Leaf vein network geometry can predict levels of resource transport, defence and mechanical support that operate at different spatial scales. However, it is challenging to quantify network architecture across scales due to the difficulties both in segmenting networks from images and in extracting multiscale statistics from subsequent network graph representations. Here we developed deep learning algorithms using convolutional neural networks (CNNs) to automatically segment leaf vein networks. Thirty-eight CNNs were trained on subsets of manually defined ground-truth regions from >700 leaves representing 50 southeast Asian plant families. Ensembles of six independently trained CNNs were used to segment networks from larger leaf regions (c. 100 mm 2). Segmented networks were analysed using hierarchical loop decomposition to extract a range of statistics describing scale transitions in vein and areole geometry. The CNN approach gave a precision-recall harmonic mean of 94.5% AE 6%, outperforming other current network extraction methods, and accurately described the widths, angles and connectivity of veins. Multiscale statistics then enabled the identification of previously undescribed variation in network architecture across species. We provide a LEAFVEINCNN software package to enable multiscale quantification of leaf vein networks, facilitating the comparison across species and the exploration of the functional significance of different leaf vein architectures.

Leaf vein network geometry can predict levels of resource transport, defence, and mechanical support that operate at different spatial scales. However, it is challenging to quantify network architecture across scales, due to the difficulties both in segmenting networks from images, and in extracting multi-scale statistics from subsequent network graph representations. Here we develop deep learning algorithms using convolutional neural networks (CNNs) to automatically segment leaf vein networks. Thirty-eight CNNs were trained on subsets of manually-defined ground-truth regions from >700 leaves representing 50 southeast Asian plant families. Ensembles of 6 independently trained CNNs were used to segment networks from larger leaf regions (~100 mm2). Segmented networks were analysed using hierarchical loop decomposition to extract a range of statistics describing scale transitions in vein and areole geometry. The CNN approach gave a precision-recall harmonic mean of 94.5% ± 6%, outperforming other current network extraction methods, and accurately described the widths, angles, and connectivity of veins. Multi-scale statistics then enabled identification of previously-undescribed variation in network architecture across species. We provide a LeafVeinCNN software package to enable multi-scale quantification of leaf vein networks, facilitating comparison across species and exploration of the functional significance of different leaf vein architectures.

Leaf venation networks evolved along several functional axes, including resource transport, damage resistance, mechanical strength, and construction cost. Because functions may depend on architectural features at different scales, network architecture may vary across spatial scales to satisfy functional tradeoffs. We develop a framework for quantifying network architecture with multiscale statistics describing elongation ratios, circularity ratios, vein density, and minimum spanning tree ratios. We quantify vein networks for leaves of 260 southeast Asian tree species in samples of up to 2 cm 2 , pairing multiscale statistics with traits representing axes of resource transport, damage resistance, mechanical strength, and cost. We show that these multiscale statistics clearly differentiate species' architecture and delineate a phenotype space that shifts at larger scales; functional linkages vary with scale and are weak, with vein density, minimum spanning tree ratio, and circularity ratio linked to mechanical strength (measured by force to punch) and elongation ratio and circularity ratio linked to damage resistance (measured by tannins); and phylogenetic conservatism of network architecture is low but scale-dependent. This work provides tools to quantify the function and evolution of venation networks. Future studies including primary and secondary veins may uncover additional insights.

The data set contains images of leaf venation networks obtained from tree species in Malaysian Borneo. The data set contains 726 leaves from 295 species comprising 50 families, sampled from eight forest plots in Sabah. Image extents are approximately 1 × 1 cm, or 50 megapixels. All images contain a region of interest in which all veins have been hand traced. The complete data set includes over 30 billion pixels, of which more than 600 million have been validated by hand tracing. These images are suitable for morphological characterization of these species, as well as for training of machine‐learning algorithms that segment biological networks from images. Data are made available under the Open Data Commons Attribution License. You are free to copy, distribute, and use the database; to produce works from the database; and to modify, transform, and build upon the database. You must attribute any public use of the database, or works produced from the database, in the manner specified in the license. For any use or redistribution of the database, or works produced from it, you must make clear to others the license of the database and keep intact any notices on the original database.

Leaf venation networks play a key role in resource transport for plants. The accompanying data paper provides high-resolution images of the venation networks of several hundred southeast Asian tree species collected from Malaysian Borneo. The images are paired to a range of trait and environmental data and are supplemented by hand tracings, yielding a dataset of several hundred million hand-classified pixels. The dataset may be useful for ecophysiology, systematics, and machine learning.