How does one convert a Graphics3D object into an Image3D object? E.g., start with Plot3D[x^2 - y^2, {x, -1, 1}, {y, -1, 1}].

  • $\begingroup$ Are you interested only in conversion, or creation too? $\endgroup$
    – Kuba
    Sep 30, 2013 at 21:18
  • $\begingroup$ @Kuba: primarily conversion. (The ref/Image3D page shows how to generate some Image3D objects from some 4D arrays of reals, and of course using Import with a data object that is already "Image3D") $\endgroup$
    – murray
    Sep 30, 2013 at 21:24
  • $\begingroup$ @Kuba, my question is how to obtain an Image3D object if you already have a Graphics3D object -- not how you obtain an Image3D object by starting with a function of 3 variables and picking points as in your example with UnitStep. $\endgroup$
    – murray
    Sep 30, 2013 at 21:28
  • $\begingroup$ Ok, just wasn't sure. :) $\endgroup$
    – Kuba
    Sep 30, 2013 at 21:29

4 Answers 4


If you already have a Graphics3D object, then you can recreate an Image3D object by stacking slices of your graphics along an axis. Here's an example. We start with your object:

obj = Plot3D[x^2 - y^2, {x, -1, 1}, {y, -1, 1}]

Using the following rudimentary "slice" function, we can generate slices of the function at a given value of $x$:

slice[obj_, x_, dx_] := Show[obj, ViewPoint -> {∞, 0, 0}, 
    PlotRange -> {{x, x + dx}, All, All}, Axes -> False, Boxed -> False]

slice[obj, 0, 0.01]

Now generate such slices for all $x$, rasterize and grab the ImageData and stack the frames:

frames = Table[ImageData@Thinning@ColorNegate@ColorConvert[#, "Grayscale"] &@
    Rasterize@slice[obj, x, 0.05], {x, -1, 1, 0.01}];


As you can see, the reconstruction is not perfect, and this arises from having to artificially sample the Graphics3D object by manipulating the plot ranges. Depending on how quickly the function changes within the chosen dx, the reconstruction could get worse/better. Note that you also need to choose the sampling such that the aspect ratio is maintained (I have only eyeballed it).

A much better reconstruction can be obtained either by generating frames using Plot (you probably can't avoid the Moiré patterns):

frames2 = 
  Table[ImageData@Thinning@ColorNegate@ColorConvert[#, "Grayscale"] &@
     Plot[x^2 - y^2, {x, -1, 1}, PlotRange -> {-1.5, 1.5}, 
      Axes -> False, Frame -> False], {y, -1, 1, 0.01}];


or by directly obtaining the samples as Kuba showed.

  • $\begingroup$ that's a start. I'll hold off accepting this in the hope of finding a solution that provides a much more faithful rendering of the Grahics3D object. $\endgroup$
    – murray
    Oct 1, 2013 at 13:09
  • $\begingroup$ @murray Certainly. Could you perhaps explain why you want to convert to an Image3D? I'm not seeing any advantages to it over Graphics3D, but maybe I'm just being thick... $\endgroup$
    – rm -rf
    Oct 1, 2013 at 13:57
  • $\begingroup$ @R.M. Because we can use Manipulate to inspect a 3D object slice by slice? $\endgroup$
    – matheorem
    Jan 20, 2016 at 8:50
  • $\begingroup$ @matheorem, and ClipPlanes is insufficient for your needs? Honestly, going from vector to raster is quite the step down here. $\endgroup$ Jun 26, 2016 at 20:41
  • $\begingroup$ In 11.3, Image3D[frames1] is just giving me a fuzzy gray blur of a parallelepiped, with no hint of the saddle surface. And Image3D[frames1] is not starting with the given Graphics3D object. $\endgroup$
    – murray
    Aug 8, 2018 at 14:20

You could create a region using DiscretizeGraphics and find points within a certain distance of the surface using RegionDistance

g = Normal @ Plot3D[x^2 - y^2, {x, -1, 1}, {y, -1, 1}];

f = RegionDistance @ DiscretizeGraphics @ g;

data = Array[f[{##}] &, {60, 60, 60}, {-1.1, 1.1}];

Image3D[Clip[data, {0.05, 0.05}, {1, 0}]]

enter image description here

  • $\begingroup$ The expression DiscretizeGraphics@g generates error message for me: "DiscretizeGraphics: The function DiscretizeGraphics is not implemented for Directive[Specularity...." $\endgroup$
    – murray
    Jun 27, 2016 at 14:52
  • $\begingroup$ In version 11,we should drop that Normal and the surface have a thickness? $\endgroup$
    – yode
    Nov 15, 2016 at 10:10
  • $\begingroup$ In 11.3 (whether with or without the Normal, the resulting Image3D completely changes the oriientation of the saddle surface. $\endgroup$
    – murray
    Aug 8, 2018 at 14:24

Here's something more fun than practical.

We can simulate an MRI / CT scanner by reconstructing from projected images.

g = AnatomyPlot3D[Entity["AnatomicalStructure", "LeftFemur"], PlotTheme -> "XRay"]

enter image description here

Note that it's important to have some sort of transparency in the objects being 'scanned'. This will better simulate an x-ray.

Normally a CT will only perform a half rotation, but here we will combine 2 CTs by taking a full rotation. This will give a higher quality result. Here are the simulated x-rays:

projectGraphic[g_, α_] := Show[g, ViewPoint -> {Cos[α], Sin[α], 0}, 
  ViewProjection -> "Orthographic", SphericalRegion -> True, ViewAngle -> 1.6]

fcnt = 64;
rsz = 180;

projections = Monitor[
    Rasterize[projectGraphic[g, α], RasterSize -> rsz, ColorSpace -> "Grayscale"], 
    {α, 0, 2π - π/fcnt, π/fcnt}
  ProgressIndicator[α, {0, 2π}]


enter image description here

Now we can create the slices:

radons1 = Image3DSlices[ImageRotate[Image3D[projections[[1 ;; fcnt]]], {π/2, {0, -1, 0}}], All, 2];
slices1 = InverseRadon /@ radons1;

radons2 = Image3DSlices[ImageRotate[Image3D[projections[[fcnt+1 ;; -1]]], {π/2, {0, -1, 0}}], All, 2];
slices2 = InverseRadon /@ radons2;

Reconstruct the orignal object by combining both CT scans:

recon = ImageAdjust @ ImageMultiply[
  ImageRotate[Image3D[slices2], π]

Image3D[RidgeFilter[recon], BoxRatios -> {1, 1, 1.7}] // ImageAdjust


As of version 11.2 there's RegionImage.

g = Plot3D[x^2 - y^2, {x, -1, 1}, {y, -1, 1}];


enter image description here

  • 1
    $\begingroup$ This works - "sort of ": it is very slow, and the result, which does have head Image3D has an unwanted Moire-like pattern on the surface and an unwanted light-gray parallelepiped-shaped blob filling the box. $\endgroup$
    – murray
    Aug 8, 2018 at 14:26
  • 1
    $\begingroup$ @murray, "an unwanted light-gray parallelepiped-shaped blob filling the box" - at least for that part, you just need to change the ColorFunction setting: Image3D[RegionImage[DiscretizeGraphics[g]], ColorFunction -> "WhiteBlackOpacity"] $\endgroup$ Mar 28, 2019 at 4:00
  • 2
    $\begingroup$ @murray The Moire-like pattern comes from antialiasing. RegionImage returns a grayscale image where a voxel value indicates how much of the region intersects with it. In addition to ColorFunction, changing volume lighting can help hide this effect: Image3D[RegionImage[DiscretizeGraphics[g]], Method -> {"VolumeLighting" -> "EnhancedEdge", "InterpolateValues" -> True}]. $\endgroup$
    – Greg Hurst
    Mar 28, 2019 at 15:59
  • 1
    $\begingroup$ And FWIW specifying a thicker surface with RegionImage[DiscretizeGraphics[g], Method -> {"Thickness" -> 3}] seems to speed things up. $\endgroup$
    – Greg Hurst
    Mar 28, 2019 at 16:02

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