I am looking to extract a large matrix from an InterpolatingFunction (roughly, 500x500x500), is there an easier way than extracting a Table ?

I want a matrix of the greyscale image data. Apologies for the lack of greyscale definition in the example I couldn't think how better to phrase it without attaching all my images. (my aim is to create a matrix of brain density from the greyscale data of scan slices.)

For example:

a = Import["ExampleData/CTengine.tiff", "Image3D"]
b = Image3DSlices[a];
c = Image3D[b, ColorFunction -> "Grayscale"];
d = ListInterpolation[ImageData[c]];

d[70, 70, 70]


m =  ParallelTable[d[x, y, z], {x, 1, 10}, {y, 1, 10}, {z, 1, 10}] 

Seems to be a hefty run time ( AbsoluteTiming=25 for example above) , I'm sure there's a better way


  • 2
    $\begingroup$ I think you need ArrayResample. For example, ArrayResample[ImageData[c], {10, 10, 10}] returns in less than a second on my machine. $\endgroup$ – Jason B. Apr 5 '18 at 21:14
  • $\begingroup$ @JasonB. Thanks! Perfect! Interesting function $\endgroup$ – Awkward Panda Apr 5 '18 at 21:46

Your ImageData[c] is a 3-dimensional array with dimensions {110, 256, 256}. To down-sample this to a {30,30,30} array, it's as easy as

ArrayResample[ImageData[c], {30, 30, 30}]

This is going to do the interpolation for you, but in a (hopefully) optimized way.


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