Digiplante is a common project with Ecole Centrale Paris and CIRAD. The GreenLab team at LIAMA is an “associate team” with which very strong links exist. The team became an EPI on July 1 st, 2008.
Digiplante's main focus is the mathematical modelling of plant architectural growth by developing the GreenLab model. Several issues are concerned:
Formalism of the organogenesis model based on stochastic grammars
Integration of the functioning into plant structure: bud functioning, biomass production and partitioning in both deterministic and stochastic cases
Interactions between Organogenesis and Photosynthesis
Plant-environment interactions (light, temperature, water)
Tree structure simplification and multi-scale representation
Transition from the individual plant to plant populations
Optimization and Control of the dynamical growth to improve yield under constraints
Connexion with others research fields: mechanics, radiosity, genetics
Visualization of plants from individual to population and landscape level with different computer graphic techniques
Developing software for the simulation of the GreenLab model (Scilab and C++).
The cultivated areas of Europe, including agricultural land and exploitation forests, have a strong impact on global environmental conditions. Erosion, resource impoverishment due to over-exploitation, and pollution by fertilizers or pesticides are crucial problems that agronomy and forestry hope to solve through harmonious cultivation modes and exploitation strategies. For this purpose, they must take into account production needs on one hand and the environment on the other; that is to say, both quantitative and qualitative criteria. In this context, mathematical models of plant growth describing interactions between the architecture of the plant and its physiological functioning have a key role to play. They allow the exchanges (of water, carbon, minerals etc) between plants and their natural environment to be quantified. GreenLab is such a functional-structural model, and is the result of a long dialogue between botanists, physiologists and mathematicians. We have developed mathematical tools and their corresponding software for a variety of objectives:
Optimization and control of the cultivation modes: in the case of limited resources, there is an optimal strategy of fertilizing and watering during plant growth. Likewise, controlling plant density or partial forest thinnings can bring benefits. In this way, we can improve water resources and land management and reduce pollution by fertilizers.
Control of plant sanitation and pesticides treatment: by coupling the plant growth model and insect population dynamics, we can control the use of pesticides and thus reduce costs and pollution.
Selection of crop variety: we are currently working with geneticists, in order to prove that the plant genes directly determine the physiological parameters of the GreenLab model. In this way, we expect to propose better strategies for crop selection.
Virtual simulation and visualization of plantations: computer graphics techniques allow the results of numerical simulations to be visualized. This is very important in urbanism or landscaping for predicting the long-term evolution of projects.
The results of this research seem to show that in the near future, new tools of prediction, optimization and control could be effectively used in agriculture and forest exploitation on a large scale, and would drastically improve the management of the environment.
PhD defense of Vincent Le Chevalier, Centrale, May 2010.
PhD defense of Sébastien Lemaire, AgroParisTech, May 2010.
HDR defense of Marc Jaeger, University Blaise Pascal (Clermont-Ferrand), December 2010.
Derived from the AMAP model developed in the 1990s at CIRAD , GreenLab's new formulation was introduced at LIAMA (Beijing) in 2000, through the GreenLab Associate Team with INRIA. Today, the model is studied and improved owing to the DigiPlant research team that is a joint team of researchers from INRIA, CIRAD and Ecole Centrale Paris. Some very close partnerships exist with LIAMA, China Agriculture University, Wageningen University, INRA, SupAgroMontpellier and AgroParisTech. The development of the GreenLab model is shared between all these partners, with strong interactions (International exchanges, common publications and joint PhD).
Our approach to develop the mathematical model of plant growth strongly relies on the plant organization described by botanists. This leads to relevant choices in order to obtain an efficient method of factorization based on plant instantiations . Plant development concerns organogenesis, i.e. the appearance of organs. Growth depends on photosynthesis that insures organ expansion. On the common assumption of the existence of a global pool of reserves, it is not necessary to consider local conditions and we can distinguish 3 steps to control plant development and growth.
Computing organogenesis. It provides the number of organs produced by the buds. It may be determined by plant functioning and the level of trophic competition .
Computing biomass production and allocation. Leaf surface area is used to determine photosynthesis and the neat biomass production is shared between the different organs (whose numbers are known by the organogenesis step) according to their sinks to insure their expansion. The yield is thus computed according to the sizes and the weights of the different organs produced.
Building plant architecture for visualization or to study interactions with the environment. This last step involves geometry applied to the results of the two previous steps.
For most applications in agronomy, only the first two steps are necessary, and no geometry is required.
GreenLab combines both organogenesis and functional growth in a mathematical dynamic system. A dual-scal automaton was initially used to describe GreenLab organogenesis. However, it was shown to be equivalent to a growth grammar , and this formalism is used from now on to describe the GreenLab organogenesis model. In this section we recall the basic botanical hypotheses used to construct the model of organogenesis, how it defines a growth cycle that is used to synchronize the computation of both organogenesis and functional growth. The construction of the growth grammar is also recalled, with its fundamental property: its factorization, taking advantage of all instantiations in plant architecture. Based on this growth grammar, the functional equations of biomass acquisition and distribution can be derived.
As explained in , organogenesis results from the functioning of undifferentiated cells constituting the apical meristem and located at the tip of axes. When in active phase, this meristem forms buds that will develop into new growth units composed of one or several metamers (also called phytomers). A metamer is a botanical entity chosen as the elementary scale to model plant architectural development in this study. It is composed of an internode bearing organs: axillary buds, leaves, flowers. Depending on species, metamers are set in place rhythmically or continuously.
In the rhythmic case, see Figure , the plant grows by successive shoots of several metamers produced by buds. The appearance of these shoots defines the architectural Growth Cycle. A Growth Unitis the set of metamers built by a bud during a growth cycle. These metamers can be of different kinds and ordered according to botanical rules, like acrotony. For example, most temperate trees grow rhythmically, new shoots appearing at spring. For such plants, and if we do not consider polycyclism and neoformation, the architectural growth cycle corresponds to one year.
Plant growth is said continuous when meristems keep on functioning and generate metamers one by one, see Figure . The number of metamers on a given axis (that is to say generated by the same meristem) is generally proportional to the sum of daily temperatures received by the plant, see . The growth cycle is defined as the thermal time unit necessary for a meristem to build a new metamer, it can be quite short, corresponding to a couple of days. The growth unit is thus simply composed of one metamer. The growth of tropical trees, bushes or agronomic plants is often continuous.
So far, Digiplante does not consider time scales that are smaller than the architectural growth cycle and we study the development of new growth units as a discrete process. The Chronological Age(CA) of a plant (or of an organ) is defined as the number of growth cycles it has existed for.
Since metamers may bear axillary buds, plant
architecture develops into a hierarchical branching system.
underlined that architectural
units can be grouped into categories characterized by a
particular combination of morphological parameters. Thus,
the concept of
Physiological Age(PA) was introduced to represent
the different types of growth units and axes. For instance,
on coffee trees, there are two types: orthotropic trunk and
plagiotropic branches. The main trunk's physiological age
is equal to 1 and the oldest physiological age denoted by
Pcorresponds to the ultimate state of differentiation
for an axis, it is usually short, without branches. We need
less than 5 physiological ages to describe the axis
typology of most trees. The apical meristem or bud of an
axis is thus characterized by the physiological age of the
growth unit that it may produce and a metamer is
characterized by its physiological age
i(which is the physiological age of the growth unit
that it belongs to) and that of the buds that it bears
j. Except in some very rare cases, we always have:
ij. Moreover, along an axis, the morphological
features of the growth unit may evolve with the age of the
apical meristem. This process is described as the meristem
sequence of differentiation by
, and corresponds to a
transition to a superior physiological age of the
meristem.
This section summarize results presented in
,
,
. In GreenLab, the alphabet
is given by the set of metamers
and buds
. A metamer is defined with four indices and is
denoted by
mpqt(
n):
its chronological age:
n,
its physiological age:
p,
the physiological age of its
axillary buds:
q,
(
q
p),
the chronological age of the plant:
t.
A bud is defined by three indices and is denoted by
bpt(
n):
its physiological age:
p,
the number of growth cycles
kfor which bud's physiological age has been p -
in the sequel, we will call it
ontogenic ageof a bud,
the chronological age of the plant:
t.
If
Tis the maximum growth time, the organogenesis
alphabet is given by:
, with
We do not consider symbols for organs since the constitution of a metamer is supposed fixed by botanical rules (an internode and a given number of leaves and fruits). If, for example, flowering is particularly studied, symbols denoting flowers could be introduced in the alphabet.
Definition 1 (Set of words over an alphabet)The set of words over an alphabet is defined as the monoid generated for the concatenation operator ".", seen as an internal, non-commutative operation, by , where 1is the neutral element for the concatenation operator (which corresponds to the empty word). It is denoted .
will thus represent all the possible topological
structures composed with buds and metamers. For example,
represents at growth cycle
ta structure composed of an internode of
physiological age 1, bearing a lateral bud of physiological
age 2 and an apical bud of physiological age 1. We will see
that of course the structures of interest, that is to say
botanically relevant, form a small subset of
(corresponding to a language over
). It is important to consider concatenation as
non-commutative when studying plant topology.
As recalled in section , GreenLab organogenesis can be seen as the combination of two phenomena, branching and meristem differentiation. It can be easily modelled with the grammar formalism and we propose to define it as a F0L-system as follows:
Definition 2 (GreenLab Organogenesis)GreenLab
organogenesis is defined as a F0L-system
with the following production rules
Pr:
For all :
and for all
(
t,
n,
p,
q)
[1;
T]×[1;
t]×[1;
P]×[
p;
P]:
with:
upq(
t): number of phytomers
mpqin a growth unit of PA
p, appearing at growth cycle
t
vpq(
t): number of active axillary
buds of PA
qin a growth unit of PA
p, appearing at growth cycle
t
(
p): number of GC after which
a bud of PA
pchanges to PA
(
p). Vectors
and
characterize meristem differentiation.
A fundamental result was surprisingly never used in the context of models of plant development: it is the ability to factorize the L-system productions. It showed particularly adapted to the concept of physiological age, cf. , . We are thus able to factorize plant structure into smaller parts that may repeat themselves a large number of times.
Definition 3 (Substructure)At growth cycle
t0, a substructure of physiological
age
p, 1
pPand chronological age
n, 0
ntis a word in
defined as the complete plant structure that is
generated after
ncycles by a bud of physiological age
p. It is also characterized by the ontogenic age
kof the bud generating it. It is denoted by
Spt(
n,
k)(corresponding to the structure
generated by
bpt-
n(
k)after
ngrowth cycles).
We show how the structural factorization allows the inductive computation of all the substructures, providing an efficient algorithm to simulate plant organogenesis. We deduce the following important result.
Theorem 1 (Dynamic Equation of Plant Development)For
all
t1,
,
,
,
, we have:
This decomposition is illustrated on
S1(2)in Figure
. If we suppose that all the
elements of the alphabet (set of metamers
mpqt(
n), set of buds
bpt(
n)) as well as the sequences
and
are known, Theorem 1 shows us how to build the
topological structure of the plant at any growth cycle
trecursively, as follows:
Substructures of chronological age 0 are buds:
,
and if all the substructures of chronological age
n-1are built, we deduce the
substructures of chronological age
nfrom Equation
as functions of
mpqt(
n),
upq(
t-
n+ 1)and
vpq(
t-
n+ 1).
Substructures and metamers will be repeated a lot of times in the tree architecture, but they need to be computed only once for each kind.
If we only consider topology, we do not need to
characterize the metamers by their chronological ages nor
by the plant age.
mpqt(
n)can thus be simply be denoted
by
mpq. But if we consider the functional growth of a
plant, metamers of different chronological ages have
different masses and sizes, as well as metamers of the same
chronological age, but at different plant ages.
introduced how the dynamic development equation can be extended to build plant geometry with geometric operators replacing the concatenation operator. We will not detail this point here since our objective is to study plant functional growth which only relies on topology and not geometry in GreenLab.
Plant toplogy can simply be seen as a function of:
the sequences
and
for all
(
p,
q)such that
1
p
q
P(they will be called
development sequences),
the vectors , in case of meristem differentation.
The GreenLab organogenesis model has been derived in 3 forms:
GL1 corresponds to the deterministic
organogenesis model, without influence of the plant
functioning. Mathematically, it corresponds to
upqand
vpqconstant, see
. In
such case,
Spt(
n)are (topologically)
independent of
t, and the construction does not have to be done
at each growth cycle but only once.
GL2 corresponds to a stochastic
model of organogenesis,
upqand
vpqare stochastic variables. As a consequence,
substructures of the same chronological and
physiological ages can be very different:
Spt(
n)is a stochastic variable
with values in
. More details are given in section
and in
.
GL3 corresponds to a deterministic
model with total retroaction between organogenesis and
photosynthesis.
upq(
t)and
vpq(
t)are functions of the
biomass produced by the plant at growth cycle
t-1and
trespectively, see
.
Utwill denote the vector
and
the associated sequence of vectors. Likewise,
Vtwill denote the vector
and
the associated vector of sequences.
Literature is already abundant on the functional concepts underlying the GreeLab model and its various versions ( , , , , ). The fundamental principles common to all these versions are actually very general and are shared (to some extent) with various other models (for example LIGNUM , TOMSIM , GRAAL ...). The central equation of GreenLab describes the growth of an individual plant potentially in a population (field crops, forest stands...). Competition with other individuals for light, water, nutrients can thus be taken into account and affects the computation of biomass production, see regarding competition for light or for competition for water.
GreenLab aims at describing the source-sink dynamics during plant growth. Sources correspond initially to the seed and then to biomass production and reserve remobilization. Sinks are demands for biomass of all living organs. So far, all sinks have access to all sources since we consider a common pool of biomass. However, this hypothesis is not fundamental and could be relaxed. Since structural development is described in GreenLab at the level of organs, the computation of demands is coupled with organogenesis. For this reason, a consistent time unit for architectural growth and photosynthetic production is defined in order to handle a constant structure. It allows the derivation of the discrete dynamic system of growth, see Figure
It is not necessary to build the tree structure to compute biomass production and partitioning at a given chronological age. We only have to compute organ production, plant demand and photosynthesis. All these data can be derived recursively by applying structural morphisms to the dynamic equation of plant development ( ) giving the number of metamers in the plant as we know the number of organs per metamer and their life spans. The functional growth is then described by the two following steps, biomass acquisition (production) and distribution among living organs.
Biomass acquisition :
Different strategies were used and are currently used
in GreenLab according to plants to compute
Qt, the biomass production at growth cycle
t. There are mostly 3 sources to provide biomass for
allocation: seed, resource acquisition by photosynthesis
and reserve remobilization (from roots, layers or senescent
organs). We will not speak about the seed, which usually
gives
u0and may be considered as emptying on several growth
cycles, that is to say also contributing to
u1,
u2...
Classically, the biomass production at growth cycle
t
Qtis taken as a parametric function of
, the total photosynthetic leaf area, and of the
environmental conditions. To keep it simple, we sum up all
the environmental effects in
Et, which may be chosen as a function of the
Photosynthetically Active Radiation (PAR), hydric stress
(Fraction of Transpirable Soil Water), temperature (for
biologic efficiency)... Only simple functions have been
tested so far in GreenLab. A possible production function
inspired by classical crop models and Beer-Lambert's law (
and
for details) can be
written:
where and are empirical parameters.
It is helpful to rewrite this equation by changing the parametric structure:
with the parameters having now a more
relevant physical meaning:
is an energetic conversion efficiency,
kis the extinction coefficient of the Beer-Lambert
law and
Spis related to a characteristic surface for resource
acquisition.
In her PhD, V. Letort proposed that, after some time, a proportion of organ biomass is given back to the common pool and reallocated to new organs in expansion.
Biomass partitioning :
We recall that
mpt(
n)denotes at growth cycle
ta metamer of physiological age
pand chronological age
n. It contains organs of type
o(where
o=
b,
p,
i,
f, for blades, petioles, internodes, flowers or
fruits respectively) whose masses are denoted by
qo,
pt(
n)at growth cycle
t. Let
To,
pdenote the maximal life span of organs of type
oand physiological age
p. The allocation equation is thus given for all
t0by:
where:
po,
pt(
n)is the sink of an organ of
type
oin
mpt(
n)
Dtis the total demand of the plant at growth cycle
t(that is to say the sum of all sinks)
where
No,
pt(
n)is the number of organs of
type
o, physiological age
p, chronological age
nat time
t.
Qtis the biomass available for allocation.
Eventually, the organ volume depends on its apparent density and its dimensions on allometric rules. All this features can be measured directly from organ forms.
Remark 1This general formulation concerns primary growth of the above ground organs. For the complete model, we need to consider the root system demand, and for trees, the ring demands (for the secondary growth). A detailed presentation of the different types of modelling strategies can be found in the PhD thesis of V. Letort .
The shape chosen for the sink variation function
pis up to the user, but it should be able to fit
properly any kind of numerical variations of the sinks
according to the organ chronological age. Beta laws were
found to be suitable for the purpose.
During her PhD, A.Mathieu modelled a retroaction of plant functioning on plant topology controlled by the state of trophic competition (GL3 model). Such model illustrates in a very simple way how plant plasticity is expressed under environmental constraints.
The vectors
Utand
Vtthat give the rules of the organogenesis model (that
is to say that control the bud behavior) are chosen as
functions of the ratio of available biomass to demand.
Integer part of linear functions are usually chosen. In
Figure
, we see the difference between
the GL1 model (with constant sequences
,
) and the GL3 model, (with sequences
,
functions of
ut).
Utis a function of
and
Vta function of
(they are usually chosen as linear functions). The
behaviour of the system was studied by A. Mathieu during
her PhD. The conditions of the growth stabilisation were
determined according to the parameters. Moreover, an
interesting emerging property was obtained: under some
conditions, rhythmic phenomena may be generated by the
system (Biomass production, fruiting and branching
alternation, number of internodes per growth unit ..., see
Fig.
). Such phenomena are often
observed during plant growth but were poorly modelled so
far.
As detailed in the section giving the new research results of the team, some important results concerning the calibration of the thresholds of fructification have been obtained on cucumber plants (in collaboration with the Chinese Agricultural University and Wageningen).
The objective is now to give a parobabilistic framework to this model of interaction.
The results on single plant growth modelling are extended at the field and stand level, in order to simulate crop and forest production. It needs to integrate the competition for light and for soil resources among plants.
A model of competition for light :
The empirical production equation of GREENLAB is extrapolated to stands by computing the exposed photosynthetic foliage area of each plant. The computation is based on the combination of Poisson models of leaf distribution for all the neighbouring plants whose crown projection surfaces overlap, .
To study the effects of density on architectural development, we link the proposed competition model to the model of interaction between functional growth and structural development introduced by Mathieu .
The model was applied to mono-specific field crops and forest stands.
The application of the model to trees illustrates the expression of plant plasticity in response to competition for light, cf. Figure . Density strongly impacts tree architectural development through interactions with the source-sink balances during growth. The effects of density on tree height and radial growth that are commonly observed in real stands appear as emerging properties of the model.
For high density crops at full cover, the model is shown to be equivalent to the classical equation of field crop production (Howell and Musick, 1984) . However, our method is more accurate at the early stages of growth (before cover) or in the case of intermediate densities. It may potentially account for local effects, such as uneven spacing, variation in the time of plant emergence or variation in seed biomass.
Functional landscapes :
Models of landscape functioning aims at simulating, crop plantations and small landscape with a “reactive” environment. The goal is to simulate water exchanges (rain, runoff on terrain and absorption, diffusion in soil, plant water uptake and evapotranspiration) and competition in interaction with the GreenLab growth model. The difficulty of the approach lies in the multiphysics and multiscal models to implement. After some prelimnary works carried out at LIAMA, it is now the PhD subjet of V. Le Chevalier, under the supervision of Marc Jaeger.
Two successive prototypes were developped. The first prototype, voxel based, was a simple simulator synchronizing all events at a daily schedule (water rain, run-of, diffusion, plant growth). Models were basic, and run-of simulated as a diffusion process on the land surface , using a discrete volume spatial grid. This model was implemented in C++ under QT environment and tested on BULL Novascale HPC (16 cores). The second prototype, is still based on a spatial discrete grid, but limited to the layer. It involves an appropriate water run-off model, and the plant model is a simple version of the GreenLab crop model and involves more advanced visualisation tools.
At this stage, visualisation of functional landscape simulations aims at visualizing combination of maps (among terrain altitudes, water soil content, run off, daily biomass, cumulated biomass, temperature, ...). Classical surface mesh tools were written, as well as histogram, and curve display tools, allowing comparisons during a given period, or spatial heterogeneity comparisons at a given stage. The orginality of the developped tools lays in the fact that all these maps are dynamic (daily change), and thus not compatible with classical approaches (all in memory). Vegetation representation is rougth, limited to a simple color definition merged with the relief texture. A "pseudo realistic" landscape visualisation can be preformed representing the cumulated biomass by spheres, converting some how the crop production to a "tree crow". The correponding tool (SURFVIEW) is written in C++ with GLUT and OpenGL librairies.
The system was tested on synthetic cases, with real climate conditions and published in JCST journal .
Both prototypes show strong conceptual limitations especially on two crucial points: model synchronism and data integrity. Time synchronism is a strong critical aspect in our case since we have to face calendar asynchronism processes (rain, run off) with thermal time cycles (plant development). However plant functioning must be simulated at short periods of calendar time in order to uptake the appropriate water supply. Concerning data now, and more precisely water ressources, the various models (run off, absorbtion, plant growth interact spatially on the same data with high risk of collusion). Since end 2006, concepts to develop the design of landscape functional simulators are extensivily studied leading slowly to discrete event simulation formalisms.
The plant architecture is a target for the mathematical model, and it is the visual result of the growth process. The hidden parameters of source and sink functions must be estimated in order to fit the weights and sizes of all the organs produced by the plant development at each stage of growth. Theoretically speaking, this inverse method should be able to assess also the effect of the environment (climate and density), biomass production and biomass partitioning to each organ during the growth from the architectural data. However, the identifiability issue has not been studied yet. Only a lot of numerical tests on a wide variety of real plants have helped us define a proper experimental framework for identification, see for example .
The Generalized Least Square Method was used for parameter estimation of the model. The application of this method to GreenLab was described by Zhan et al. and Guo et al. . Advantages of this method are that it provides rapid convergence and the standard error linked to the parameter values thus indicating the accuracy of the solution. Fitting can be done on a single architecture (single fitting), or on several stages of growth to follow the trajectory of the dynamical process (multi-fitting). This second one is more accurate, since it helps retrieving the dynamics of sink variation more easily. In both cases all the data are adjusted at the same time by the same parameter set.
This methodology for parametric identification was implemented in Digiplantsoftware, and used on several plants: Maize , Arabidopsis , Pine saplings , Cucumber , Sugar-Beet , Cotton , Beech , Chrysanthemum , Grapevine ...
We give beneath an example on the sugar beet. It corresponds to an industrial partnership with the French institute for Sugar Beet Research (ITB). Concerning the experimental data from which the model parameters are estimated, biomass measurements were carried out at seven different stages. At each date, seven individuals plants were selected and the dry mass of every individual organ (blades, petioles and root storage) was measured. The average of the seven plants was constructed. The numerical values of the parameters as well as their variances are given in and are not recalled here. As an illustration, Figure shows the fitting curves.
If the goodness of fit is excellent, the statistical analysis of the estimation results is not properly done yet. The variances of the estimates are given under the assumption that the error model chosen is the good one. But the hypothesis of a diagonal noise covariance matrix which is used in the generalized least square method, is quite gross. It corresponds to using only the deterministic part of the dynamical model, which is really restrictive since in dynamic models, errors propagate. Current studies aim at improving estimation by modelling the dynamics of the covariance matrix of the model noise.
The computer graphics in Digiplante inherits from the long tradition of AMAP works , and is mostly conducted since 2004 in close partnership with the GreenLab team at LIAMA (Dr. ZHANG XiaoPeng and his students).
Principles and main research axis hold in the frame of the project :
Plant simulated visualization in DigiPlante project is still based on the AMAP prinicples , characterized by a high level, device independant simulation output, called the line-tree. Geometrical ouput is a final process in the simulation stage, that can be processed or not. The Linetree structure describes a plant by a list of organs, refered by basic indetification information (organ type, age) and organ positioning in space 3D origin relative to seed position, and 3D orientation. Orientations (main direction, normal and secondary) are scalled, story thus internode diameter/length and other organ sizes. These geometrical informations are stored in a 3 by 4 mattrix, similar to a classical OpenGl Mattrix Model Viewer. This data structure shows several interests and drawbacks:
The Line tree structure does not store an exhaustive geometry, but just the list of each plant componant with its orientation
The structure is flat, no hierarchy or topology information is given. However, extension were developped, using a separated structure storing the componant father-son relations. From these, pruning operatin are available as well as branch per branch output or other hierarchical tree based data exploring schemes.
The structure cannot be displayed directly; each componant must be given an exhaustive geometrical description, build from instance from CAD-CAM tools. On the other side, the tree skeletton is obvious to be extracted and displayed; each componant can be simply represented by a simple line linking its origin to the end point of its main direction (which is scalled). This approach allows thus a wide range of representations, open to many graphical systems. It can be compared to a classical Display List, in which primitive objects are to be defined according to the viewing system for each kind of organ (usually a simple cilinder for branch, and specific shapes for the other organs). Organ representation must be normalized; i.e. each organ must be defined using the same main axis and normal axis and normalized in size: unit volume or length for branch/fruits, unit area for leaves.
Graphical rendering aspects, including illumination properties, textures are thus independant for the line tree, since define at the organ geometry descrition level.
The structure allows Level of Details approaches and simplifications. According to componant sizes (length / diameter ) selection can be done in order to extract componants of interest (trunk and main axis). Coupled to statistical selection of leaves/flower, fruits, lower graphical model can be generated, without losing the global sahpe of the simulated plant. On branches, successive componants can be concataneted, remplacing list of internodes by a straith branch piece.
The Line tree structure has shown a large interest for easy visualisation of complex trees on a wide range of systems, but is poorly adapted to advanced LOD models (such as hybrid polygonal/billboards models)and fast huge scene representation.
Scenes such as crops, forest, up to landscape visualisation was, up to now, mainly developped on a plant basis (not on a landscape use basis, as it is more and more the case in commercial products); and also without advanced dynamics, especially without plant/environment dynamics.
In the frame of the digiplante project, computer graphics development axis aims at developing new methods and approaches aiming to visualize large vegetation scenes in acceptable time (close to real time), in respect to plant structure and functioning. Prior is thus given to approaches keeping biological consistency (for instense leaf area) to appraoches keeping aesthetic aspects. Research axis do concern single plant LOD model definition, and new landscape simulation/visualisation approaches.
Single Plant LOD Models. :
Concerning single plant representation. In cooperation with LIAMA, we developped a set of algorithms dedicated to generate continuous LOD geometrical model from a Line tree and its associated hierarchical topology. The principles of the approach are the following:
The tree structure (trunk and branch) is converted to a Frenet Diagram. This diagram can be compressed, merging consecutive elements together, under control (error controlled). A branch part of the diagramm is then described by an equation. At the rendering stage, according to the viewing parameter, the appropriate Diagram is retrieved, and the discretisation of branch in polygons is performed, also according to viewing parameters. If branch diameter gets lower than a pixel, transparent lines are used for rendering.
For foliage, the proposed approach is to merge leaves two by two until reaching a simple quad for the whole plant crown . Various methods were explored to obtain an efficient merging process. The main idea is to collapse leaf candidates within specific clusters, faithful to botanical hierarchical structures. Hierarchical Leaf Union keeps more leaf surface area, keeping functional consistency of the DigiPlant model. In the various collapsing models, principles of the LOD schemes are unchanged, while preprocessing stages are revisited, making the approach operative for huge trees and heavy forest scenes .
in order to avoid multiple exchanges between GPU and CPU, scenes are rendered according to tree species and individuals (to optimise instanciations). The full foliage lod models are stored in a simple table, compressed and send to the GPU. wWile rendering, CPU computes the adequate LOD model, sending then the corresponding indexes of the table to the GPU. GPU draws then all items lying in the table between these indexes.
Specific LOD shemes were also defined for coniferes, replacing graphical primitives (cylinders) by lines, and defining line set replacement patterns by simple lines on far trees.
An extensive summary paper covering many aspects developped in the past four years has been published by Wesley in Computer Anination and Virtual Words journal CAVW08
This topic started two years ago at LIAMA, in the frame of the GreenLab project, with the objective to generate plant geometry from laser range point data. The work of PhD Zhu Cao is dedicated to the foliage crown. The proposed approach uses alpha shape (extension of voronoi diagrams). Originality of the approach lies in the automate definition of the alpha parameter (that controls the "smoothness" of the crown shape) , using a topological criteria: we want the surface to be a manifold. This approach, presented at Edutainment 08 shows also a high interest on simulated plants, generating thus simplified shapes of crowns. 3D reconstruction from laser range point becomes a hot topic in forestry sciences. Both LIAMA GreenLab team and Digiplante were sollicited to participate to an ANR Bioenergy project "EMERGE", planning to evaluation wood ressource for energy (project is accepted and started begining 2009)
The main application domains of the Digiplante team are: Agriculture, Forestry, Ecology, Computer Graphics.
In the context of an increasing importance of the biomass resources (both for alimentary or non-alimentary purposes), it is crucial to both predict and control crop yields or forest productions, both from a quantitative and qualitative points of view. Such goals can be achieved by proper simulations and optimization of the dynamic system modelling plant growth in interaction with the environment. We are mainly confronted to two types of optimization problems, direct optimization for the design of ideotypes and optimal control to design optimal cultivation modes (management of water, nitrogen, pesticide supplies).
Regarding ecology applications, they are mostly based on the techniques developed in functional landscape simulation and visualization. In our scope of research, the strategy is to study the impacts of several climatic scenari on landscape evolution: what is the consequence of an increase of 1 degree in temperature, what is the consequence of two conecutive years of drought...Some classical aspects in plant ecology (like seed dispersion and plant generations) should still be implemented to widen the scope of potential applications.
Finally, computer graphics and plant or forest visualization can be of great help for town and landscape planning, architectural projects, ecosystem management, but also video games or different types of simulators. A company born from AMAP (Bionatics) is specialized in this type of applications. The results of the Digiplante team on functional growth and functional landscapes is a key to improve plant realism and broaden the perspectives of applications.
The first prototype of the plant toolbox built in Scilab and named GreenScilab that runs the GreenLab model has been completed and is available on the Liama web site since July 2006. It is intended to teaching activities and to spread the model in the research communities on plant modelling. Main developer is at the project GreenLab-Liama (M.Z. Kang). It is co-developed by the Digiplant team (Qi Rui, Letort). GreenScilab should increase each year as well for the possibilities (calibration and optimization on plants) as for the documentation support for teaching and training. It has been for a common course between INA-PG, Master of Orsay Univeristy and Ecole Centrale Paris. A GreenSciLab page is now also on line on SciLab site.
See:
http://
And, on SciLab site:
http://
P.H. Cournède has developed the Digiplant software since 2002, with the help of P. Labatut, A. Mathieu, V. Letort. It is dedicated to the simulation of the GreenLab model and its parametric identification on real experimental data. Compared to GSL, which is mainly devoted to teaching activities, Digiplant is used in the partner institutions for research: CAU, INRA Montpellier, INRA Grignon, ITB, Univ. of Wageningen, China Academy of Forestry, CIRAD, IRD.
With the work of the two INRIA engineers, B. Bayol and T. Guyard, and 1 Centrale engineer (C. Mouton) new software products based on the simulation module of Digiplante were developed: DGP Modelizer, with a new editor insuring a better compatibility between the different software versions ( cf. exxEditor), and a new visualization module DGP Builder. Moreover, a simplified user-friendly version was also developed DGP Creatorallowing simulations of predefined plants, at different ages and in different environmental conditions.
Finally, DGPScene allows the simulation and management of plant populations. A configuration file (with plant positions, varieties, initial times) is given as input, an analysis of plant competitions is performed and individual-plant growth is then simulated. The scene can then be visualized . Note that the input file can be generated with SIMEO Software developed by F. de Coligny (INRA, UMR AMAP).
All the DGP software is developed in C++ (with libraries Qt, STL, BOOST, OSG, Xerces, Xalan, EXX, ColladaDom) and runs on LINUX, WINDOWS, MAC OS.
M. Jaeger has developed a tool for the visualization of functional landscape simulations. Several prototypes of functional landscape simulators exist (at LIAMA and in the Digiplante team) and rely on this tool for the scientific visualization of the simulation results.
exxEditor is an XSD based XML editor created by Thomas
Guyard. For our research projects we have to parametrize
complex simulations. We use a tree data structure to store
these input parameters. The simulator include a widget to
modify these parameters and then launch a simulation. During
the research process the simulator is modified and the
structure of the input parameters may change. Thomas Guyard
(INRIA IA) developed a solution a very generic solutions,
which allows to include these changes without a lot of
modifications in our software. We store the input data in an
XML file. We developed an XML editor named
exxEditor, using an XMLSchema to generate a tree based
GUI. This software is developed using Qt4 and Xerces c++. The
idea is simple : First we read the XMLSchema file then we
generate a Qt4 tree (using the model view Framework in Qt).
So we have a very easy to use tool to edit XML files, that
can be modify just by modifying the XMLSchema file. Due to a
good software design we can include this editor in every Qt
based program. The program
exxEditorand the generic libraries used to construct
it are free software. You can download the source code in
license CECILL-C at
https://
A platform for Plant Growth Model Analysis and Identification. B Bayol, PH Cournède, C Mouton develop this software dedicated to the statistical and mathematical analysis of plant growth models and their parametric estimation, in C++. Several models are implemented in this plateform: different version of the GreenLab model (discrete and continuous), PILOTE, SUNFLO, SUNLAB, CORNFLO, STICS and others ...
Digiplante at Amap-Cirad develops the Gloups software both in Matlab and Java that integrates interesting new features : stochastic growth and development including pre and neoformation, polycyclism, herbaceous growth with basipetaly and acropetaly, remobilization etc... The inverse methods are available for new complex plants that are arriving for the sources and sinks studies.
The stochastic version of GreenLab (GL2) was developed by M.Z. Kang . A stochastic formal language adapted to the botanical concepts underlying the GreenLab organogenesis model was introduced in . It is based on stochastic L-systems (parallel rewriting grammars) and on multi-type branching processes: stochastic processes control bud productions and at each growth cycle, each new growth unit is the result of a random variable.
From 2008, these preliminary results were extensively revisited by a new PhD student, C. Loi. A new probabilistic framework for stochastic L-systems was introduced, and linked to multitype branching processes. The results were applied to the Greenlab organogenesis model in order to characterize the probability distributions and moments of the numbers of organs in plant structure. Plant organogenesis can be seen as the combination of two subprocesses driving the bud population dynamics, branching and differentiation. The generating function of the whole process is shown to be the composition of the generating function associated to the two subprocesses. The modelling of stochastic branching is classical but, to model differentiation, we introduced a new framework based on multivariate phase-type random vectors. By differentiating the generating function of the whole process, we were able to write the recursive relationships for the expectation and the variance of the number of metamers in the plant. These results were published .
Plants as Combinatorial Structures and Development of a Symbolic Method :
A new generalization of these results was also developed, in collaboration with Jean Françon (Univ. Strasbourg), based on the symbolic method of Flajolet . A symbolic method is proposed in to compute the distribution associated to the number of occurences of a specific pattern in a random text generated by a stochastic 0L-system. To that purpose, a semiring structure is set for combinatorial classes composed of weighted words. This algebraic structure relies on new union and concatenation operators which, under some assumptions, are admissible constructions. Decomposing the combinatorial classes of interest by using these binary operators enables the direct translation of specifications into a set of functional equations relating generating functions thanks to transformation rules .
A specific application of this method is the parametric identification of stochastic model of plant development : counting the number of phytomers in trees or observing their ages is not always easy. So the classical methods of parameterization of the stochastic processes of organogenesis based on the observation of the distributions of the number of organs is not always appropriate. The new method allows considering distributions of patterns easier to observe, like the number of apical buds (branch tips) or Y structures (forks).
Tree Crown Analysis :
The method of 'tree crown analysis' developed in UMR Amap by Philippe de Reffye also allows to compute the parameters of the stochastic model of tree development, using the means and the variances of the number of phytomers of the observed branches at the rank K from the top of the stem. The system has been upgraded for variable probabilities and applied to Eucalyptus (cooperation with CAF institute China) and coffee tree (cooperation with IRD). This system has successfully provided the main parameters of the tree development from the analysis of architectural data. It is possible to simulate the tree development in order to obtain random structure or to define an average tree for the branching and death patterns, cf.fig:stochPdR. The parameters of the tree development are essential to assess the plant demand made of the sum of all the sink organs. An article has been submitted on the results obtain in China (CAF) on the Eucalyptus tree development. A genetic study of the variability of the Coffee tree development among different species (Arabica, robusta, racemosa) is carrying on in the PHD of Akafou (IRD).
A new type of target for trees :
Computing the sources and sinks parameters needs to adapt the Data measured from Tree to the stochastic case. The notions of physiological age and common pool of biomass allow to arrange the data in a very efficient way, quite disconnected from the topological structure. Considering the alive branches of a given physiological age, all the phytomers situated at the rank K from the top of the branch are identical. This is a consequence of the common pool of biomass. So an average branch can be constructed from data for each physiological age. The plant development gives the number of phytomers corresponding to a given rank. As it is its simplify a lot the way to fit the plant architecture as it was used in GreenLab. More over the method can be extended to the stochastic case. But the age of the phytomer of the rank K is no more K, but follows a binomial negative distribution K,b where b is the growth probability of the meristem. Then fitting the sources and sinks parameters follows the same way than in the deterministic case.
Estimation of GreenLab parameters in the frame of Hidden Models :
Instead of considering the state variables as the
vector of organ masses varying with time, the observed
organ masses are organized into ordered sequences, in which
the ordering is taken with respect to the growth cycle of
organ appearance. Such sequences lead to an equivalent
description of the dynamic system in the framework of
hidden (latent variable) models (
cf.): model equations can be
interpreted as a bidimensional stochastic process, which
describes the evolution of system variables. More
precisely, let
be the sequence of observed organ biomasses, ordered
as described above with
nthe growth cycle of appearance. Each
Ynis generally a multidimensional vector, that can be
divided into subvectors
Yo,
n, each one corresponding to a different type of
organ. Let also
be the sequence of successively produced biomasses
Qn, at each growth cycle
n, where
Q0corresponds to the seed mass.
Qnis considered to be distributed to the different
organs at cycle
n+ 1. The following assumptions
describe generally the representation of the model in this
framework, and the dependence relations among system
variables: Therefore, simulation based methods are in
progress in order to implement proper stochastic versions
of the EM algorithm and stochastic gradient methods for
state and parameter estimation. In this direction, the
class of sequential Monte-Carlo (or particle filter)
algorithms, which can be used for maximum likelihood
estimation (see
), seems particularly adapted
to our case. When the complete likelihood function belongs
to the exponential family, the EM algorithm is usually well
suited and a set of sufficient statistics simplifies the
maximization step. In our case, the model parameterization
makes the maximization step more complicated, and thus
stochastic gradient as well as stochastic EM algorithms
will be developed and compared.
Bayesian Estimation of GreenLab parameters for stochastic models of plant growth :
When organogenesis is stochastic, we propose a new mathematical descriptions of FSPM (and GreenLab in particular) with stochastic organogenesis in the frame of Jump Markov Systems We can then and to apply bayesian estimation methods adapted to this frame, namely Rao-Blackwell Particle Filtering and Convolution Particle Filter to estimate the functional parameters of the model.
Process Based Models (PBM) in agronomy work at the level
of the
m2. They assess the production of a population of
plants without consideration about the plant density and
the individual plant. The inputs are the Leaf Area Index
(LAI) , the daily environmental parameters (radiation,
temperature, irrigation), the harvest index (proportion of
the biomass going to the yield) and the outputs is the
cumulated biomass produced by the photosynthesis and the
the yield. We have chosen to use Pilote, that is the PBM
developed by CEMAGREF. As GreenLab model works like a PBM
at the plant level for biomass production, using a
individual and optimized LAI. It is interesting to compare
the performance of GreenLab model and Pilote on the same
Data coming from field. This is the subject of the PhD of
Feng Lu at Cirad.
At the field level there are two sources of variation
that are mixed up if only the yield/
m2and the LAI is considered. First one is the variable
delay of germination. So the development of the plants
follows a distribution according to the time. This makes a
mixture of plant growths. Second one is that the
competition for space is not homogeneous. So the there is a
distribution of the plant weights.
By inverse method we can match the LAIs and the Biomass
productions produced by both models by optimizing the law
of delay of the germination, see Figure
. In another hand using
"differential statistics" we can assess the variance of the
parameter
Spthat optimized the LAI/plant in order to fit the
variability of weights between plants. Results were
successful and GreenLab model can simulate a field of Maize
that integrates the plant growth and development
variability and provide the same prediction that Pilote.
Thus GreenLab model could be an interesting extension of
PBMs to go further in the study of the components of the
yield.
In order to make the model more robust and suitable for applications, it is necessary to master its uncertainty. For this purpose, mathematical studies on model structure and parameterization are carried out. It concerns Qiongli Wu's PhD with PH Cournède.
It first involves a proper parameter sensitivity analysis of the model, in order to assess the importance of each parameter and their potential source of uncertainty . Sobol's method is used. The complexity of the functional structural model and of the number of parameters involved led us to develop new powerful computing techniques based on an efficient use of model evaluation to compute variance decomposition. Moreover, an estimation of the error of computation (as a function of the number of samples or model evaluations) was computed. The results are submitted to J of Rel. Eng. and Sys. Safety for publication.
Moreover, the method was tested on a wide variety of functional-structural plant models, in order to set in place a specific methodology adapted to this type of models : GreenLab model of maize and sugar beet growth, GL3 model of tree growth (characterized by strong interactions between functioning and architectural development) and finally the NEMA model of Nitrogen and Carbon budget in plant growth, a complex ecophysiological model involving more than 80 parameters.
To model plant-environment interactions, the synchronization of the plant growth model with biophysical models has revealed limitations of the discrete formulation of the GreenLab model at the growth cycle step. Therefore, a continuous approach to model functional-structural plant growth was developed by V. Le Chevalier and Z. Li, based on the discrete GreenLab model. The continuous dynamics is driven by a system of differential equations with respect to calendar time, with a continuous mechanism of senescence introducing delay terms. A numerical scheme for solving the system was developed. It was tested on the model of sugar beet growth, to compare different approximation methods including the classical discrete model. With a higher precision, the simulation based on the continuous approach reveals significant differences with the discrete model. Moreover, an approximation of the continuous model is derived with a daily time step, which makes it suitable for agronomy applications .
The coupling of this continuous model with the Pilote model of soil water budget ( ) was achieved in collaboration with Jean-Claude Mailhol (Cemagref, UMR G-EAU, Montpellier), and likewise a numerical scheme was derived. This work is submitted for publication.
The next step of this study concerns the implementation of optimal control techniques to optimize irrigation strategy. Previous studies have been achieved in the GreenLab context, based on a variational formulations. However the non-convexity of the problem forced the use of heuristic methods (genetic algorithms) to solve a simplified version of the problem (parametric function of water supply). The method implemented is the iterative dynamic programming, which both allows to handle the non-convexity and, more efficiently than what was done previously, the time-delay system.
The post-doc of Jessica Bertheloot helped develop a model integrating fully both Carbon and Nitrogen metabolisms , in collaboration with Bruno Andrieu (INRA, UMR EGC). Different sub-modules are defined: organogenesis, senescence, photosynthesis, Carbon distribution, Nitrogen acquistion, Nitrogen fluxes, with strong interactions between these modules. The parameterization of the model is difficult. The first evaluations of the model was conducted for wheat. Global sensitivity analysis was conducted in order to deduce the most important parameters. Experimental results were then used to estimate these parameters.
Another study is to represent 3D landscapes from the outputs of the classical Process Based Models (PBM) used to compute yield of crops in agronomy and from the outputs of Empirical Forestry Models (EFM) used to assess wood quality and quantity in forestry. The data provided by these models are uncomplete, but it is possible to add a relevant botanical knowledge, coming from similar plants previously studied. For instance PBMs provide only dry biomass, LAI, harvest index, and EFMs provides only lengths, diameters and branch numbers on the trunk. Adding GreenLab knowledge about plant functioning and plant architecture allows to reconstruct 3D representations faithful to plants and thus to visualize a field, which is a first step towards "functional landscapes". PBMs and EFMs are numerous so it could be a chance for the GreenLab model to be widely used in Agronomy. This is the PhD subject of Feng Lu cosupervised by Digiplante and the Chinese University of Agriculture. The PBMs and EFMs used come from Cemagref (Pilote), Inra (Stics), Wageningen (Tomsim), CAF (Simtree).
An important component of the yield that was not taken in account until now in GreenLab model is the production of seeds. Cirad working on tropical trees (Palm tree, Cocoa tree, Coffee tree) has developed previously such model to simulate the seed production from the ovules distribution in the flowers, the distribution of pollen seeds, and the abortion laws of seeds and pods. Few parameters calibrated from the measurements on flowers and fruits control quite well the seeds distribution in the pods. This allows separating the environment effect (weak pollination) from genetic effects (ovule fertility). Such issue occurs also on temperate crops such as rapeseed. A PhD Wang Xiujuan coming from CAU and cosupervised by Digiplante, Inra EGC, and CAU adapted the model to rapeseed. A statistical analysis of data collected in 2008 and 2009 in Grignon was conducted. Different versions of the model were compared. 2 articles were submitted.
Since 2009, activities hold in cooperation with LIAMA in Computer Graphics areas move its gravity center from LoD model developments to 3D reconstructions from laser scans. do increase as well as studies involving GPU and Web visualization. At Cirad, specific new trends are also explored, involving high level structural and functional data.
Level of Detail single plant models, is considered as a closed research topic at this stage. However, engineering valorisation is still operative. French and Chinese plant growth simulator 3D ouput (line trees) were normalized and can be visualized with the same tools. The graphical tool "LIGDRAW" dedicated to single tree visualization and graphical material property definitions, designed by M. Jaeger includes new animation output facilities, and plug-ins implementing several LoD approaches. allowing conversions of line-trees to LOD models (branches only so far). The tool is used at ECP and LIAMA, and at Cirad was used to define several animations presented at "Arbre, regard croisés" exhibition (September 2010, Jardin du Luxembourg, Paris).
This topic has shown significant progress at LIAMA. In the collaboration with DigiPlante, the work mainly adresses reconstruction from 3D laser scans on urban vegetalized scenes and forest scenes. Significant progress were gained on point cloud segmentation, using combinations of three different criteria: distance, local normals, local curvatures on practical complex data set of forest. In this term, INRA Lerfob provided numerous complex acquisition of forests. Specific developments were hold on fast automated tree trunk detection. The scan set is divided into a lower part the detection is performed on, and an upper one, mainly containing branches and crown points. After trunk detections, the lower trunk parts are used to refine the terrain surface. trunk direction are then used to assign crowns points at the various trunks. The approach seems efficient and fast, tested on several heterogeneous forest scans coming from France (in the frame of the ANR EMERGE project) and China (publication at VRCAI) . The proposed algorithms may thus show interest in the forestry community, and quantitative aspects are now to be studied such as automated trunk diameters and volume estimations.
In the late 2009 months we show that internal simulation structures allowing stop and go actions, representing the simulated plant with a flat metamer graph and its functional properties (leaf volume, metamer volume, pith volume) can be used to generate the plant geometry. First tries were hold on this point, defining metamer lengths and diameters from production. With simple angle rules, and allometry rules, we have shown that we could easily generate 3D outputs from this very compact internal data structure. In 2010, significant new results were gained using this approach. We first demonstrated that a simple topological metamer graph avoiding substructure redundancies reduces drastically the topology encoding complexity. This encoding was shown being efficient on GreenLab dual scale automaton and also on other structural models such as L-systems. Second we show that this approach can be used to generate past geometrical reconstruction. We demonstrated that the tree graph is thus an interesting new approach to reconstruct a wide range of plant geometries from a single simulation (MCCSIS in Freiburg - Germany in July 2010).
After exploring the potential of rule based Web visualizations , this new tree graph structure applications for graphics becomes an interesting basis for further research developments related to plant plasticity as underlined in M. Jaeger recent Habilitation à diriger des recherches .
The team and associated team was invited to publish an extended paper on tree structure extractions form voxel shapes, on the basis of the publication to journal IJVR . This collaborative work on voxel image tree data hierarchical segmentation was recently edited soon as a book chapter in Pattern Recognition . Past volume imaging applications led this year again to a publication. In cooperation with CAU, we developed an application on serial colored wheat root microscopic images. Those images are aligned in order to build an image volume set. Images are segmented and vessels extracted. Statistical analysis is done on these vessel and 3D Vrml models are built. The techniques applied on several data sets on the root tip to top allows then biologist to study and interpret vessel structure changes and development. A first paper is published in PMA09 , an another one more detail was submitted end 2010 to Annals of Botany.
Running contracts
- 2007-2011: ANR project (07-CIS) 3Worlds project linking INRIA-DigiPlante with ENS, CNRS, IRD (Geodes), IFI Hanoi, Australian National University. Co-ordinator: ENS
- 2008-2012: ANR Bioenergy EMERGE (involved M. Jaeger)
- 2006-2010: ARCUS Languedoc Roussillon ChongMing Project (involved M. Jaeger)
- 2009-2010: RTRA-INRIA integrative landscape modeling (Co-ordinator M. Jaeger, involved V. le Chevalier)
- 2009-2010: RTRA-INRIA plateforms for landscape modeling (involved M. Jaeger, V. le Chevalier)
- 2010-2012: CANTIA project (pôle de compétitivité Industrie Agro-Ressources): developing models and methods for decision-aid in agriculture (project leader: S2BVisio)
- 2009-2010: RTRA-INRIA Regional network to promote virtual reality tools for landscape applications
- 2010-2011: Project INRA-INRIA with UMR EGC (Grignon): modeling of rapeseed growth
Beside conference attendance, several international visits have been done by Digiplante researchers for scientific collaboration:
P. de Reffye in China (2 months, LIAMA, CAU, CAF, Hanzhou) and Canada (2 weeks, Institute of Botany and Uqam University)
V. Letort in China (1 month, LIAMA, CAU, CAF) and USA (1 week, Univ. of Columbus)
PH Cournède in China (2 weeks, LIAMA, BUAA, CAF)
Pr. Zhang Bao Gui (China Agriculture University) (1 month at Centrale, July 2010, Digiteo Fundings)
Kang Meng Zhen (LIAMA) (1 month at Centrale, July 2010, Digiteo Fundings)
Katarina Smolenova (Univ. Goettingen) (1 month at Centrale, October 2010)
Rodrigue Perleau (UC Louvain) (1 week at Centrale, October 2010)
Sun Ruoxi, 10 weeks, 1 stay in CIRAD-AMAP (Arcus ChongMing Project), March-May, Master 2 student from Graphics and image Research Center at Tongji University, in China.
Zhang Xiaopeng, 1 month, 1 stay in CIRAD-AMAP (ANR EMERGE Project), August-September, Professor at Liama-Casia in China
Li HongJun, 1 month, 1 stay in CIRAD-AMAP (ANR EMERGE Project), August-September, Doctorate student at Liama-Casia in China
Zhang YiKan, 1 month, 1 stay in CIRAD-AMAP (ANR EMERGE Project), June, Associate Professor at Liama-Casia in China
Hua Jin, 1 month, 1 stay in CIRAD-AMAP (GreenLab associate team Project), June, Doctorate student at Liama-Casia in China
Hu Baogang, 1 week, 1 stay in CIRAD-AMAP (for M. Jaeger HdR), December, Professor at Liama-Casia in China
Benedicte Wenden (UK) (2 weeks at CIRAD-AMAP)
Elodie Vavitsara (Madagascar) (3 months at CIRAD-AMAP)
Hery Ranarijaona (Madagascar) (3 months at CIRAD-AMAP)
Doffou Akafou (Ivory Coast) (3 months at CIRAD-AMAP)
M. Jaeger co-chaired the LANDMOD2010 Conference (February 3-5, Montpellier)
M. Jaeger is main board and scientific
editor of 3rd international Symposium of Plant Growth
Modelling, Simulation, Visualisation and Applications
(PMA09), help in Beijing November 9-13, 2009, Beijing,
China.
http://
M. Jaeger gave an invited talk at 92th congress of Morphologist association, University of Medecine of Montpellier, March 11-13, 2010
PH Cournède and V Letort teach at Centrale Paris in applied mathematics and bio-mathematics for their services as Professor and Associate Professor.