Li Yang, Teng Qizhi, He Xiaohai, Ren Chao, Chen Honggang, Feng Junxi
College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China.
Phys Rev E. 2019 Jun;99(6-1):062134. doi: 10.1103/PhysRevE.99.062134.
The three-dimensional (3D) structure of a digital core can be reconstructed from a single two-dimensional (2D) image via mathematical modeling. In classical mathematical modeling algorithms, such as multipoint geostatistics algorithms, the optimization of pattern sets (dictionaries) and the mapping problems are important issues. However, they have rarely been discussed thus far. Pattern set (dictionary)-related problems include the pattern set (dictionary) size problem and the one-to-many mapping problem in a pattern set (dictionary). The former directly affects the completeness of the dictionary, while the latter is manifested such that a single to-be-matched 2D patch has multiple matching patterns in the library and it is hence necessary to select these modes to establish an optimal mapping relationship. Whether the two above-mentioned problems can be properly resolved is directly related to the accuracy of the reconstruction results. Super-dimension reconstruction is a new 3D reconstruction method proposed by introducing the concepts of training dictionary, prior model, and mapping into the reconstruction of the digital core from the field of super-resolution reconstruction. In addition, mapping relationship extraction and dictionary building are also key issues in super-dimension reconstruction. Therefore, this paper discusses these common dictionary-related problems from the perspective of super-dimension dictionaries. We propose dictionary optimization using augmentation dictionaries and clustering based on the boundary features of the dictionary elements to improve the completeness and expand the expression ability of the dictionary. Furthermore, we propose constraint neighbor embedding-based dictionary mapping to establish a more reasonable dictionary mapping relationship for super-dimension reconstruction, and we solve the one-to-many mapping problem in the dictionary. Our experimental results show that the performance of the super-dimension dictionary can be improved by the above-mentioned algorithm. Thus, through the optimized dictionary structure and mapping relationship determined by the above-mentioned methods, the 2D patch to be reconstructed can match a more accurate 3D block in the dictionary. Consequently, the reconstruction precision is improved.
数字岩心的三维（3D）结构可以通过数学建模从单个二维（2D）图像重建得到。在经典的数学建模算法中，如多点地质统计学算法，模式集（字典）的优化和映射问题是重要问题。然而，到目前为止它们很少被讨论。与模式集（字典）相关的问题包括模式集（字典）大小问题和模式集（字典）中的一对多映射问题。前者直接影响字典的完备性，而后者表现为单个待匹配的2D面片在库中有多个匹配模式，因此需要选择这些模式来建立最优映射关系。上述两个问题能否得到妥善解决直接关系到重建结果的准确性。超维重建是一种新的3D重建方法，它通过将训练字典、先验模型和映射的概念从超分辨率重建领域引入到数字岩心的重建中。此外，映射关系提取和字典构建也是超维重建中的关键问题。因此，本文从超维字典的角度讨论这些常见的与字典相关的问题。我们提出使用扩充字典和基于字典元素边界特征的聚类进行字典优化，以提高字典的完备性并扩展字典的表达能力。此外，我们提出基于约束邻域嵌入的字典映射，为超维重建建立更合理的字典映射关系，并解决字典中的一对多映射问题。我们的实验结果表明，上述算法可以提高超维字典的性能。因此，通过上述方法确定的优化字典结构和映射关系，待重建的2D面片可以在字典中匹配更准确的3D块。从而提高了重建精度。
