Beyond Voxels

Winter 2009


Making a computer model of a porous material such as sand used to be simple. All you had to do was model a bunch of average sized sand grains separated by average sized pores, and run your simulation.

Unfortunately, the simple method was a little too simple. It turns out that sand is a lot more complex than that, and if you’re studying how pollutants leach through water-soaked sand, for instance, the models just weren’t good enough. The same goes for researchers trying to understand the behavior of snow, sea ice, or any other multiphase material.

Now Markus Hilpert, associate professor in the Department of Geography and Environmental Engineering, and Roland Glantz, a postdoctoral fellow in the department, have developed a new technique that allows them to create much more sophisticated and accurate models of materials, which could lead to better predictions about pollution transport or climate change.

“Basically, there have been a lot of advances in three-dimensional imaging,” Hilpert says. “The resolution of these imaging devices is getting better and better.” New devices such as the X-ray synchrotron at Argonne National Labs, for instance, can produce 3-D images down to a resolution of a micrometer or two.

But the techniques to analyze and model these images are still relatively crude, Hilpert says—“like we’re living in the Stone Age.” The common technique is to convert the image into “voxels,” which are the 3-D equivalent of pixels. But voxelizing an image results in a “chunky” representation that throws away a lot of important information.

The technique developed by Hilpert and Glantz instead represents the image as both a connected network of pores, and a connected network of pore bodies. An image of sand, for instance, would consist of a smooth image of the connected grains of sand, and a smooth image of the connected pores between the grains.

To generate these images, Hilpert and Glantz use mathematical techniques that first transform the images into millions of much smaller 3-D shapes, and then fuse the shapes into connected networks.

These images are still simplified compared to the complexity of the originals. But they retain enough information to allow them to model the behavior of the material much more accurately, Hilpert says.

The technique could be valuable to studies of pollutant transport, oil recovery, water evaporation from soils, snow melting, and sea ice formation, he says.

The researchers received funding from the National Science Foundation Collaboration in the Mathematical Geosciences program, and have made their software freely available.