Department of Mathematics, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovak Republic.
Med Image Anal. 2010 Aug;14(4):510-26. doi: 10.1016/j.media.2010.03.003. Epub 2010 Apr 10.
We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which are artificially connected due to acquisition error intrinsically linked to physics of LSM. In all studied aspects it turned out that the nonlinear diffusion filter which is called geodesic mean curvature flow (GMCF) has the best performance.
我们提出了非线性扩散方程、用于求解它们的数值方案以及它们在过滤从活体斑马鱼胚胎激光扫描显微镜 (LSM) 获得的 3D 图像中的应用，目的是确定最佳的过滤方法及其参数。在处理 3D+时间胚胎发生图像的大规模应用中，一个重要的目标是正确检测细胞核的数量和位置，从而生成胚胎发生的时空细胞谱系树。过滤是图像分析链的第一步也是必要的步骤，必须得到正确的结果，去除噪声，锐化细胞核边缘，并纠正与虚假连接子区域相关的采集误差。在本文中，我们研究了正则化 Perona-Malik 模型和广义平均曲率流方程在水平集公式中的这些性质。还包括与其他非线性扩散滤波器（如张量各向异性扩散和 Beltrami 流）的比较。所有数值方案都基于相同的离散化原则，即在空间中使用有限体积方法和在时间中使用半隐式方案来求解非线性偏微分方程。这些数值方案无条件稳定、快速且自然可并行化。首先使用原始数据和过滤数据的不同等位面之间的平均 Hausdorff 距离来评估和比较过滤结果，然后将感兴趣区域 (ROI) 中原始数据和过滤后检测到的等位面连通分量的数量与黄金标准中相应的核数量进行比较。这种分析证明了这种类型的数据的边缘保持非线性扩散滤波的健壮性和可靠性，并为所研究的模型和数值方案找到了最佳的滤波参数。进一步的比较包括由于与 LSM 物理相关的采集误差而人为连接的非常接近的物体的分离能力。在所有研究的方面，结果表明称为测地平均曲率流 (GMCF) 的非线性扩散滤波器具有最佳性能。
