# Correspondence between intrinsic axes and world axes for imref objects

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Matt J on 6 Jun 2019
Edited: Matt J on 7 Jun 2019
Suppose I have a 3D array of image samples I(i,j,k), i=1...M, j=1...N, k=1...P.
In world coordinates, pixel spacing in millimeters along the i,j, and k sampling directions are di, dj,and dk respectively. Now, I wish to create an imref3d object relating these samples to my world coordinates.
Question: According to the conventions of imref3d, are the world X, Y, and Z axes considered to be aligned respectively with increasing i,j, and k? Or is it j,i, and k like with meshgrid? Or something else entirely?
I am trying to determine whether, when using the construction syntax
R = imref3d(imageSize,pixelExtentInWorldX,pixelExtentInWorldY,pixelExtentInWorldZ)
the proper substitions of my parameters are as follows,
R = imref3d([M,N,P] , di, dj, dk)
or something else? And what about imref2d? Any fundamental differences between the 3d and 2d conventions?

Catalytic on 6 Jun 2019
Or is it j,i, and k like with meshgrid?
It is this one, sad to say. You can check it like this
M=50; N=40; P=30;
ir = imref3d([M,N,P])
ir =
imref3d with properties:
XWorldLimits: [0.5000 40.5000]
YWorldLimits: [0.5000 50.5000]
ZWorldLimits: [0.5000 30.5000]
ImageSize: [50 40 30]
PixelExtentInWorldX: 1
PixelExtentInWorldY: 1
PixelExtentInWorldZ: 1
ImageExtentInWorldX: 40
ImageExtentInWorldY: 50
ImageExtentInWorldZ: 30
XIntrinsicLimits: [0.5000 40.5000]
YIntrinsicLimits: [0.5000 50.5000]
ZIntrinsicLimits: [0.5000 30.5000]
As you see, the image extents in X,Y,Z are N,M, and P, so the usual meshgrid interchanging of X and Y is at work here as well :-(
Matt J on 7 Jun 2019
Edited: Matt J on 7 Jun 2019
It is this one, sad to say
I tend to agree that it is sad, although I guess I also understand why some people like to have their X-axes run horizontally on the screen.

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