Vis 2008 Papers: Continuous Scatterplots

The list of accepted papers for Vis 2008 has been out for a while now, but I only now have time to talk a little bit about some of the papers I read. I’ll start with Bachthaler and Weiskopf’s Continuous Scatterplots, a really cool paper that tackles a problem we also have been looking at for a while now.

The problem setting is as follows: in visualization, we are typically interested in computing the joint histogram of a dataset. If you think of a simple dataset as a mapping $R^d \to R^k$, where k is the number of features, then what we want to visualize is a histogram where we pick two of the dimensions of the data space R^k and look at the joint distribution. This is the well-known scatterplot. Scatterplots work pretty well for sparse data, but for a dense sampling of volume data, they tend to look like that.

What Bachthaler and Weiskopf noticed is that we should not sample the data at all: we can compute a continuous function $R^2 \to R$ that is the limit of dense sampling. Even better, they show that the function can be computed with a traditional scivis technique: projected tetrahedra with an emission-only additive optical model. This means it can be very quicklycomputed on a GPU. The result looks much, much better.

Their main mathematical result is the need to carefully compute the tetrahedron density in PT: if the values in data space are close together, the tetrahedron should be “dense”, because, intuitively, there’s a lot of domain space packed into a small part of the data space (ie, a comparatively large part of $R^n$ in it). Their argument involves mass conservation and changes of densities in mappings between these different spaces. This turns out to be essentially the same argument that we make in our own paper, but we have a totally different application. It’s somewhat surprising that the same idea pops up for these two different places (and that it had not been previously noticed in the literature). I think it’s because this density change problem only happens in mappings between continuous spaces: it’s one of those tricky places where probability density functions are fundamentally different from probability mass functions (unless you’re a measure theorist and thinks of pmf’s as Dirac deltas).

I also think it’s kind of unfortunate that Bachthaler and Weiskopf’s paper ended up at the “Information Visualization” section (kind of like our paper from last year at the “Navigating in Parameter Space” section). However, having a “Information Visualization” section in the Visualization conference, to me, is just evidence for the silliness about the Vis and InfoVis dichotomy. Why is it there in the first place? Aren’t our shared interests stronger than our differences? And what are our differences, really?