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Image3D

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Image3D[data] is a volumetric image, normalising to Image3D[data, type]. The data is a depth x height x width array of voxels, or depth x height x width x channels for colour, so it is indexed data[[z, y, x]] with slices outermost. ImageDimensions reports {width, height, depth} -- FULLY REVERSED from that order, which is Mathematica's convention. Type inference and the accessors match Image: ImageQ is False for a volume (use Image3DQ), while ImageDimensions, ImageChannels, ImageType and ImageData all accept either rank.

Examples (67)

Every input below was run against the current Mathilda build and its output recorded.

Basic Examples (14)

In[1]:= SeedRandom[5];

Uniform noise fills the volume to its boundary, so the block shows what it holds

In[2]:= Image3D[RandomReal[1, {24, 24, 24}], "Real"]
Out[2]= -Image-

Three channels, one per axis: the faces of the block are three colour gradients

In[3]:= Image3D[Table[{N[x/16], N[y/16], N[z/16]}, {z, 1, 16}, {y, 1, 16}, {x, 1, 16}], "Real"]
Out[3]= -Image-

In[4]:= ball = Image3D[Table[N[Boole[(x - 16)^2 + (y - 16)^2 + (z - 16)^2 <= 100]], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[5]:= shell = Image3D[Table[N[Mod[Floor[Sqrt[(x - 16.)^2 + (y - 16.)^2 + (z - 16.)^2]/3], 2]], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[6]:= cube = Image3D[Table[If[Mod[Quotient[x - 1, 4] + Quotient[y - 1, 4] + Quotient[z - 1, 4], 2] == 0, 0., 1.], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[7]:= ball
Out[7]= -Image-

In[8]:= ImageDimensions[ball]
Out[8]= {32, 32, 32}

In[9]:= Dimensions[ImageData[ball]]
Out[9]= {32, 32, 32}

In[10]:= ImageChannels[ball]
Out[10]= 1

In[11]:= ImageType[ball]
Out[11]= "Real"

In[12]:= Image3DQ[ball]
Out[12]= True

In[13]:= shell
Out[13]= -Image-

In[14]:= cube
Out[14]= -Image-

Scope (28)

In[15]:= colvol = Image3D[Table[{N[x/16], N[y/16], N[z/16]}, {z, 1, 16}, {y, 1, 16}, {x, 1, 16}], "Real"];

In[16]:= bitvol = Image3D[Table[Boole[Mod[x + y + z, 2] == 0], {z, 1, 8}, {y, 1, 8}, {x, 1, 8}]];

In[17]:= rampz = Image3D[Table[N[(z - 1)/31], {z, 1, 32}, {y, 1, 24}, {x, 1, 24}], "Real"];

In[18]:= ball = Image3D[Table[N[Boole[(x - 16)^2 + (y - 16)^2 + (z - 16)^2 <= 100]], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[19]:= shell = Image3D[Table[N[Mod[Floor[Sqrt[(x - 16.)^2 + (y - 16.)^2 + (z - 16.)^2]/3], 2]], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[20]:= cube = Image3D[Table[If[Mod[Quotient[x - 1, 4] + Quotient[y - 1, 4] + Quotient[z - 1, 4], 2] == 0, 0., 1.], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[21]:= colvol
Out[21]= -Image-

In[22]:= ImageChannels[colvol]
Out[22]= 3

In[23]:= bitvol
Out[23]= -Image-

In[24]:= ImageType[bitvol]
Out[24]= "Bit"

In[25]:= rampz
Out[25]= -Image-

In[26]:= ImageDimensions[rampz]
Out[26]= {24, 24, 32}

In[27]:= GaussianFilter[ball, 2]
Out[27]= -Image-

In[28]:= MeanFilter[ball, 1]
Out[28]= -Image-

In[29]:= MedianFilter[ball, 1]
Out[29]= -Image-

In[30]:= Dilation[ball, 2]
Out[30]= -Image-

In[31]:= Erosion[ball, 2]
Out[31]= -Image-

In[32]:= Opening[ball, 2]
Out[32]= -Image-

In[33]:= Closing[ball, 2]
Out[33]= -Image-

In[34]:= Binarize[shell]
Out[34]= -Image-

In[35]:= LocalAdaptiveBinarize[shell, 3]
Out[35]= -Image-

In[36]:= DistanceTransform[ball]
Out[36]= -Image-

In[37]:= ImagePad[cube, 2]
Out[37]= -Image-

In[38]:= ImageReflect[cube, Front]
Out[38]= -Image-

In[39]:= ColorConvert[colvol, "Grayscale"]
Out[39]= -Image-

In[40]:= DerivativeFilter[cube, {0, 0, 1}]
Out[40]= -Image-

In[41]:= CornerFilter[ball, 2]
Out[41]= -Image-

In[42]:= ImageCorners[ball]
Out[42]= {{9, 16, 9}, {16, 9, 9}, {16, 23, 9}, {23, 16, 9}, {9, 16, 23}, {9, 23, 16}, {16, 9, 23}, {16, 23, 23}, {23, 16, 23}, {23, 23, 16}, {9, 9, 16}, {23, 9, 16}, {7, 12, 16}, {25, 12, 16}, {12, 16, 7}, {12, 16, 25}, {16, 12, 7}, {16, 12, 25}, {16, 25, 20}, {20, 16, 7}, {20, 16, 25}, {7, 20, 16}, {12, 7, 16}, {12, 25, 16}, {16, 7, 12}, {16, 20, 7}, {16, 20, 25}, {16, 25, 12}, {20, 7, 16}, {20, 25, 16}, {25, 20, 16}, {7, 16, 12}, {7, 16, 20}, {16, 7, 20}, {25, 16, 12}, {25, 16, 20}, {7, 19, 13}, {13, 13, 7}, {13, 13, 25}, {13, 25, 13}, {19, 13, 7}, {19, 13, 25}, {19, 25, 13}, {25, 19, 13}, {7, 13, 13}, {25, 13, 13}, {7, 13, 19}, {7, 19, 19}, {25, 13, 19}, {25, 19, 19}, {13, 7, 19}, {13, 19, 7}, {13, 19, 25}, {13, 25, 19}, {19, 7, 19}, {19, 19, 7}, {19, 19, 25}, {19, 25, 19}, {13, 7, 13}, {19, 7, 13}, {6, 16, 16}, {16, 6, 16}, {16, 16, 6}, {16, 16, 26}, {16, 26, 16}, {26, 16, 16}, {10, 10, 10}, {10, 22, 10}, {22, 10, 10}, {22, 22, 10}, {10, 10, 22}, {10, 22, 22}, {22, 10, 22}, {22, 22, 22}}

Applications (8)

In[43]:= ball = Image3D[Table[N[Boole[(x - 16)^2 + (y - 16)^2 + (z - 16)^2 <= 100]], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[44]:= shell = Image3D[Table[N[Mod[Floor[Sqrt[(x - 16.)^2 + (y - 16.)^2 + (z - 16.)^2]/3], 2]], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[45]:= Image[Part[ImageData[ball], 16]]
Out[45]= -Image-

In[46]:= Image[Part[ImageData[GaussianFilter[ball, 2]], 16]]
Out[46]= -Image-

In[47]:= Image[Join[Part[ImageData[shell], 8], Part[ImageData[shell], 16], Part[ImageData[shell], 24], 2]]
Out[47]= -Image-

In[48]:= Total[Flatten[ImageData[ball]]]
Out[48]= 4169.0

In[49]:= Total[Flatten[ImageData[ball] - ImageData[Erosion[ball, 1]]]]
Out[49]= 1640.0

In[50]:= Max[Flatten[ImageData[DistanceTransform[ball]]]]
Out[50]= 10.0499

Properties & Relations (12)

In[51]:= ball = Image3D[Table[N[Boole[(x - 16)^2 + (y - 16)^2 + (z - 16)^2 <= 100]], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[52]:= cube = Image3D[Table[If[Mod[Quotient[x - 1, 4] + Quotient[y - 1, 4] + Quotient[z - 1, 4], 2] == 0, 0., 1.], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[53]:= colvol = Image3D[Table[{N[x/16], N[y/16], N[z/16]}, {z, 1, 16}, {y, 1, 16}, {x, 1, 16}], "Real"];

In[54]:= ImageDimensions[ball] === {32, 32, 32}
Out[54]= True

In[55]:= Reverse[ImageDimensions[ball]] === Dimensions[ImageData[ball]]
Out[55]= True

In[56]:= ImageData[ImageReflect[ImageReflect[cube, Front], Front]] === ImageData[cube]
Out[56]= True

In[57]:= ImageData[Dilation[ball, 0]] === ImageData[ball]
Out[57]= True

In[58]:= ImageData[Opening[Opening[ball, 2], 2]] === ImageData[Opening[ball, 2]]
Out[58]= True

In[59]:= ImageDimensions[GaussianFilter[ball, 2]] === ImageDimensions[ball]
Out[59]= True

In[60]:= ImageChannels[ColorConvert[colvol, "Grayscale"]] === 1
Out[60]= True

In[61]:= Image3DQ[ball] && Not[ImageQ[ball]]
Out[61]= True

In[62]:= Max[Flatten[ImageData[CornerFilter[Image3D[Table[If[x <= 16, 0., 1.], {z, 1, 16}, {y, 1, 16}, {x, 1, 16}], "Real"], 2]]]]
Out[62]= 0.0

Neat Examples (5)

In[63]:= shell = Image3D[Table[N[Mod[Floor[Sqrt[(x - 16.)^2 + (y - 16.)^2 + (z - 16.)^2]/3], 2]], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[64]:= cube = Image3D[Table[If[Mod[Quotient[x - 1, 4] + Quotient[y - 1, 4] + Quotient[z - 1, 4], 2] == 0, 0., 1.], {z, 1, 32}, {y, 1, 32}, {x, 1, 32}], "Real"];

In[65]:= shell
Out[65]= -Image-

In[66]:= Image[Part[ImageData[shell], 16]]
Out[66]= -Image-

In[67]:= Image[Part[ImageData[Dilation[cube, 1]], 16]]
Out[67]= -Image-

Implementation notes

Attributes: Protected.

References

See also: ImageDimensions, ImageQ, Image3DQ, Image, ImageData, ImageChannels, ImageType