Generation of 3D representations of maize canopies from simple measurements: a tool for visualization or use with models involving plant

architecture.

Jean-François Ledent Crop Physiology and Plant Breeding , Université Catholique de Louvain, Belgium

jean-francois.ledent@uclouvain.be

Abstract

We present a method to build 3D representation of maize plants and canopies from simple measurements not requiring sophisticated equipment. A special attention is given to leaf emergence and unfolding and to other geometrical features affecting the visual aspect of the plant. The model can be used directly on any computer where Excel is installed.

1. Introduction Possible applications of 3D models of plants have been described in many publications (e.g. de Visser et al., 2002, Evers et al., 2005, Guo et al., 2006). Our aim was to provide a method to build realistic 3D virtual representations of maize plants that could be used for further studies with 3D models, starting with simple measurements and visual observations. This implied providing indications on the characteristics to observe, a methodology to measure or characterise them quantitatively and a method for reconstructing their geometry. A special attention was given to leaf emergence and unfolding out of the whorl and to the various deformations giving raise to the shape of the leaf surface.

2. Material and characteristics measured Detailed observations on the evolution of the architecture of maize plants through the season were made over several years. All trials were conducted at or near Louvain-la-Neuve (Belgium). Plant sowing density and row width were 100.000 plants/ha and 75 cm, respectively. Cropping techniques(fertilisation, weed control) were those classically used for intensive production of forage maize. The model requires the measurements of the following parameters: height of the ligular zone (collar), lamina inclination at its base (leaf angle), inclination of the symmetry axis of the parabola representing the shape of the midrib, lamina

azimuth, lamina length, lamina maximum width when fully expanded, length and diameters of the funnel part of the whorl (see below), of the ear and of the stem sections. Visual estimations of the number of undulations along the lamina margins or (and) the number of torsions (twisting) of the lamina around its midrib as well as of the position along the lamina length of the maximum of the parabola representing the midrib are made. In emerging lamina, the distance from the base of the emerged parts to the point where the lamina is completely unfolded (transverse unrolling) is also recorded. Measurements were made on tagged plants with common equipment (clinometer, ruler, compass, protractor, camera) on series of plants (usually 20 to 60 according to year). 3. General approach The construction of the static model is based on wire structures (triangle mesh surfaces) and elementary mathematics. We use a surface based and direct approach method based on measured parameters describing the shapes and positions of organs as opposed to the methods based on digitised data collected with a 3D digitiser (Drouet, 2003). It is based on sampling (mostly without harvest) of subsets of plants. 4. Leaf shape factors in fully expanded laminas The variation of lamina width from the base of a fully expanded lamina to its tip is obtained using normalised length and width i.e. width divided by maximum width and distance to the lamina base divided by total length (Bonhomme and Varlet-Granger,1978, Evers et al., 2005 and 2007). In our case normalised values were fitted to a quadratic polynomial (parabola) and shape factors were calculated according to Bonhomme and Varlet-Granger (1978) and Prévot et al. (1991).

Second International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications

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5. Template for the construction of fully expanded laminas, twisting and undulations Fully expanded leaf laminas are initially simulated in the horizontal plane as a series of up to 20 8-triangle sections whose width is derived from the shape factors mentioned above, ending with a 2-triangle tip section (Fig.1).

Figure 1. Lamina templates: A Template for fully expanded lamina, example for two sections plus tip; B template with 20 sections plus tip after application of shape factor. Vertices are them moved along the z-axis up to an elevation calculated from the parabola equation of the midrib. Corrections of the coordinates of margin vertices are then applied to take into account twisting and undulation, by rotating these vertices around the midrib. Undulations are generated as series of alternating increases and decreases of the rotation angle. The length on which undulations or twists occur in the lamina and the number of undulations or half twists (rotation of 180° of the leaf width) is obtained from the visual observations mentioned above. The application of twisting angle allows also to represent the angle formed by the two sides of the lamina around the midrib. Twisting angles are also used to represent unfolding in emerging laminas as explained below.

Figure 2. A and B: Examples of separate laminas produced by the model; C view from above of leaf expanding in the whorl A different type of undulations may be generated by the model through the application of sinusoidal variations to the z coordinates of the points in the leaf margins.

6. Midrib curvature in fully expanded laminas (leaf bending) A parabola is used as a first approximation of midrib shape of fully expanded leaves and the midrib is considered to belong to a vertical plane. The equation of the parabola is calculated from leaf angle, leaf (lamina) length, inclination of the parabola axis and a parameter pMo measured or estimated visually as the ratio of the length of the midrib from its base to the maximum of the parabola and the total midrib length. Since there is no simple relation between the position of a point on a parabola (as defined by the distance along the curve from the chosen origin) lengths along the parabola were calculated by triangulation and the parameters of the parabola were adjusted using an iterative procedure to fit simulated lamina length and pMo to observed values. The equation is z=ax2+bx+c (for a leaf with azimuth zero and vertical symmetry axis); the value of coefficients differ from leaf to leaf and have no straightforward relation with pMo and length. The inclination of the distal part of the lamina (lamina tip) is not routinely measured. However when it appears from visual observation to be too different from what would be expected from a leaf whose midrib is represented by a parabola, corrections of inclination can be imposed applying a rotation to the distal part. 7. Observation of expanding laminas, funnel structure In this work we consider only the visible part of the foliage and therefore the whorl is defined as the foliage parts situated above the collar of the last fully expanded leaf lamina. During a great part of the period of leaf emergence, the whorl contains two or more visible emerging laminas which appear to emerge from a funnel structure formed by the base of the visible parts of the two lower (older) expanding leaves in the whorl. This structure is due to the opposite position and inclination of these leaves, and to the overlapping of their margins. These leaves have a predominant role in the funnel structure and we call them dominant. We consider the funnel structure as limited upwards by the level where the margins of each of the two dominant laminas do not overlap any more. Above this level the surfaces of the laminas visible in the whorl are free from each other and can be considered as emerged out of the funnel (see below).

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Figure 3. Plants at the 4, 6, 11 leaves stage (collar

visible) and one week after silking; the scale differs).

The downward limit is taken relatively to the last fully expanded leaf, either at the level of its collar or where its two margins do not overlap with each other. The diameter at the top of the funnel is related to the width of the two dominant leaves at that level. During the short period when a large number of expanding leaves are visible it may be useful to consider the whorl as formed by more than one of these funnels. Funnels are observable in Fig. 3. 8. Reverse construction of expanding laminas and lamina unfolding The shape of the midrib of the emerging laminas (defined as the midrib part emerged above the upper limit of the funnel) is reconstructed from the structure of the same leaf when fully expanded. This is done taking into account its length and leaf angle at the time of observation (angle of emergence). The model virtually eliminates the parts not visible, it relocates by translation the emerged parts on the top of the funnel and applies an inclination corresponding to the emergence angle. This procedure assumes that the shape of a midrib does not change appreciably after its emergence out of the funnel part of the whorl. This hypothesis was verified by repeated observations of 5 to ten plants photographed at least every two days during the whole period of leaves emergence. Changes were rather limited, a result consistent with those of Moulia et al., 1994 and Hay et al., 2000. Expanding laminas are also characterized by unfolding, i.e. increase of the angle between the two sides (halves separated by the midrib) of the lamina. At a given time this angle increases from the base of the visible part where it is taken as 90° in accordance to the representation of the funnel (Fig. 2 C) to the distance where the two sides are at an angle of about 180°. This distance is recorded and is taken into account to build the 3D structure of the complete lamina (Fig. 2 C).Twist angles in an expanding lamina do not therefore correspond to those found in the fully expanded lamina.

9. Template for stems, ears, funnel part of the whorl Other structures as stems, ears, funnel part of the whorl are represented from a prism template with eight lateral faces. Length of sheaths were not recorded and sheaths are not represented separately from stems or pseudostems (elongated structure resembling to a stem but formed by leaf sheaths). The prism is divided into sections whose size is calculated from information on variation of diameter with distance from the base. Diameters have therefore to be recorded at different heights at least on a subset of typical plants. The branches of the tassel (two ranks of spikelets) are simulated as narrow leaves using the lamina template whereas the central axis is simulated using the prism template. In the case of ears the base and the ear proper (rachis plus grains+ part of husks) are distinguished . To calculate the variation of the radius of the ear (part corresponding to the ear proper + husks) from its base to its tip we applied the same method as for lamina width using normalised lengths and radius. The lower part (peduncle + part of the husks covering it) is taken as an inverted pyramid cone, the tip (vertex) being oriented downwards and corresponding to the insertion of the peduncle (Fig. 5). Roots, aerial or not, are not represented.

Figure 4. A. adult plant B. ear 10. Construction of whole canopies Virtual representations of whole plants or entire canopies can be built from input data entered in an Excel sheet using a table produced automatically by the VBA program that implements the model. Plants in the canopy may be chosen (at random or not) by the model from a subset of whole plants representations obtained . Clones or variants may be created by the model if the number of plants in the canopy is large compared to the subset of whole plants representations available. When creating variants a random variation around a mean position between chosen limits is applied to the original plant representation. The variations can affect the azimuths of the successive leaves, their height of insertion and the position of the plant within a row. Observations on a large number of plants of the variations of azimuths,

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heights or positions are necessary to define realistic ranges of deviations. At this stage the model uses random numbers generated by the VBA software. 11. Software The source code is written in Visual Basic for Application. The output is given in Excel worksheets where each triangle is represented by a row where the 3 coordinates of each 3 vertices are given. The model can be run directly on any lap-top computers where Excel is installed and only a minimum knowledge of Excel is required. The plants can be visualised with a 3D viewer either available with the program and using a small in house application based on the Java3D API (Draye, personal communication) or available in other softwares like VegeStar from INRA (Adam et al 2004). 12. Validation and examples The model presented in this paper is essentially descriptive and uses mostly observed input values for the characters represented. Thus quantitative validation through comparison of these values and their representation in the model would be mostly irrelevant. Validation by simulating light interception might also be inadequate since detailed description of foliage elements has been reported to affect simulated canopy processes like light interception less than expected. This applies to leaf undulations or size and number of triangles used (España et al., 1999), leaf azimuth (Drouet et al, 1999), plain methods of estimating leaf area (Ruget et al., 1996) etc… At this stage a comparison between drawings (as presented in Ledent et al., 1990) or photos (Fig. 5) of real plants and their representation by the model may be used to obtain some qualitative validation..

Figure 5. Photos of plants at 4 leaves stage and adult plant 13. References [1] Adam, B., Dones, N., Sinoquet, H. VegeSTAR v.3.1. A software to compute light interception and photosynthesis by 3D plant mock-ups. In: 4th International Workshop on Functional-Structural Plant Models, 7-11 june 2004-Montpellier,France. Montpellier : Publication UMR. AMAP, 2004. pp 414.

[2] Bonhomme, R, Varlet-Granger, C. Estimation of the gramineous crop geometry by plant profiles including leaf width variations. Photosynthetica 12, 193-196. 1978. [3] de Visser, P.H.B., Marcelis, L.F.M.., van der Heijden, G.W.A.M., Vos, J.A., Struik, P.C., Evers, J.B. 3D modelling of plants : a review. Report of the virtual plant network Wageningen, Report 52., Wageningen: Plant Research International B.V., 2002. [4] Drouet, J.L. MODICA and MODANCA : modelling the three-dimensional shoot structure of graminaceous crops from two methods of plant description. Field Crops Research 83, 215-222. 2003. [5] Drouet, J.L., Moulia, B., Bonhomme, R. Do changes in the azimuthal distribution of maize leaves over time affect canopy light absorption? . Agronomie 19, 281-294. 1999. [6] España, M., Baret, F., Aries, F. , Andrieu, B., Chelle, M. Radiative transfer sensitivity to the accuracy of canopy structure description. The case of a maize canopy. Agronomie 19, 242-254. 1999. [7] Evers J.B., Vos J., Fournier C., Andrieu B., Chelle M., Struik P.C. Towards a generic architectural model of tillering in Gramineae, as exemplified by spring wheat (Triticum aestivum) .New Phytologist 166, 801-812. 2005. [8] Guo Yan, Ma Yuntao, Zhan Zhigang, Li Baoguo, Dingkuhn M., Luquet D., De Reffye P. Parameter Optimization and Field Validation of the Functional–Structural Model GREENLAB for Maize. Annals of Botany 9, 217–230. 2006. [9] Hay, J., Moulia, B., Silk, W., Lane, B., Freeling, M. Biomechanical analysis of the rolled (Rld) leaf phenotype of maize. Am. J. Bot., 87, 625-633. 2000. [10] Ledent, J.F, Henkart T., Jacob B. Phénologie du maïs, visualisation de la croissance et du développement. Revue de l’Agriculture 43, 391-408. 1990. [11] Moulia, B., Fournier, M., Guitard, D. Mechanics and form of the maize leaf : in vivo qualification of the flexural behaviour. J. Mater. Sci. 29, 2359-2366. 1994. [12] Prévot, L., Aries, F., Monestiez, P.. Modélisation de la structure géométrique du maïs (A model of maize plant morphology). Agronomie 6, 491-503. 1991 [13] Ruget, F., Bonhomme, R. , Chartier, M. Estimation simple de la surface foliaire de plantes de maïs en croissance (A simplified method for estimating the leaf area growth of field-grown maize from a reduced number of measurements). Agronomie 16 , 553-562. 1996.

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