Multidimensional E-spline sampling theory and applications

提出了以E-Spline函数为采样模型的阶梯线边缘提取方法。直线边缘可以用方向、偏移量和幅度三个参数来描述。提取这些参数的标准方法是Hough变换，该方法在原理上存在亚像素精度的限制。这种限制可以通过引入像素获取模型来解决。这种情况下的传统方法使用三个参数的解析解，这三个参数对像素中的噪声敏感。为了解决这一问题，我们提出了一种优化方法。我们首先定义了一个标准，用来评估从噪声像素值获得的指数矩与其理论闭合形式之间的距离。它的优化是通过简单的从粗到精的搜索来进行的。计算机仿真结果表明，该方法不仅大大提高了图像的抗噪能力，而且比Hough变换更准确地提取了图像中的直线边缘。

We proposed step line edge extraction method using E-spline functions as sampling model. A straight line-edge can be described by three parameters of orientation, offset, and amplitude. The standard method to extract these parameters is Hough transform, which has a limitation in principle to achieve sub-pixel accuracy. Such a limitation can be resolved by introducing a pixel acquisition model. Conventional approaches along this context used analytic solutions for the three parameters, which are sensitive to noise in pixels. To solve the problem, we proposed an optimization approach. We first define a criterion that evaluates a distance between exponential moments obtained from noisy pixel values and its theoretical closed form. Its optimization is conducted by a simple coarse-to-fine search. Computer simulations showed that not only noise resilience is much improved by the proposed method but also it extracts line-edges from real images more accurately than the Hough transform.