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Endless forms most irregular

Measuring plankton volume causes computational headache

In the viscous, tiny world of plankton, there is endless, beautiful variation.

There are tiny organisms that look like panes of stained glass. There are phytoplankton that can swim. There are phytoplankton that can form groups and those who choose to abandon them. These organisms are living in a very different world; for us it would feel like swimming in molasses. And despite the fact that they are almost invisible to the naked eye, they come in a dazzling array of colors and shapes, from spheres, to crosses, to stars, to footballs and many more.

Unfortunately for me, this dazzling array of shapes makes it hard to calculate certain properties — namely volume — from microscopic images. I was working with Heidi Sosik ’87 on a project at the Woods Hole Oceanographic Institution to understand how carbon and chlorophyll are regulated in coastal phytoplankton. But to calculate carbon, we needed volume. For simple shapes like spheres, volume is easy — just revert to the techniques from calculus and rotate the boundary. For shapes like stars, it ended up being maddeningly difficult.

We had hundreds of millions of pictures of different tiny photosynthetic marine organisms that we wanted to get volume from, which meant that doing anything by hand was prohibitively time-consuming. You can break the shape into pieces and do these calculations for each piece, but being even a couple of pixels off on the intersection can result in huge errors. And teaching a computer to break shapes ever so perfectly was proving very computationally slow.

We could get the computer to automatically recognize what geometrical shapes parts of an image were closest to, like microscopists do when they say the alga Ceratium is a sphere with three cylinders tacked on. But again, this was really slow. I had read paper after paper that addressed other volume calculation issues, for automatic image recognition in cars, to medical journals looking for centerlines to guide surgical procedures. Nothing was improving the efficacy of my volume calculations.

But then, the eureka moment that defines the life of every scientist! Or, actually, an idea that snuck into my head one day while I wasn’t paying attention. I like to think of it as attacking the problem from an entirely different direction. Instead of thinking about rotation about a local axis (for example, around an “arm”) I realized I could get data about the whole image and use geometrical rules to extrapolate overall volume. I would treat my plankton as a step pyramid with heights defined by their distances from the edge. If you have a rectangle, this would look like a jagged diamond in the cross-section with pinched edges near the short end of the rectangle. Diamonds can be easily related to circles by a multiplication factor and voila, we have a simple way to calculate volume! It would be three lines of code (more or less). It would be elegant and efficient.

Of course, it took me another month (and several notebooks of meticulous drawings of step-pyramids, test shapes, and calculations; I am sure my middle-school geometry teacher would have been so proud) to iron out all the details — like smoothing those steps into a line — and show that my technique worked. But once I stepped outside my mental bubble and explored new options, the rest seemed easy.

Overall, my insight changed how I perceive the research process. That defining “eureka” moment was not at all how I had imagined; I didn’t know at first if my crazy new method would work. The critical part was trying out my new idea and not giving up on it. Now, I try to give myself the flexibility to follow new ideas, no matter how strange they may first appear.

This is a new column and a space for students and researchers to share their exploits, experiences, and knowledge. If you are interested in contributing, please contact Emily Moberg at and cc