Modern automated and semi-automated methods of shape analysis depart from the coordinates of the points in the outline of a figure and obtain, based on artificial vision algorithms, descriptive parameters (i.e., the length, width, area, and circularity index). These methods omit an important factor: the resemblance of the examined images to a geometric figure. We have described a method based on the comparison of the outline of seed images with geometric figures. The J index is the percentage of similarity between a seed image and a geometric figure used as a model. This allows the description and classification of wheat kernels based on their similarity to geometric models. The figures used are the ellipse and the lens of different major/minor axis ratios. Kernels of different species, subspecies and varieties of wheat adjust to different figures. A relationship is found between their ploidy levels and morphological type. Kernels of diploid einkorn and ancient tetraploid emmer varieties adjust to the lens and have curvature values in their poles superior to modern “bread” varieties. Kernels of modern varieties (hexaploid common wheat) adjust to an ellipse of aspect ratio = 1.6, while varieties of tetraploid durum and Polish wheat and hexaploid spelt adjust to an ellipse of aspect ratio = 2.4.

Ampelography, the botanical discipline dedicated to the identification and classification of grapevine cultivars, was grounded on the description of morphological characters and more recently is based on the application of DNA polymorphisms. New methods of image analysis may help to optimize morphological approaches in ampelography. The objective of this study was the classification of representative cultivars of Vitis vinifera conserved in the Spanish collection of IMIDRA according to seed shape. Thirty eight cultivars representing the diversity of this collection were analyzed. A consensus seed silhouette was defined for each cultivar representing the geometric figure that better adjusted to their seed shape. All the cultivars tested were classified in ten morphological groups, each corresponding to a new model. The models are geometric figures defined by equations and similarity to each model is evaluated by quantification of percent of the area shared by the two figures, the seed and the model (J index). The comparison of seed images with geometric models is a rapid and convenient method to classify cultivars. A large proportion of the collection may be classified according to the new models described and the method permits to find new models according to seed shape in other cultivars.

Morphometric methods based on artificial vision algorithms provide measurements for magnitudes descriptive of seed images (i.e., the length, width, area, and surface circularity index). Nevertheless, their results frequently omit the resemblance of the images to geometric figures that may be used as models. A complementary method based on the comparison of seed images with geometric models is applied to seeds of Vitis spp. The J index gives the percentage of similarity between a seed image and the model. Seven new geometric models are described based on the heart-shaped and piriform curves. Seeds of different species, subspecies and cultivars of Vitis adjust to different models. Models 1 and 3, the heart curve and the water drop, adjust better to seeds of V. amurensis, V. labrusca and V. rupestris than to V. vinifera. Model 6, the Fibonacci’s pear, adjusts well to seeds of V. vinifera, in general, and better to V. vinifera ssp. vinifera than to V. vinifera ssp. sylvestris. Seed morphology in species of Cissus and Parthenocissus, two relatives of Vitis in the Vitaceae, is also analysed. Geometric models are a tool for the description and identification of species and lower taxonomic levels complementing the results of morphometric analysis.

Fruit and seed shape are important characteristics in taxonomy providing information on ecological, nutritional, and developmental aspects, but their application requires quantification. We propose a method for seed shape quantification based on the comparison of the bi-dimensional images of the seeds with geometric figures. J index is the percent of similarity of a seed image with a figure taken as a model. Models in shape quantification include geometrical figures (circle, ellipse, oval…) and their derivatives, as well as other figures obtained as geometric representations of algebraic equations. The analysis is based on three sources: Published work, images available on the Internet, and seeds collected or stored in our collections. Some of the models here described are applied for the first time in seed morphology, like the superellipses, a group of bidimensional figures that represent well seed shape in species of the Calamoideae and Phoenix canariensis Hort. ex Chabaud. Oval models are proposed for Chamaedorea pauciflora Mart. and cardioid-based models for Trachycarpus fortunei (Hook.) H. Wendl. Diversity of seed shape in the Arecaceae makes this family a good model system to study the application of geometric models in morphology.