Analysis of the spatial organisation of maize vascular
bundles
David Legland1 , Marie-Françoise Devaux2 , Fabienne Guillon2
1
INRA Versailles - IJPB
2
INRA Nantes - BIA
SSIAB 2012 - Avignon
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Context: valorisation of agro-resources
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Objectives
Quantify relationships:
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bio-chemical
composition
cellular morphology &
organisation
cell wall degradability
Quantify histology
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Macroscopy imaging
BlueBox imagery
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4000 × 4000 pixels2
Resolution ' 3.6
µm/px
eld of view:
1.5 × 1.5 cm2
Can observe
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cells
vascular bundles
their relative position
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Maize sampling
Sampling:
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2 genotypes
8 stems by genotype
3 slabs by stem
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Image Processing
Vascular bundles segmentation
Contour segmentation and simplication
Results in a bounded point pattern
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Descriptive functions
Ripley's K-function
Pair-correlation function
(PCF)
K (r ) = #{X \x ∩λ b(x , r )}
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g (r ) = K2π(rr )
0
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Group-wise analysis
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Average by group
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Multivariate Analysis of Variance (MANOVA)
computation of p-value for each distance, plot -log(p)
model = genotype + slab + interaction
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Principal Components Analysis of functions
each curve is seen as a
point in R
analysis of variations
around the mean curve
interpret loadings as curve
tendencies
p
f (r ) =f (r )
+ c , · v (r )
+ c , · v (r )
i
0
i
1
1
i
2
2
+...
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Interpretation of eigen vectors
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Testing hypotheses
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Summary
PCA on PCF
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allows groupwise
analysis
synthetic curves
detection of dierences
Limits
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loadings interpretation
non homogeneity
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Density Estimation
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Slab imagery and segmentation
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Slab imagery and segmentation
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Shape analysis on contours
Apply PCA on contours
Reference contour +
eects:
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genotype
slab
stem
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Contour modelling
by genotype
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by slab
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sample stem
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Spatial normalisation
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Projection onto reference slab
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Computation of density maps
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Average densities
Mutant
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All
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WildType
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Perspectives
non-inhomogeneous
estimation of K and PCF
localisation of functions
fusion with other
acquisitions
towards stem modelling...
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Any questions ?
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Synopsis
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