位模型的正弦分量的观察到的纹理。代入推导出的线性关系，未知的相位估计使用相位差分算法，我们得到一个封闭的形式，分析，和计算效率的解决方案，估计的倾斜和倾斜角度的问题。该算法的性能被证明是接近的Cramer-Rao界，即使是低信噪比，在计算复杂度，这是大大低于任何现有的算法。
This paper presents a computationally and statistically efficient 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. From the physical model of the perspective projection, we derive the Cramer-Rao lower bound on the error variance of estimating the tilt and slant of the observed surface in the presence of observation noise. It is shown in this paper that the phase of each of the sinusoids can be expressed as a linear function of some variables that are related 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 performance is shown to be close to the Cramer-Rao bound, even for low signal-to-noise ratios, at computational complexity which is considerably lower than that of any existing algorithm.