Rohr Karl
Computer Vision Group (BMCV), University of Heidelberg, Germany.
IEEE Trans Biomed Eng. 2007 Sep;54(9):1613-20. doi: 10.1109/TBME.2007.902589.
In this paper, we analyze the accuracy of estimating the location of 3-D landmarks and characteristic image structures. Based on nonlinear estimation theory, we study the minimal stochastic errors of the position estimate caused by noisy data. Given analytic models of the image intensities, we derive closed-form expressions of the Cramér-Rao bound for different 3-D structures such as 3-D edges, 3-D ridges, 3-D lines, 3-D boxes, and 3-D blobs. It turns out that the precision of localization depends on the noise level, the size of the region-of-interest, the image contrast, the width of the intensity transitions, as well as on other parameters describing the considered image structure. The derived lower bounds can serve as benchmarks and the performance of existing algorithms can be compared with them. To give an impression of the achievable accuracy, numeric examples are presented. Moreover, by experimental investigations, we demonstrate that the derived lower bounds can be achieved by fitting parametric intensity models directly to the image data.
在本文中，我们分析了估计三维地标和特征图像结构位置的准确性。基于非线性估计理论，我们研究了由噪声数据引起的位置估计的最小随机误差。给定图像强度的解析模型，我们推导了不同三维结构（如三维边缘、三维脊线、三维线条、三维盒子和三维斑点）的克拉美-罗下界的闭式表达式。结果表明，定位精度取决于噪声水平、感兴趣区域的大小、图像对比度、强度过渡的宽度以及描述所考虑图像结构的其他参数。推导得到的下界可作为基准，现有算法的性能可与之进行比较。为了给可实现的精度一个直观印象，我们给出了数值示例。此外，通过实验研究，我们证明了通过将参数强度模型直接拟合到图像数据可以达到推导得到的下界。
