Siliceous and Delicious

After the MSI breakfast lecture I went to this morning (already an auspicious beginning to the day, a fascinating talk about the microbiome of the human mouth), I found emails from both Jacques and Sébastien waiting for me in my inbox, inviting me around for a chat about my morphospace.

I dropped everything and literally ran over to see them. I walked them through what I’d been working on over the course of the week; they asked lots of (really good) questions and hummed and hawed. In principle, I think, they seemed to like it, but Jacques noted the similarity of the approach to a Fourier decomposition of the outline, and brought up the good question of how I was going to go about matching my observed outlines (those of the actual diatoms) to the model. The answer, which I hadn’t really explicitly addressed myself, was that I was imagining just tinkering with the parameters I came up with until I found a reasonably well-matching shape. This, of course, is not a very scientific way of doing things….

Jacques suggestion was to begin by digitizing the actual outline I was hoping to describe, and obtaining the first few modes of the fourier transform of that function (curvature as a function of distance along the outline), however many terms as would be considered necessary to get a ‘decent’ fit (perhaps four or five, maybe ten—we’d have to play around with it to see). This all sounded very familiar to me, as it rang bells that had been gathering dust since I stopped reading all the Lohmann, Zahn & Roskies, Bookstein and what not last year. I started to chime in that the problem with using these functions to describe the outline was that those functions had to start at some point along the outline, and that it was impossible to determine homologous points between, say, a two-sided and a three-sided shape… but then I realized that what Jacques was suggesting was different, and only a stone’s throw away from what I had been suggesting: not to describe the whole outline of the valve using this Fourier decomposition, but just one of the “sides” or arcs composing the outline… And all of a sudden, it made sense.

It was an incredibly exciting meeting, and even after David Hewitt (visiting today from Philly) came in and ended our meeting, I followed Sébastien to his office to discuss a little further about how we might go about implementing this in code. It turns out that the MATLAB programs he has written may be fairly easy to modify to produce the shapes I want from a set of parameters (a set of x Fourier mode amplitudes). The code to take images of diatoms and extract from them the correct values of those parameters is going to be a little harder to program, but should not be impossible.

Needless to say, this was a crowning moment for an already pretty exciting week. I’m trying not to get my hopes up too high, lest they are crushed again, but this all seems pretty promising. In the afternoon, I met with Andy and presented him with the summary of what I’d done so far this week, and my best summary of what Jacques and Sébastien had added to it—and he seemed to agree that this was a promising path to follow. There wasn’t much feedback… but the customary verbal pat on the back with the encouragement to keep doing what I’m doing.

One slight wrinkle in all this was thrown up when I followed up on one of Jacques’ questions—which concerned whether anyone had done this before. I confidently proclaimed that I didn’t think anybody had, but when I launched a quick Google scholar search for “diatom fourier shape” or words to that effect, I found that there does indeed appear to be quite a body of literature on using fourier analysis and computer vision to identify diatoms. Now, this isn’t exactly what I’m aiming to do—namely, documenting the occupancy of morphospace through time—but it comes as a bit of a shock to the system to have suddenly found a pile of papers on the topic, papers I somehow managed to miss entirely the first time around.