image processing - How to create a 3D model based on MRI cross-sections?

Recently, I stumbled upon the following surreal MRI-scan of broccoli:

and ever since the moment that I saw this I've been wondering whether it is possible to recreate the broccoli based on these images.

So is it possible to do this efficiently in Mathematica?

Answer

Image3D can do this if we overcome two problems.

imgs = Import["http://i.stack.imgur.com/CQX0Q.gif"];
imgs = MapThread[SetAlphaChannel, {imgs, Binarize /@ imgs}]
Image3D[imgs, Background -> Black]

The second line makes all black in all the images transparent, this was the first problem.

The second problem is that the broccoli will be very flat. In order to fix this you may select the the image and click the "show options" button in the toolbar. If you change the voxel aspect ratio so that z is stretched five times compared to the x and y axis, you get this:

It is also possible to give it color:

colored = Colorize[#, ColorFunction -> ColorData["AvocadoColors"]] & /@ imgs;

imgs = MapThread[SetAlphaChannel, {colored, Binarize /@ imgs}];
Image3D[imgs, Background -> Black]

Animated:

Comments

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

list manipulation - Selecting multiple columns from a matrix?

Sample data: data = { {{2013, 1, 1}, 24.13, 167.67, 231.82}, {{2013, 1, 2}, 32.15, 170.92, 225.99}, {{2013, 1, 3}, 35.43, 172.68, 221.67}, {{2013, 1, 4}, 36.73, 173.05, 218.32}, {{2013, 1, 5}, 58.19, 165.96, 197.05}, {{2013, 1, 6}, 69.99, 163.50, 187.52}, {{2013, 1, 7}, 71.37, 154.21, 175.58}, {{2013, 1, 8}, 72.51, 149.66, 163.25}}; I want a DateListPlot with three graphs, so for a matrix formed by columns 1 and 2, one for columns 1 and 3, and 1 for columns 1 and 4. At the moment I'm using this code: data2 = Transpose[{data[[All, 1]], data[[All, 2]]}]; data3 = Transpose[{data[[All, 1]], data[[All, 3]]}]; data4 = Transpose[{data[[All, 1]], data[[All, 4]]}]; DateListPlot[{data2, data3, data4}, Joined -> True, Filling -> {3 -> {1}}] but I have a hunch that this can be done more efficiently. I don't like the Transpose s in particular. Any ideas? edit (for extra credit) What if I need to multiply the second column by 2, which in my solution is simp...

plotting - How to draw some 2D curves in a 3D plot?

I want to plot several 2D curves ( Sin[x] at y=0 , Cos[x] at y=1 ) in a 3D plot, what function should i use? f[x_, y_] := Piecewise[{{0, y 0}, {Sin[x], y == 0}}] g[x_, y_] := Piecewise[{{0, y 1}, {Cos[x], y == 1}}] Plot3D[{f[x, y], g[x, y]}, {x, 0, 10}, {y, 0, 10}] doesn't work. Any ideas? Answer ParametricPlot3D[{{Sin[u], 0, u}, {Cos[u], 1, u}}, {u, 0, 20}, BoxRatios -> 1, PlotRange -> {{-2, 2}, {-.5, 2}, {0, 20}}] === update - general thoughts === I've seen the comments to this question and a few other approaches to the waterfall (or wire) plot are given in this question: Plotting several functions . Also I cannot not mention one of my favorite Mathematica blogs - Archery with this post on the story of discovery of 1st pulsar and an its infamous graphics - code is given in the post:

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