Magnetic Resonance Imaging (MRI) is a technology for non-invasive imaging of anatomical features in detail. It can help in functional analysis of organs of a specimen but it is very costly. In this work, methods for (i) virtual three-dimensional (3D) reconstruction from a single sequence of two-dimensional (2D) slices of MR images of a human spine and brain along a single axis, and (ii) generation of missing inter-slice data are proposed. Our approach helps in preserving the edges, shape, size, as well as the internal tissue structures of the object being captured. The sequence of original 2D slices along a single axis is divided into smaller equal sub-parts which are then reconstructed using edge preserved kriging interpolation to predict the missing slice information. In order to speed up the process of interpolation, we have used multiprocessing by carrying out the initial interpolation on parallel cores. From the 3D matrix thus formed, shearlet transform is applied to estimate the edges considering the 2D blocks along the $Z$ axis, and to minimize the blurring effect using a proposed mean-median logic. Finally, for visualization, the sub-matrices are merged into a final 3D matrix. Next, the newly formed 3D matrix is split up into voxels and marching cubes method is applied to get the approximate 3D image for viewing. To the best of our knowledge it is a first of its kind approach based on kriging interpolation and multiprocessing for 3D reconstruction from 2D slices, and approximately 98.89\% accuracy is achieved with respect to similarity metrics for image comparison. The time required for reconstruction has also been reduced by approximately 70\% with multiprocessing even for a large input data set compared to that with single core processing.

翻译：磁共振成像（MRI）是一种能够对解剖特征进行详细非侵入性成像的技术，有助于对标本器官进行功能分析，但成本高昂。本文提出以下方法：（i）基于人类脊柱和大脑沿单轴方向的单序列二维磁共振切片进行虚拟三维重建；（ii）生成缺失的层间数据。该方法有助于保持被成像物体的边缘、形状、大小以及内部组织结构。沿单轴的原始二维切片序列被分割成更小的等长子部分，随后采用保边缘克里金插值法进行重建，以预测缺失的切片信息。为加速插值过程，我们通过并行核心进行初始插值，利用多进程处理。基于生成的三维矩阵，应用剪切波变换，通过沿Z轴考虑二维块来估计边缘，并利用提出的均值-中位数逻辑最小化模糊效应。最后，为进行可视化，将子矩阵合并为最终三维矩阵，再将该新生成的三维矩阵分解为体素，并应用移动立方体法得到可供查看的近似三维图像。据我们所知，这是首个基于克里金插值及多进程处理从二维切片进行三维重建的方法，在图像对比的相似性指标上实现了约98.89%的精度。即使面对大规模输入数据集，与单核处理相比，多进程处理也将重建所需时间减少了约70%。