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Seed Shape Description and Quantification by Comparison With horticulturae Opinion Seed Shape Description and Quantification by Comparison with Geometric Models Emilio Cervantes * and José Javier Martín Gómez IRNASA-CSIC, Cordel de Merinas, 40, E-37008 Salamanca, Spain * Correspondence: [email protected]; Tel.: +34-9-2321-9606 Received: 21 May 2019; Accepted: 6 August 2019; Published: 19 August 2019 Abstract: Modern methods of image analysis are based on the coordinates of the points making the silhouette of an image and allow the comparison between seed shape in different species and varieties. Nevertheless, these methods miss an important reference point because they do not take into consideration the similarity of seeds with geometrical figures. We propose a method based on the comparison of the bi-dimensional images of seeds with geometric figures. First, we describe six geometric figures that may be used as models for shape description and quantification and later on, we give an overview with examples of some of the types of seed morphology in angiosperms including families of horticultural plants and addressing the question of how is the distribution of seed shape in these families. The relationship between seed shape and other characteristics of plant species is discussed. Keywords: geometric curves; J index image analysis; morphology; seed; shape 1. Introduction Shape is an important property of plants that has been used for the description of organs and structures since the origins of botany. Some plant species were termed on the basis of the shape of their leaves (for example Drosera rotundifolia, Plantago ovata), others according to the shape of their fruits (Coronilla scorpioides, Eugenia pyriformis), and others following the forms of their seeds (Vicia platysperma). Seed shape is an interesting property that has been used in the taxonomy of the Caryophyllaceae [1–3], Orchidaceae [4], Papilionaceae [5], and Zingiberaceae [6]. Seed shape is related to dispersal. The potential for dispersal is increased by the growth of extra-ovular structures such as plumes, wings, hooks, oil bodies, and diverse types of arils [7] that complicate the analysis of seed morphology. But, leaving out such structures, seed description may be based on similarity to geometrical figures such as the oval, ellipse, cardioid, and others. The comparison of seed images with these figures gives a precise description that can be quantitative, allowing the comparison between genotypes or seeds grown in different conditions. Recent methods for the comparison of seed shapes depend on high-throughput systems based on digital image analysis [8,9]. The methods combine artificial vision technologies with statistical algorithms and may be very efficient for the discrimination of seeds and fruits in a range of plant species and varieties [10–13]. Nevertheless, these methods have two main drawbacks: (1) Their results do not give a magnitude that can be associated with seed shape for a particular group of seeds, and (2) they do not take into consideration the similarity of seeds with geometrical figures, missing an important reference point. This has resulted in a “gap” in the current scientific literature on seed shape. Current methods based on artificial vision, algorithms, and statistical analysis need to go back to the initial seed images, combining geometric models with quantitative and statistical methods to analyze seed shapes. Horticulturae 2019, 5, 60; doi:10.3390/horticulturae5030060 www.mdpi.com/journal/horticulturae Horticulturae 2019, 5, 60 2 of 18 HorticulturaeIn this 2019 review,, 5, x FOR we PEER first REVIEW describe the geometric models that may be applied for seed shape2 of 19 quantification in diverse plant families including important horticultural plants. Then, we present somesome examplesexamples of of families families where where the the models models have have been been applied applied and discuss and discuss possible possible models inmodels families in offamilies interest of ininterest horticulture. in horticulture. Finally, Finally, we discuss we discuss the relationship the relationship between between seed shape seed andshape other and plantother characteristicsplant characteristics and the and potential the potential of seed of morphology seed morphology in taxonomy. in taxonomy. 2.2. GeometricGeometric ModelsModels FigureFigure1 1 presents presents a a summary summary of of the the geometric geometric models models used used for for the the description description and and quantification quantification ofof seedseed shape.shape. TheseThese are:are: The cardioid and derivatives;derivatives; thethe ellipse;ellipse; thethe oval;oval; thethe contourcontour ofof Fibonacci’sFibonacci’s spiral,spiral, heart-shapedheart-shaped curves,curves, andand lenseslenses ofof variedvaried proportions.proportions. Figure 1. Main models used in the description and quantification of seeds. (1) Cardioid and derivatives; (2) ellipse; (3) oval and elongated oval; (4) the contour of Fibonacci’s spiral; (5) heart-shaped curves; Figure 1. Main models used in the description and quantification of seeds. (1) Cardioid and (6) lens. derivatives; (2) ellipse; (3) oval and elongated oval; (4) the contour of Fibonacci’s spiral; (5) heart- Inshaped this section, curves; ( we6) lens. describe each of these models. The origin of the images used is indicated in the AppendixA. In this section, we describe each of these models. The origin of the images used is indicated in 2.1.the Cardioidappendix A. 2.1. CardioidThe cardioid is the curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. Another definition is that of the envelope of a pencil of circles formed in a way thatThe theircardioid mid is points the curve lie on traced the perimeter by a point of the on fixedthe perimeter generator of circle a circle [14]. that The is cardioid rolling around has been a longfixed recognized circle of the as same a tool radius. to describe Another biological definition structures is that duringof the envelope development of a pencil because of itcircles corresponds formed toin thea way figure that generated their mid by points an organ lie on that the grows perimeter from of a fixedthe fixed point generator of insertion circle [15 [14].]. Thus, The plane cardioid figures has ofbeen animal long embryos, recognized leaves, as a and tool seeds to describe resemble biol theogical cardioid structures (Figure2 ).during development because it corresponds to the figure generated by an organ that grows from a fixed point of insertion [15]. Thus, plane figures of animal embryos, leaves, and seeds resemble the cardioid (Figure 2). Horticulturae 2019, 5, x FOR PEER REVIEW 3 of 19 HorticulturaeHorticulturae2019 ,20195, 60, 5, x FOR PEER REVIEW 3 of3 18 of 19 Figure 2. (a) The cardioid visualized as the envelope of a pencil of circles formed in a way that their Figure 2. (a) The cardioid visualized as the envelope of a pencil of circles formed in a way that their midpoints lie on the perimeter of the fixed generator circle. The cardioid shape is common in embryos midpointsFigure lie 2. on(a) theThe perimeter cardioid ofvisualized the fixed as generator the envelope circle. of The a pencil cardioid of circles shape isformed common in a in way embryos that their (b) and leaves (c). (b) andmidpoints leaves (liec). on the perimeter of the fixed generator circle. The cardioid shape is common in embryos (b) and leaves (c). 2.2.2.2. Ellipse Ellipse 2.2.TheThe Ellipse ellipse ellipse is is defined defined as as a regulara regular oval oval shape, shape, traced traced by by a pointa point moving moving in in a planea plane so so that that the the sumsum of of its its distances distances from from two two fixed fixed points points (the (the foci) foci) is is constant, constant, or or resulting resulting when when a conea cone is is cut cut by by an an The ellipse is defined as a regular oval shape, traced by a point moving in a plane so that the obliqueoblique plane plane that that does does not not intersect intersect the the base base [16 [16].]. An An ellipse ellipse is is defined defined by by the the length length of of the the major major sum of its distances from two fixed points (the foci) is constant, or resulting when a cone is cut by an andand minor minor axes. axes. Changing Changing the the relations relations between between the the axes axes results results in in di differentfferent ellipses, ellipses, more more or or less less oblique plane that does not intersect the base [16]. An ellipse is defined by the length of the major elongated.elongated. Leaves Leaves of of many many species species tend tend to to an an elliptical elliptical shape, shape, which which is is also also common common among among diverse diverse and minor axes. Changing the relations between the axes results in different ellipses, more or less animalsanimals like like for for example exampleStylostomum Stylostomum ellipse ellipse, a, platelmyntha platelmynth (Figure (Figure3)[ 3)17 [17].]. elongated. Leaves of many species tend to an elliptical shape, which is also common among diverse animals like for example Stylostomum ellipse, a platelmynth (Figure 3) [17]. Figure 3. (a) The ellipse is a regular oval curve, traced by a point moving in a plane so that the sum of its distances from two other points (the foci, F1 and F2) is constant. The ellipse is observed in the image ofFigure a platelmynth 3. (a) The (b )ellipse and in is leaves a regular of many oval speciescurve, traced (c). by a point moving in a plane so that the sum of its distances from two other points (the foci, F1 and F2) is constant. The ellipse is observed in the Figure 3. (a) The ellipse is a regular oval curve, traced by a point moving in a plane so that the sum image of a platelmynth (b) and in leaves of many species (c).
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