Find the volume of a nx3 Dataset

Question

Jose Andrés 2015-6-12

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/223608-find-the-volume-of-a-nx3-dataset

评论： Jose Andrés 2015-6-21

Hello everybody, I have an easy question:

I have seen this great explanation about how to integrate the volume underneath a set of nonuniformly spaced data: http://blogs.mathworks.com/videos/2009/09/08/integrating-to-find-the-volume-underneath-a-set-of-nonuniformly-spaced-data/

but the interpolation here it´s done between 0-1 because of his dataset. My question is: if my dataset has a large number of different values (like a ball), how should I do this interpolation? I have thought about to change the

interpZ(0.5,0.5) %test interpolation
vol = quad2d(interpZ,0,1,0,1) %volume should be close to 1

like this:

interpZ(¿?,¿?) %test interpolation
vol = quad2d(interpZ,min(min(z)),max(max(z)),min(min(z)),max(max(z)))

Thank you.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Image Analyst 2015-6-13

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/223608-find-the-volume-of-a-nx3-dataset#answer_182566

You have to decide what constitutes the "volume". Let's say your N by 3 data are the (x,y,z) coordinates in a scatter cloud/cluster that looks roughly like a peanut. Now, is your 3D volume the bounding box of the peanut? Or do you want it to be the volume of only the peanut itself? Finding the bounding box of the whole peanut is trivial = just use max() and min() on each of the three dimensions, x, y, and z. If you want a peanut shaped volume, then you have to decide if some arbitrary (x,y,z) point is to be included inside the peanut or outside of it, so that if you have a regular grid (like a CT or MRI volumetric image) then you can find the volume of the irregular peanut shape.

11 个评论
显示 9更早的评论隐藏 9更早的评论

Image Analyst 2015-6-16

You said "integrate the volume underneath a set of nonuniformly spaced data". Do you want the volume under only that data - those locations - or do you want to "fill out" the data to other missing (x,y) locations, and get the volume under those locations also? If you only want data under the existing data, then no, you don't need the other points. Imagine your data was like skyscrapers of a city on some flat plain, and you want the volume of the skyscrapers. Assume unit width of one block for each skyscraper. Do you need to know where the sky scraper is located in the city to know its volume? No, you don't.

But what if you want to drape a huge blanket over the tops of the skyscrapers and assume that the blanket height represents the height of unknown buildings in between the known buildings? Now you will need to interpolate to get/estimate those missing heights, and that will require knowing which (x,y) each building is at. But once you have the building height at each block, you can simply add up the heights to get the volume. At least that's one way. The other way is to assume triangular buildings instead of rectangular blocks, and then you'd have to do something more complicated like using trapz or something.

Image Analyst 2015-6-17

spatial_calibration_demo.m

If you want the volume in real world units you have to know the width of a voxel. What is your field of view? What is the number of voxels across it? Divide those to get the real world units of a voxel - essentially the cross sectional area. See my attached spatial calibration demo.

Jose Andrés 2015-6-21

Ok, that was the information I hadn't. My providers forgot to add this voxel's width information and I didn't know how could I do it.

Thank you so much, your last message made me realize what was the problem.

请先登录，再进行评论。

Find the volume of a nx3 Dataset

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

11 个评论
显示 9更早的评论隐藏 9更早的评论

更多回答（0 个）

另请参阅

类别

标签

Community Treasure Hunt

Find the volume of a nx3 Dataset

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

11 个评论 显示 9更早的评论隐藏 9更早的评论

更多回答（0 个）

另请参阅

类别

标签

Community Treasure Hunt

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

11 个评论
显示 9更早的评论隐藏 9更早的评论