Distance maps to estimate cell volume from two-dimensional plankton images

We describe and evaluate an algorithm that uses a distance map to automatically calculate the biovolume of a planktonic organism from its two-dimensional boundary. Compared with existing approaches, this algorithm dramatically increases the speed and accuracy of biomass estimates from plankton images, and is thus especially suited for use with automated cell imaging technologies that produce large quantities of data. The algorithm operates on a two-dimensional image processed to identify organism boundaries. First, the distance of each interior pixel to the nearest boundary is calculated; next these same distances are assumed to apply for projection in the third dimension; and finally the resulting volume is adjusted by a multiplicative factor assuming locally circular cross-sections in the third dimension. Other cross-sectional shape factors can be applied as needed. In this way, the simple, computationally efficient, volume calculation can be refined to include taxon-specific shape information if available. We show that compared to traditional manual microscopic analysis, the distance map algorithm is unbiased and accurate (mean difference = ?0.25%, standard deviation = 17%) for a range of cell morphologies, including those with concave boundaries that deviate from simple geometric shapes and whose volumes are not well represented by a solid of revolution around a single axis. Automated calculation of cell volumes can now be implemented with a combination of this new distance map algorithm for complex shapes and the solid of revolution approach for simple shapes, with an automated decision criterion to choose the appropriate approach for each image.