Extract 2D slice parallel to an arbitrary plane in 3D image.

Hi,

I have a 3D medical image (IM) containing grayvalues. (size: 352 229 277, data type double).

I want slice through the 3D image, parallel to a plane.

The plane is defined by a line.

The line is defined by selecting 2 points in 2D view of the 3D image. (This 2D view is obtained by IM(:,123,:) )

Points:

A=[104,123,111]; 
B=[253,123,153]; 

The plane is defined with a normal vector orthogonal to this line.

I want to slice the 3D image with a slice parallel to this plane.

Then I want to view these slices in 2D setting. Like the function sliceViewer. (sliceViewer doesn't support arbitrary angle slices).

I tried to use the slice function, following this example: https://www.mathworks.com/help/releases/R2016b/matlab/ref/slice.html#f33-509125.

Tbh I don't understand much:

Firstly I don't understand how to define a surface with this:

I seems that I can't give a value to the meshgrid indices from my image: slice(x,y,z,V,XI,YI,ZI)

Secondly:

I have 3 points to define the plane.

I have the normal vector.

But I don't know how to use it with the slice function: slice(x,y,z,V,XI,YI,ZI)

Thanks in advance!

%% load
I=Tiff('im','r'); 
        im=read(I); 
        im=uint8(squeeze(im)); 
        imf=imgaussfilt3(im,0.5); 
        imf=im2double(imf); 
       
%% isometric
sz_im=size(imf); 
average=(sum(sz_im))./3; 
imc=imresize3(imf,[average,average,average]);

%% plane equation
%  points on slice y=123. Line runs through A and B.  http://www2.math.umd.edu/~jmr/241/lines_planes.html
A=[104,123,111]; 
B=[253,123,153]; 
%third point for determining the plane
C=[104,124,111];
%normal is cross product
normal = cross(A-B,A-C);

%% meshgrid 
[row,col,z] = meshgrid(0:1:average,0:1:average,0:1:average); 
v = imc(row,col,z); %ERROR: dimensions 

row_slice= %WHAT should I enter here?
col_slice= %WHAT should I enter here?
z_slice= %WHAT should I enter here?
slice(row,col,z,V,row_slice,col_slice,z_slice)

Answer 1

[KALYAN ACHARJYA]

I want to slice the 3D image with a slice parallel to this plane.

Let suppose image3d is 3D image, which you want to slices

Slice 1

image3d_1= image3d(:,:,1);

Slice 2

image3d_2= image3d(:,:,2);

so on... or you can store the all slices in cell array

[M W]

In your example you obtain slices which are parallel to one of the axis.

I want to slice the 3D image in a plane definied by these 3 points, not parallel to one of the axis.

A = [104,122,111];

B = [253,122,153];

C = [104,124,111];

I guess the function slice should do this, if I give the right definition of the following:

row_slice= %WHAT should I enter here?
col_slice= %WHAT should I enter here?
z_slice= %WHAT should I enter here?
slice(row,col,z,V,row_slice,col_slice,z_slice)

But I don't know how to define a plane by matrices.

[KALYAN ACHARJYA]

Are you looking for this one, right?

https://www.mathworks.com/help/matlab/math/multidimensional-arrays.html

[M W]

Thank you, but I would like to know what the input for the last 3 variables in the slice function should be:

slice(x,y,z,V,XI,YI,ZI)

[KALYAN ACHARJYA]

Have you seen this example in MATLAB documentation?

[X,Y,Z] = meshgrid(-2:.2:2);
V = X.*exp(-X.^2-Y.^2-Z.^2);
xslice = [-1.2,0.8,2];   
yslice =0;
zslice = 0;
slice(X,Y,Z,V,xslice,yslice,zslice);

Here xslice,yslice,zslice represents the position of slices with respect to x,y,z axis

xslice = [-1.2,0.8,2] represents the position of slices in the x axis, where yslice =0 (Parellel to y axis) & zslice = 0(Parellel to z axis)

[M W]

Yes I did!

But I don't understand how to define an plane that is not parallel to one of the axis, by matrices.

For example a plane that runs through these points:

A=[104,123,111]; 
B=[253,123,153]; 
%third point for determining the plane
C=[104,124,111];