Persistent homology demarcates a leaf morphospace

Abstract

45Current morphometric methods that comprehensively measure shape cannot compare the 46 disparate leaf shapes found in seed plants and are sensitive to processing artifacts. We explore 47 the use of persistent homology, a topological method applied across the scales of a function, to 48 overcome these limitations. The described method isolates subsets of shape features and 49 measures the spatial relationship of neighboring pixel densities in a shape. We apply the 50 method to the analysis of 182,707 leaves, both published and unpublished, representing 141 51 plant families collected from 75 sites throughout the world. By measuring leaves from 52 throughout the seed plants using persistent homology, a defined morphospace comparing all 53 leaves is demarcated. Clear differences in shape between major phylogenetic groups are 54 detected and estimates of leaf shape diversity within plant families are made. This approach 55 does not only predict plant family, but also the collection site, confirming phylogenetically 56 invariant morphological features that characterize leaves from specific locations. The 57 application of a persistent homology method to measure leaf shape allows for a unified 58 morphometric framework to measure plant form, including shape and branching architectures. 59 60 Introduction 61 62As generally flattened structures, leaves provide a unique opportunity to quantify morphology 63 as a two-dimensional shape. Local features (such as serrations and lobes) and general shape 64 attributes (like length-to-width ratio) can be measured, but numerous methods also exist to 65 measure leaf shape more globally and comprehensively. A popular method to quantify leaf 66 shape is to place ( , ) coordinates, known as landmarks, on homologous features that are 67 related by descent from a common ancestor on every sample (Bookstein, 1997). The set of 68 landmarks from each leaf can be superimposed by translation, rotation, and scaling using a 69Generalized Procrustes Analysis (Gower, 1975). Once superimposed, the Procrustes-adjusted 70 coordinates of each shape can be used directly for statistical analyses. Landmark analysis excels 71

Specimen-based analysis of morphology and the environment in ecologically dominant grasses: the power of the herbarium

“…Awn area was also estimated independently. In addition, overall spikelet shape was characterized using methods of PH described by Li et al [19,21,22,26]. Here, we used a 2D application that is robust to noise, and orientation-invariant [19,26].…”

Morphometrics Reveals Complex and Heritable Apple Leaf Shapes

“…The number of connected components is recorded as a function of density for each annulus, resulting in a curve (a reduced version of persistent barcode) that quantifies shape as topology. The topology-based PH approach can also be applied to serrations and root architecture, allowing a similar framework to be used across disparate plant shapes and structures (Li et al, 2017a , b , c ).…”

Image-based phenotyping for identification of QTL determining fruit shape and size in American cranberry (Vaccinium macrocarponL.)

“…In addition to measuring fruit shape using basic attributes such as LW ratio and eccentricity, we applied a topological approach called persistent homology (adapted from Li et al 2017a , and ran in MATLAB). Briefly, this method assigns a value to each pixel in an image depending on the density of neighboring pixels.…”

“…Computer vision methods, such as landmark-based methodologies ( Costa et al, 2011 ) that describe complex shape features in addition to the basic shape descriptors, are widely available. Landmark-based methodologies use strategically located coordinates to mark identifiable features in fruit or leaves, and since the homologous landmarks among different samples can be compared, their use often reveals genetic and developmental features in fruit and leaf shape variation ( Chitwood et al, 2016 ; Li et al, 2017a ). Although this methodology is easy to implement, major limitations arise when landmark placing is ambiguous or when obvious homologous features are unavailable for coordinate location.…”

“…Although this methodology is easy to implement, major limitations arise when landmark placing is ambiguous or when obvious homologous features are unavailable for coordinate location. To overcome these limitations, Li et al (2017a) recently created a landmark-free persistent homology method to numerically quantify the shape features of more than 200,000 leaves representing 141 plant families. Using this methodology, the authors successfully classified leaf shapes into their corresponding family even when shape references (or landmarks) between different leaves were absent.…”