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，我想从这些图像中构建3D图像.这是我第一次进行图像处理，并且从CT 2D图像中构造3D图像对我来说听起来很复杂.我进行了很多搜索，经过搜索之后，我终于想到了
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,
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要从2D图像构建3D图像，您需要找到深度图，该深度图指示物体距相机多远或近.然后，此地图将有助于构造3D图像(我不知道如何，并且我也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).
存在多种用于这种重构的算法，例如解析，迭代和统计.经过搜索，在我看来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.
我阅读了太多的资源，例如研究论文和调查论文，但是它们非常技术性，我无法连接其中提到的信息.
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.
以下是我搜索过程的结果，
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说明该过程.
None of the above resources explains the process in a simple way.
我知道有些软件可以完成这项工作，但是在使用任何软件之前，我都希望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.
任何人都可以分步说明从2D CT图像重建3D图像的算法是如何工作的，特别是对于迭代和统计方法?
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作为2D图像(3D对象的切片)进行了处理.CT图像的重建由CT设备制造商的软件执行，这是使用诸如反投影之类的算法将检测器收集的原始数据转换为体素的3D矩阵的过程.
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数据中复制3D图像，您只需要切片之间的距离(切片厚度)和2D图像像素的大小即可.如果您有DICOM图像，则有一个标签:切片厚度，表示以mm为单位的切片厚度.
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，建议从迭代重建方法开始.主题很广，可以在单个帖子中进行详细介绍，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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