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Goal

This paper is about finding a better way to inspect tensor values. By "inspect" I mean being able to pick out one value and see all the degrees of freedom at that sample.

Data inspection is something we normally don't worry about for scalar data, when we have a single value, we can just use grayscale or a colormap.

In vector data, we have three values, and this becomes are more interesting problem.

I'm interested in tensor data, specifically symmetric tensors, which for all practical purposes are 3x3 symmetric matrices. I'm most familiar with diffusion tensor data, where you use MRI to measure the extent to which the rate of water diffusion is a function of direction.

Here's an example of water diffusion in two-dimensions. Here I've put some food coloring on Kleenex, and you can see that its spreading out in all directions equally. But here, in the newspaper, its diffusing faster in this direction than the other, because of the microscopic structure of the paper fibers.

The ideal shape here is an ellipse, and actually these ellipses are examples of the inspection method that I'll be talking about: glyphs, or icons, where the shape and configuration of some base object is varied to convey the various degrees of freedom in a data value.

I think its important for the glyph design for tensor data to be informed by the mathematical properties of the tensors themselves.