中文摘要：

多孔介质中孔隙空间的结构描述和问题求解是许多复杂形态实体微观分析和科学计算的基础，而实际的多孔介质孔隙空间结构由于异常复杂，采用简单的造型方法往往不能满足绘制和进一步计算的要求。为此，针对自然岩石核磁共振的3维体数据，提出了一种适用于多孔介质孔隙空间的造型方法。该方法首先通过最大球方法识别体数据中的孔隙空间，然后根据孔隙的层次关系和连通关系，通过建立孔隙空间的孔洞一网络模型来描述孔隙空间的拓扑结构，并结合隐式曲面造型方法来构造多孔介质孔隙空间的模型。将该方法运用到自然岩石的3维图像分析中的实验结果表明，该方法不仅使得多孔介质孔隙空间的复杂拓扑结构得以保留，而且保证了重建曲面的光滑性。

英文摘要：

The description of the pore structure in porous media is the base of microcosmic analysis and scientific computation of many complex shape entities. Traditional approaches do not fit for efficient rendering and further computation because the actual pore space in porous media is extra complex. In this paper, a new approach to study the morphology （shapes and connectivity） of the pore space of sandrock is presented. This approach uses an efficient algorithm to describe the 3D pore structure based on the pore-network model and implicit polynomials. The pore-network model uses maximal balls to recognize the pore space in magnetic resonance imaging data, and to distinguish between the ＂pore bodies＂ and ＂pore throats＂, and then establishes their respective connectivity. After the pore bodies of the pore-network model are constructed, a smooth implicit surface is generated to describe the pore space using the technique for blending implicit functions. This algorithm has been tested on the natural sandrock＇ s magnetic resonance images. The experimental results show that this model not only remains the complicated topological structure, but also assures the smoothness of the reconstructed surface. The results also show the microstructure characters of the pore space are in accord with the fractal model.