2nd Degree polynomial fit for the 3D array

2016 9 22
1 个回答
回答已采纳
更新时间：2020 7 22
2 次查看（30 天）

0 个投票

I am trying to find the 2nd degree polynomial fit for the 3d array which contains the magnetic field distortion information of water in MR imaging. I have two 3D arrays, one having fieldmap values and the other having magnetic field distortion around the MR sample. I am using the expression (Bfieldmap-Xi*Bsample), where Xi is a random value for susceptibility to find the data and try to fit this. But I am not quite sure how to find the fit for the 3D array, since it will have 10 coordinates including all three directions. Please help if someone has already an info on this.
Thanks,
Guru

3 个评论
显示 1更早的评论 隐藏 1更早的评论

John D'Errico
John D'Errico 2016-9-22
编辑：John D'Errico 2016-9-22
You need to explain, CLEARLY, what is/are the independent variable(s) in this model. So far, clear as mud.
jupiter
jupiter 2016-9-23
Basically there are 256 voxels each in all three directions. I need to find the fit in all three directions for the above expression. This is to ultimately find the background field in the water. Using the function 'polyfit', I can get only three coordinates, but thats in 2D space, for the 3D space, I need all ten coordinates, for (1,x,y,z,xx,yy,zz,xy,yz,zx). I hope now, the question is clear.
Jason Stockmann
Jason Stockmann 2020-7-22
编辑：Jason Stockmann 2020-7-22
Guru, you could try the code below. This worked for me. 'data' is your distortion map. 'polyorder' is the scalar input specifying the order of polynomial you'd like to fit to the data. You need to vectorize both your MRI distortion map (dependent variable) and the coordinate system (independent variable). I am also fitting a 3D polynomial to MRI field map data. I just picked integer indices for the coordinate system (independent variables). I didn't bother scaling them into meaningful values for the image field of view. You could replace them with physically meaningful values if you intend to use them for plotting, etc. later on.
dims=size(data);
[XX,YY,ZZ] = ndgrid(1:dims(1),1:dims(2),1:dims(3));
polymodel = polyfitn([XX(:) YY(:) ZZ(:)],data(:),polyorder);
ypred = polyvaln(polymodel,[XX(:) YY(:) ZZ(:)]);
ypred_array = reshape(ypred,dims);

请先登录，再进行评论。

请先登录，再回答此问题。

 采纳的回答

Steven Lord
Steven Lord 2016-9-23

0 个投票

If you have Curve Fitting Toolbox it can perform surface fitting. Use the Curve Fitting App to perform the fitting interactively or see "Fit and Plot a Polynomial Surface" on this documentation page for instructions on how to do it programmatically.
If you don't have Curve Fitting Toolbox, see the "Multiple Regression" section on this documentation page.

更多回答（0 个）

类别

在 帮助中心 和 File Exchange 中查找有关 Linear and Nonlinear Regression 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by