3D Reslicing using COMKAT image tool (basic)

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Reslicing 3D image volume using COMKAT image tool (basic)

Overview

Reslicing a 3D (or 3D vs time) image dataset can be accomplished using various components of COMKAT including the function sliceVolume() which is a method of ImageVolumeData. This example explains how to create a 2D image by slicing from a volume at a position, plane orientation, and magnification specified by the user. The approach is to load the image volume dataset into an instance of an ImageVolumeData (abbreviated IVD) object and to use the sliceVolume() method.

Background

sliceVolume() is a mex-file written in c with an interface to MATLAB that makes the operation particularly efficient. COMKATImageTool uses sliceVolume() and you can use it too.

Approach I. Demonstrate the method for coordinate transformations

Create an instance of an IVD and load it with an image volume. 

  ivd = ImageVolumeData(); % create an instance of an ImageVolumeData object
  ivd = read_DICOM(ivd, pathName, fileName); % load volume into an instance of IVD object;


Create lists of indices of all pixels in the 2D slice (rectangular grid) that we are creating 

  [i, j] = meshgrid(0 : Nc-1, 0 : Nr-1); % i and j will be 2D arrays, meshgrid is a function built into MATLAB
  ij = [c(:)’ ; r(:)’];  % make matrix, each column corresponding to a single pixel in the slice we are creating

The first and second rows of ij are the indices corresponding to column and row indices of all voxels in the desired slice. So the dimension of ij is 3 x ( # of desired voxels ).

For example, the first column of ij could be [ 0 ; 0 ] ; the second column could be [ 0 ; 1 ] , etc.


Compute the physical x,y,z locations, in mm, from pixel indices according to the DICOM coordinate system ref [1] p. 275.

This is a two-step process. The first step is to compute the coordinate transformation matrix. Note that pixel spacing/zoom, orientation, and position for the slice are specified in the transformation matrix. 

  M = ( Insert the method for generating the transformation matrix );


The second step is to use the transformation matrix to calculate the physical (mm) location of each pixel in the desired slice 

  xyz = M * ij;   % xyz is a matrix consisted of three rows the physical x, y, and z location (m) of all the desired voxels. The dimension of xyz is 3 x ( # of desired voxels ).


These xyz locations are the same as those in the image volume that is being sliced to make the 2D image. From these xyz locations, we find the corresponding 3D indices, (u,v,w), into the volume. This uses the transformation matrix for the volume, Mhat, that relates the indices to the xyz physical location. This is analogous to M used for the desired slice but here the pixel spacing, orientation, and position indicate how the volume data are stored.

Specify the matrix for reverse mapping ( index space of the original image volume (uvw) --> xyz ) 

  Mhat = ( Insert the method for generate the mapping);


Calculate voxel indcies into the volume corresponding to xyz physical location 

  uvw =  inv( Mhat ) * xyz;    % uvw is the matrices consisted of the indices in the domain of the original volume

uvw is a matrix consisted of three rows corresponding to row, column, and plane indices of the original volume data. The dimension of uvw is identical of that of xyz.


Separate uvw into the components 

    u = ( row indices in the domain of original of volume data );
    v = ( column indices in the domain of original of volume data );
   w = ( plane indices in the domain of original of volume data );

Therefore, the u, v, w are the first, second, and third rows of uvw.


Use sliceVolume() to interpolate the slice 

  slice = sliceVolume(idv, v, u, w, rawbackgroundPixelValue , 'linear');

backgroundPixelValue is a value that used for the interpolation when it is nothing there for calculating the interpolation value. The value is a unscaled raw background value of images.

In gerneral, rawbackgroundPixelValue = (scaled_pixel_value - rescale_intercept) / (rescale_slope) ;

e.g. For PET, the scaled background value is usually zero. 

==>    rawbackgroundPixelValue  = ( 0 - rescale_intercept) / rescale_slope ;

So rawbackgroundPixelValue can be calculated as follows: 

  s = get( ivd, 'VolumeFrameBufferScaleFactor');           % rescale_slope
  o = get( ivd, 'VolumeFrameBufferRescaleIntercept');  % rescale_intercept
  rawbackgroundPixelValue  = - o / s;


Display new slice 

  figure, imagesc(slice); axis image % isotropic


Approach II. Use coordinateGen() to do the coordinate transformation

  • This should create same result as approach I but require fewer lines of coding since coordinateGen() does most things that are needed.


Read the image volume into an ImageVolumeData object 

  ivd = ( Insert the method for reading data );


Use coordinateGen() to generate uvw 

  [u, v, w] = coordinateGen(ivd, Nc, Nr, pixelSpacing, planePos, orientation); % Input the desired pixelSpacing, planePos and orientation matrices


Use sliceVolume() to interpolate 

  slice = sliceVolume(idv, v, u, w, backgroundPixelValue, 'linear');


Display slice 

  figure, imagesc(slice); axis image % isotropic


Examples (Cardiac-PET)

We're going to describe four examples.

We'll use the approach I to do the first example and use the approach II to accomplish the others.

Obtain a new slice

First, let's use the approach I to obtain a new slice. 

ivd = (read data into IVD);


To obtain a new slice, we need to specific the number of rows and columns in the new image 

  Nc = 370;  % # of columns
  Nr = 370;  % # of rows

Create the indices of each voxel 

  [i, j] = meshgrid(0 : Nc-1, 0 : Nr-1);
      ij = [c(:)’ ; r(:)’];

Specify the sampling pixel size and the position of sampling plane 

  pixelSpacingOrg = [1.5501; 1.5501];   % Set pixel size (mm)
  
  planePosOrg = [-0.7751; -0.7751; 88.0000];   % Set the reslicing plane location

Set the orientation matrix 

  orientationInput = [1, 0; 
                                 0, 1;
                                 0, 0];

Now, we're going to calculate physical location (mm) of voxels in the desired image 

  xyz = orientationInput * pixelSpacingOrg* ij + repmat(planePosOrg ,1 , Nr * Nc);


After obtaining the physical location, we need to calculate the indices of each voxel in the original volume space.

Use the inverse mapping method to calculate the indices in the original image volume

We need to obtain the original pixel size, orientation, and image position matrices for the inverse mapping

You can specify your image information. Here we use function get() to obtain the information we need from the IVD 

  [ny, nx, nz, nf] = get(ivd, 'VolumeDimension'); 
  pixDim = get(ivd, 'PixelSpacing');
  vol_Uspacing = pixDim(2);
  vol_Vspacing = pixDim(1);
  vol_Wspacing = pixDim(3);
  
  vol_pos  = get(ivd, 'ImagePositionPatient');
  vol_orient  = get(ivd, 'ImageOrientationPatient');

Therefore, the inverse mapping can be done as follow: 

  uvw =  diag([1./vol_Uspacing 1./vol_Vspacing 1./vol_Wspacing]) * inv(vol_orient) * ( xyz - repmat(vol_pos, 1, Nr * Nc) );


In order to use sliceVolume() to do the interpolation, we need to separate uvw in three separate matrices. 

  u =  ( reshape(uvw(1,:), [Nr, Nc]) ) + 1;
  v =  ( reshape(uvw(2,:), [Nr, Nc]) ) + 1;
  w =  ( reshape(uvw(3,:), [Nr, Nc]) ) + 1;
  
  * Note: the indices in original image volume are defined to start from 1. After performing the inverse mapping, the indices need to be add by 1.


As we described in the approach I, the raw background value of PET can be calculated as follows: 

  s = get(ivd, 'VolumeFrameBufferScaleFactor');
  o = get(ivd, 'VolumeFrameBufferRescaleIntercept');
  
  rawBackgroundPixelValue = -o/s;

Finally, we can interpolate the new slice using the sliceVolume(). 

  slice = sliceVolume(ivd, v , u , w, rawBackgroundPixelValue,'linear');

Show the new slice 

  figure, imagesc(slice), axis image, colormap(hot) % show org image

The new image could be looked like the first image in the figure.


Zooming

We're going to use the approach II to zoom-in the slice.

Set the zoom factor 

  zoomFactor = 3;  % set zoom factor

Calculate the new pixel size 

  pixelSpacing = pixelSpacingOrg / zoomFactor;  % adjust pixel size


After zooming you may need to translate the image center, or you may see nothing 

  originalFOV = [Nc; Nr] .* pixelSpacingOrg;  % calculate the original FOV (mm)
  zoomShift = originalFOV / 2 * (zoomFactor - 1) / zoomFactor ;
  planePos = planePosOrg + [zoomShift ; 0] ;


Generate new slice using coordinateGen() and sliceVolume(). 

  [u, v, w] = coordinateGen(ivd, Nc, Nr, pixelSpacing, planePos, orientationInput);
  
  slice = sliceVolume(ivd, v , u , w, rawBackgroundPixelValue,'linear');

Show the new slice 

  figure, imagesc(slice), axis image, colormap(hot) % show org +zoom

The new slice is the second image in the figure. It really required fewer lines when coding using the approach II.


Translation

Let's try to do the translation using the approach II.


First of all, set the translation matrix 

  transMat = [-35.0; -5; 0];  % the translation in x, y, and z directions

Apply the translation matrix to obtain new plane position 

  planePosTrans = planePos + transMat;

% Generate new slice 

  [u, v, w] = coordinateGen(ivd, Nc, Nr, pixelSpacing, planePosTrans, orientationInput);
  
  slice = sliceVolume(ivd, v , u , w, rawBackgroundPixelValue,'linear');

Show the new slice 

  figure, imagesc(slice), axis image, colormap(hot) % show org +zoom+translation

The third picture in the figure is an example of the new slice.


Rotation

In this section, we're going to rotate the original image (counter-clockwise).

Set the angle we want to rotate 

  rotAngle = 25/180*pi;   % rotate 25 degree


The rotation will change the orientation matrix. You can find more detail in [2] Let's try to rotate the image counter-clockwisely about z-axis. 

  orientationInputRot = [ cos(rotAngle), -sin(rotAngle),        0;
                                        sin(rotAngle),  cos(rotAngle),        0;
                                                          0,                     0,        1];  % rotate the orientation matrix (counter-clockwise)


% After rotation, we adjust the center of the rotated image 

  newFOV = [Nc; Nr] .* pixelSpacing;
  transMat2 = orientationInputRot([1, 2], :) * ( newFOV / 2 ) - newFOV / 2;  % calculate the shift of the original center after rotation
  planePosTrans2 = planePosTrans - [transMat2 ; 0];  % translate the rotated image center


% Generate new slice 

  [u, v, w] = coordinateGen(ivd, Nc, Nr, pixelSpacing, planePosTrans2, orientationInputRot);
  slice = sliceVolume(ivd, v , u , w, rawBackgroundPixelValue,'linear');

Show the new slice 

  figure, imagesc(slice), axis image, colormap(hot) % show org+zoom+translate+rotate

The new slice can be seen in the fourth image in the figure.


The slicing images may look like this:

Fig eg3Dslicing.png

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