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imagematlabimage-processing3dradial

How do you map a point(x,y) on a 2D image to 3D space? (illustration provided)

I have a stack of images (about 180 of them) and there are 2 stars (just basic annotations) on every single image. Hence, the position (x,y) of the two stars are provided initially. The dimensions of all these images are fixed and constant.

The 'distance' between the image is about 1o with the origin to be the center (width/2, height/2) of every single 2D image. Note that, if this is plotted out and interpolated nicely, the stars would actually form a ring of an irregular shape.

Enter image description here

The dotted red circle and dotted purple circle are there to give a stronger scent of a 3D space and the arrangement of the 2D images (like a fan). It also indicates that each slice is about 1o apart.

  1. With the provided (x,y) that appeared in the 2D image, how do you get the corresponding (x,y,z) in the 3d space knowing that each image is about 1o apart?

  2. I know that MATLAB had 3D plotting capabilities, how should I go about implementing the solution to the above scenario? (Unfortunately, I have very little experience plotting 3D with MATLAB)

SOLUTION

Based on the accepted answer, I looked up a bit further: spherical coordinate system. Based on the computation of phi, rho and theta, I could reconstruct the ring without problems. Hopefully this helps anyone with similar problems.

I have also documented the solution here. I hope it helps someone out there, too: http://gray-suit.blogspot.com/2011/07/spherical-coordinate-system.html

Solution

  • I believe the y coordinate stays as is for 3D, so we can treat this as converting 2D x and image angle to an x and z when viewed top down.

    The 2D x coordinate is the distance from the origin in 3D space (viewed top down). The image angle is the angle the point makes with respect to the x axis in 3D space (viewed top down). So the x coordinate (distance from orign) and the image angle (angle viewed top down) makes up the x and z coordinates in 3D space (or x and y if viewed top down).

    That is a polar coordinate. Read how to convert from polar to cartesian coordinates to get your 3D x and z coordinates.

    I'm not great at maths either, here's my go:

    3D coords = (2Dx * cos(imageangle), 2Dy, 2Dx * sin(imageangle))