Scatter plots of nodes, edges, and leaf area.

The slope of each regression line was 2.37 for the untreated and 3.13 for the cleared leaves (number of nodes vs. number of edges); 362.2 for untreated and 2268.5 for cleared leaves (leaf area vs. the number of nodes); 806.3 for the untreated and 6950.1 for the cleared leaf (leaf area vs. the number of edges).</p

Overview of the newly developed method for quantifying venation structures.

The method is applicable to both untreated and cleared leaf images. The deep neural network model segmented veins from leaf images. An undirected graph as a representation of the vein network was extracted from the vein image, and network features were used to characterize the venation patterns. By dimensionality reduction, a morphospace was reconstructed based on the observed data.</p

Schematic diagram of typical local vein network structures.

The blue nodes represent endpoint nodes with a degree of one, while the red nodes represent intersection nodes with a degree of three. Nodes with wavy outlines denote the reference node of an egonet, and orange nodes represent neighboring nodes within a one-hop egonet. (A) illustrated an egonet pattern with a neighborhood size of 2, which was relatively prevalent when the reference node was an endpoint node. (B) portrayed another egonet pattern with a neighborhood size of 6, commonly observed when the reference node was an intersection node. (TIF)</p

Empirical morphospace of leaf venation.

(A) Principal component analysis (PCA) of vein network features and contribution rates for the untreated and cleared leaf datasets. Each clade shows a biased distribution, and whole specimens were distributed along one-dimensional U-shaped curves in PC1–PC3 spaces of both datasets. (B) Scatter plot of PC1 and PC3 scores of the cleared leaves with the cropped image of the vein as markers. The degree of loopiness of vein networks changes along a U-shaped curve. (C) Histograms of the mean of the neighborhood of egonet (1-hop) of 10 samples for the lowest PC1, lowest PC3, and highest PC1 in the cleared leaf dataset and untreated dataset. Error bars represent the standard deviation.</p

Principal component analysis (PCA) of vein network features and representative leaf vein network structures for each clade.

The representative leaf veins for each clade were adopted as the nearest neighbors of the mean of PC scores within the PC1-PC3 space. (A) represented untreated leaves, while (B) represented cleared leaves. (TIF)</p

U-Net for leaf vein segmentation.

Images of the high-quality dataset (A) were converted to grayscale images and masked vein images were generated by conventional image processing with contrast enhancement and binarization (B) to prepare a training dataset. (C) U-Net, a CNN-based model for semantic segmentation, was trained to predict the vein image from the grayscale leaf image. Each blue box corresponds to a feature map. The numbers of channels are shown at the bottom, and the x- and y-sizes are shown on the left. The arrows denote different operations. (D) To segment the leaf veins, the tiled images of 512 × 512 pixels were obtained from the untreated and cleared leaf dataset. (E) The tiled images were converted to grayscale images. (F) The grayscale images were segmented using the trained U-Net.</p

Examples of vein network extraction.

Leaf vein networks were extracted as undirected graphs from untreated leaf images (Ficus erecta, Zelkova serrata, Quercus acutissima, Prunus × yedoensis, and Morella rubra; first five rows) and cleared leaf images (Ficus pumila, Zelkova serrata, Quercus chrysolepis, Prunus pauciflora, and Morella cerifera; last five rows). Cleared leaf images in this figure were based on partially modified images of Specimen Numbers U0604, U4304, T1574, T1426, and U0644 in the NMNS Cleared Leaf Database [36]. Original leaf images, segmented vein images, undirected graphs, and magnified portions correspond to columns. Scale bars represent 10 mm.</p

Cases of failed vein extraction from untreated leaves.

Cases of failed vein extraction from untreated leaves.</p

Segmented vein images and graph representation of leaves of the cleared leaf dataset along PC2.

Segmented vein images and graph representation of leaves of the cleared leaf dataset along PC2.</p

Undirected graph as a representation of the vein network.

(A) Two types of nodes were detected from the total vein pixels based on the number of neighboring vein pixels; endpoints with one vein pixel in their 8-neighbor pixels and branching points with three or more vein pixels in their 8-neighbor pixels. (B) Adjacent nodes were merged into a single node, and all independent nodes were indexed uniquely. An undirected graph as a representation of the vein network was obtained through an iterative search of edges between nodes.</p