从2D图像算法重建3D图像 [英] Reconstructing 3D image from 2D image algorithm
问题描述
我有一些岩石的 CT 图像，我想根据这些图像构建 3D 图像.这是我第一次从事图像处理工作，从 CT 2D 图像中构建 3D 图像对我来说听起来很复杂.搜了很多，终于有了这些想法，
I have some CT images for some rock, and I want to build a 3D image out of these images. This is the first time I work on image processing, and constructing 3D image out of CT 2D images sounds complicated for me. I've searched a lot, after searching I've ended up with these thoughts,
要从 2D 图像构建 3D 图像，您需要找到深度图，该图指示对象与相机的距离或接近程度.然后这张地图将有助于构建 3D 图像(我不知道如何，而且我没有找到明确的资源).
To construct a 3D image from 2D one you need to find depth map which indicates how far or near an object is to the camera. Then this map will help constructing the 3D image (I don't know how, and I didn't find a clear resource about that).
存在多种用于此类重建的算法，例如分析、迭代和统计.搜索后，在我看来，最后两种类型比第一种更好.
There exist multiple algorithms for such a reconstruction, like analytical, iterative, and statistical. After searching it seems to me that the last two types are better than the first one.
我阅读了太多资源，例如研究论文和调查论文，但它们的技术性很强，我无法将其中提到的信息联系起来.
I've read too many resources like research papers and survey papers, but they were very technical and I couldn't connect the information mentioned within them.
这是我搜索过程的一些结果，
Here are few results of my searching process,
https://www.aapm.org/meetings/02AM/pdf/8372-23331.pdf
https://en.wikipedia.org/wiki/Iterative_reconstruction
以上资源均未以简单的方式解释该过程.
None of the above resources explains the process in a simple way.
我知道有一些软件可以完成这项工作，但在使用任何软件之前，我想从数学上理解算法本身.
I know that there are some software that can do this job, but before using any, I want to understand the algorithm mathematically itself.
谁能分步骤解释一下从 2D CT 图像重建 3D 图像的算法是如何工作的，特别是迭代和统计方法?
Can anyone please explain in steps how the algorithm of 3D image reconstruction from 2D CT images work, specially for the iterative and statistical methods?
推荐答案
根据您的描述，我推断您已经将数据处理为 2D 图像(3D 对象的切片).CT 图像的重建由 CT 设备制造商的软件执行，这是一个将检测器收集的原始数据转换为 3D 体素矩阵的过程，例如使用反向投影等算法.
From your description I deduce that you have already processed data as 2D images(slices of 3D object). Reconstruction of CT images is performed by CT device manufacturers software and this is a process of transforming raw data gathered by detectors into 3D matrix of voxels using algorithms like for example backprojection.
您拥有的图像是该 3D 体素矩阵的 2D 切片.要从该 2D 数据再现 3D 图像，您只需要切片之间的距离(切片厚度)和 2D 图像像素的大小.如果您有 DICOM 图像，则有一个标签:切片厚度表示切片厚度，单位为毫米.
Images that you have are 2D slices of that 3D voxels matrix. To reproduce 3D image from that 2D data you only need distance between slices(slices thickness) and size of 2D image pixel. If You have DICOM image there is a tag: Slice Thickness representing slice thickness in mm.
如果您想了解重建过程，我建议从迭代重建方法开始.主题是在单个帖子中详细阐述的广泛，因此我提供了一些您可以开始的链接:
If you want to understand reconstruction process I suggest to start with Iterative reconstruction methods. Subject is to broad to elaborate in single post so I provide some links where you could start:
http://rsta.royalsocietypublishing.org/content/373/2043/20140399
http://www.dspguide.com/ch25/5.htm
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