# Basic question about the format of Image2ProbeTransform

Hello,

I have a question about the Image2ProbeTransform that is used in .mha files. As far as I can tell, all of the matrices have to be 4X4 matrices. Please correct me if I’m wrong.

I have an ultrasound probe with an attached markers, and its position in a reference system (Probe2ReferenceTransform) is known.

The thing is, the image plane itself is 2D, and while (Plus applications user manual: Definition of commonly used coordinate systems) says that the Z-axis is a cross product of the X-axis and Y-axis, I have been having some confusion about how I should define the transformation matrix.

Say that the image coordinates are in (u, v) and I want to transform it to (x,y,z) in the probe coordinates. The two are linked via

[x [a1 a2 [p1
y = b1 b2 * [u + p2 z] c1 c2] v] p3]

or [x; y; z] = [a1, a2; b1, b2; c1, c2] * [u, v] + [p1, p2, p3]. Semicolons denote new rows and commas denote new columns within a row a la MATLAB.

Values are

a1 = 0.3467;

a2 = -0.1316;

b1 = -0.2807;

b2 = -0.0620;

c1 = 0.1460;

c2 = -0.0394;

p1 = -109.1116;

p2 = 154.9904;

p3 = 5.9658;

I am thinking of a 4X4 Image2ProbeTransform

[a1, a2, 1, p1;
b1, b2, 1, p2;
c1, c2, 1, p3;
0, 0, 0 1]

but it seems that while Slicer can track an image via this method when I put it all into a .mha file, the image gets zoomed in, pixelated, and cut up from a 2D image into an odd slice like this:

I would greatly appreciate any help!

See detailed specification in the PLUS toolkit documentation.

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