Display 3D Image Slice with Line of Intersection with Second Image Slice

I'm trying to build an image viewer to visualize 3D medical images. I'd like to have 3 total slices displayed concurrently on 2D plots with lines on each indicating intersection with the other 2 slices so that the user can navigate through the image stack by dragging and rotating these lines.

I have already written the code to sample these slices from the image volume and solve for the line of intersection between two slices.

The line is just the x, y, z coordinates on either end. I can make the 2D plot with one of these two images with just imagesc(im) but I cannot figure out how to convert the 3D location of the line with its corresponding location on the 2D plot. Can anyone help me?

[Jackson Hair]

I found a solution, but I fear it might be too time-intensive so I'm open to other solutions.

My solution was to find the image pixels with coordinates closest to each edge of the line, then use their indices as the 2D plot coordinates. However, this requires that I perform 192 x 192 operations for each end of the line, so I'm not sure if this will be viable for an interactive display.

[darova]

You want to find intersection of two surfaces?

[Jackson Hair]

No I already have the intersection in 3D space. I'm trying to then display that line of intersection on top of one of the two images when it's displayed as a 2D image.

[darova]

Can't you just mesure distances?

Looks like the line has only (x,y, z=0) coordinates. Hence you have coordinates for the horizontal image

[Jackson Hair]

Well yes, for this case it is z = 0, but I need it to work for other cases where that may not always be true.

[Dheeraj Singh]

If you have the intersection points of the images, can't you use plot3 for plotting the line to show the intersection between the images.

[Jackson Hair]

Right, that's what I have in the above image, but I don't want to display the images in 3D space. I'm trying to display three 2D slices arbitrarily sampled from the total 3D data with lines representing the intersection of the other 2D slices, like in the image below: