How dense can you be? New automatic measures of vein density in angiosperm leaves.

Premise: Because of the trade-off between water loss and carbon dioxide assimilation, the conductivity of the transpiration path in a leaf is an important limit on photosynthesis. Closely packed veins correspond to short paths and high assimilation rates while widely spaced veins are associated with higher resistance to flow and lower maximum photosynthetic rates. Vein length per area (VLA) has become the standard metric for comparing leaves with different vein densities; its measurement typically utilizes digital image processing with varying amounts of human input. Methods and Results: Here, we propose three new ways of measuring vein density using image analysis that improve on currently available procedures: (1) areole area distributions, (2) a sizing transform, and (3) a distance map. Each alternative has distinct practical, statistical, and biological limitations and advantages. In particular, we advocate the log-transformed modal distance map of a vein mask as an estimator to replace VLA as a standard metric for vein density. Conclusions: These methods, for which open-source code appropriate for high-throughput automation is provided, improve on VLA by producing determinate measures of vein density as distributions rather than point estimates. Combined with advances in image quality and computational efficiency, these methods should help clarify the physiological and evolutionary significance of vein density.