Fully Automated Quantification of Leaf Venation
Structure
J. Mounsef1, and L. Karam2
School of Electrical, Computer & Energy Engineering, Arizona State University, Tempe, Arizona, USA
2
School of Electrical, Computer & Energy Engineering, Arizona State University, Tempe, Arizona, USA
1
Abstract - Recently, there has been a surge of
diverse approaches to investigate leaf vein patterning,
covering genetic analyses, pharmacological approaches and
theoretical modeling. Genetic and pharmacological
approaches remain at this stage insufficient for analyzing the
formation of vascular patterns since the molecular
mechanisms involved are still unclear. Similarly, theoretical
models are not sufficiently constrained, and thus difficult to
validate or disprove. Only few exceptions attempted to
provide a link between experimental and theoretical studies
by implementing different imaging techniques. Visual
imaging methods have been lately extensively used in
applications that are targeted to understand and analyze
physical biological patterns, specifically to classify different
leaf species and quantify leaf venation patterns. There is a
rich literature on imaging applications in the above field and
various techniques have been developed. However, current
methods that aimed to provide high precision results, failed
to avoid manual intervention and user assistance for the
developed software tools. In this paper, we introduce a fully
automated imaging approach for extracting spatial vein
pattern data from leaf images, such as vein densities but also
vein reticulation (loops) sizes and shapes. We applied this
method to quantify leaf venation patterns of the first rosette
leaf of Arabidopsis thaliana throughout a series of
developmental stages. In particular, we characterized the
size and shape of vein network reticulations, which enlarge
and get split by new veins as a leaf develops. For this
purpose, the approach uses imaging techniques in a fully
automatic way that enables the user to batch process a high
throughput of data without any manual intervention, yet
giving highly accurate results.
Keywords: fully automation; leaf venation pattern; feature
extraction; feature quantification; adaptive thresholding
1
Introduction
Over the past few years, there has been a resurgence of
interest in the leaf vein patterning. Traditional strategies
include genetic analyses, pharmacological approaches, and
theoretical modeling. Most recently, quantitative studies
attempted to provide a link between theoretical and
experimental methods. Many quantitative studies of leaf
venations patterns have resurged with the sole aim of
quantifying the response of plants to changing environments
and to breed plants that can respond to such changes.
Unfortunately, most of the suggested empirical analyses have
failed to provide a quantitative study of the complete leaf
vascular network [1],[2]. One major recent approach
successfully provided a quantitative study of the complete leaf
venation network [3]. The aforementioned approach proposed
to quantify vein patterns spatially at the tissue level
throughout leaf development. The venation forms a complex
network composed of veins of different orders within the leaf
tissue. Higher-order veins differentiate within loops that
enlarge with the leaf growth. Therefore, quantifying vein
patterns spatially at the tissue level in terms of loop shapes
and sizes, in addition to vein densities, has brought new
insights into patterning mechanisms. It has provided the
necessary spatial resolution that was lacking in traditional
methods. The procedure developed to extract venation
patterns from leaf images consisted of measuring the leaf
vascular network parameters by digitizing the vein segments
using a user interface: points along each segment were
recorded manually leading to a matrix representing all vein
segments on the leaf. From the extracted series of vein
segments, the topology of the network was calculated
allowing the identification of each vein segment and loop.
The number and position of branching points and free ending
points were also recorded. Finally, the complete venation
pattern and leaf outline for each sample was stored in matrix
form. Such an approach proved to be efficient on the
resolution side. Nevertheless, it is time consuming and
painstaking especially when the throughput is high. The
approach [3] tried to solve this issue by automatically
digitizing veins using unpublished software. Nevertheless,
the software was not sufficiently accurate to replace the
manual technique described in [3]. Another recent work
developed a user-assisted software tool (LEAF GUI) that
extracts macroscopic vein structures directly from leaf images
[4]. The software tool takes an image of a leaf and, following
a series of interactive steps to clean up the image, returns
information on the structure of that leaf's vein networks.
Structural measurements include the dimensions, position
and connectivity of all network veins, in addition to the
dimensions, shape and position of all non-vein areas, called
areoles. Although the tool is meant to enable users to
automatically quantify the geometry of entire leaf networks, it
unquestionably needs user assistance and intervention at
several steps of the images preprocessing, and cleaning.
Many fully automated image-based algorithms have been in
vain proposed for analyzing the leaf venation patterns. For
instance, two approaches, one involving scale-space analysis
and another including a combination of edge detectors [5],
have been implemented to assess the digitization results of 5
test leaf images compared to the results of a manual
technique that uses Adobe Photoshop. The main encountered
problems were the presence of too many artefacts in the
resulting processed images due to inappropriate smoothing
and edge detection. Moreover, the scale-space technique was
criticized for it resulted in broken venation structures.
Here, we propose a fully automatic approach based on
the work described in [3]. Our approach is able to quantify
the vein patterns of the first rosette leaf of Arabidopsis
thaliana by processing 135 images provided by [3], without
the need of any user assistance. It also stores the leaf venation
pattern for every sample in a matrix, yet giving the same
spatial accuracy as with the manual method, while
significantly speeding the analysis process. The algorithm is
developed in MATLAB and is based on different imaging
analysis techniques including noise cleaning, adaptive
thresholding, edge detection, and skeletonization.
2
Image analysis and pattern extraction
The image dataset collected for [3] was kindly
provided to us by the authors. The available leaves images
correspond to patterns of differentiated xylem elements.
Fifteen leaves images were captured each day for nine days:
from eight to sixteen days after sowing (DAS). The images
were stored as jpg into 9 different folders corresponding to
each DAS day. However, the algorithm can process any other
image format (tif, gif, png, bmp).
Custom programs were developed to obtain
quantitative pattern data from the first rosette leaf of
Arabidopsis thaliana images using MATLAB. The main
goal of our algorithm was speeding up the process of leaf
venation pattern extraction while keeping the same spatial
accuracy of the manual method [3]. To achieve a practical
method that enables high throughput image analysis, it is
essential to fully automate the software by avoiding any
manual intervention. The main challenge remains the
accuracy of the results without requiring any user assistance.
Our task was made harder with the presence of noisy images
with low contrast and uneven varying illumination resulting
from the fact that the images were captured at different
harvesting times (Fig. 1a). To resolve these issues, we
incorporated different image processing techniques into the
algorithm. The main steps performed by our algorithm are
described as follows for a given input image: (1) Converting
the rgb image into a grayscale image, (2) Performing
homomorphic filtering of grayscale image, (3) Denoising and
enhancing the grayscale image, (4) Removing border, (5)
Thresholding the image, (6) Skeletonizing and processing the
image, and (7) Extracting and quantifying the venation
pattern features. All the steps do not require any user
intervention since they are fully automated. Next we describe
in details the overall process that our algorithm performs to
process a leaf image and measure characteristic features of
the corresponding venation structure.
Step 1: Converting the rgb image into grayscale image
When converting from an rgb image to a grayscale image,
the value of each pixel in the resulting image is a single
sample that only represents the intensity information. The
range of intensities varies from absolute black (0) to absolute
white (255).
Step 2: Homomorphic filtering of the image
To better improve the illumination and contrast of the image,
homomorphic filtering is applied [6]. An image is a function
that is expressed as the product of reflectance and
illumination F(x,y) = I(x,y).R(x,y). In order to separate
reflectance and illumination, the function can be expressed as
a logarithmic function wherein the product of the Fourier
transform can be represented as the sum of the illumination
and reflectance components ln(x,y) = ln(I(x,y)) + ln(R(x,y)).
The Fourier transform of the previous equation is Z(u,v) =
FI(u,v) + FR(u,v). A filter function H(u,v) is applied to the
Fourier transformed signal where
2
2
H(u,v) = (  H   L )[1  e  cD (u , v ) / Do ]   L (1)
The constant c controls the sharpness of the slope of the filter
function as it transitions between  H and  L , D0 is the
cutoff frequency and D(u,v) is the distance between (u,v) and
the frequency origin. H(u,v) is designed such that it tends to
decrease the contribution made by low frequencies
(illumination,γL<1) and amplify the contribution made by
high frequencies (reflectance, γH>1). Next, the resulting
function is inverse Fourier transformed. Finally, the inverse
exponential operation yields an enhanced image.
Step 3: Denoising and enhancing the image
It is essential to attenuate the presence of background
corresponding to the leaf blade and the rest of the image with
respect to the foreground represented by the veins. Therefore,
applying a denoising technique that cleans the background,
which is considered as the unwanted part of the image, is
crucial. A non-orthogonal wavelet denoising technique is
used here [7]. One of its main characteristics is that it
preserves the phase information, which is fundamental to the
human visual perception. Also, this technique is capable of
determining denoising threshold levels automatically.
Nevertheless, the denoising step affects the venation structure
for it attenuates the pixels intensities, including the vein
pixels. Therefore, enhancing the image contrast is mandatory
at this stage of the image processing chain. For this purpose,
histogram equalization is applied, where a gray-level
transform is used to flatten the histogram of the denoised
image. Then, linear contrast stretching is applied to the
enhanced
a. Original Image
b. Grayscale Image
d. Denoised Image
e. Contrast Enhanced Image
c. Homomorphic Transformed Image
f. Contour Eroded Image
final image in code 2
g. Binarized Image
h. Skeletonized Image
i. Final Venation Pattern (Cleaned, Gap Filled
and Pruned Spurs Image)
Figure 1. Arabidopsis leaf harvested at DAS 16: Processed images corresponding to the 7 automated steps of the
leaf image processing
enhanced image where the value in the low end of the
resulting histogram is assigned to extreme black (0) and the
value at the high end to extreme white (1).
Step 4: Removing border
In order to remove the leaf perimeter, we need first to identify
the leaf lamina from the rest of the image. This is achieved
by applying global thresholding where pixels with intensities
above a certain thereshold are set to 1 (leaf pixels) and pixels
with values lower than the threshold are set to 0 (background
pixels). The resulting image shows the entire leaf blade in
white while the remaining image is black. Next, cropping is
applied to the white contour corresponding to the leaf blade
perimeter, by applying morphological erosion that uses a disk
of n pixel diameter as a structural element. Finally, all the
pixels of the eroded white area are preserved in the original
image, while the values of the remaining pixels
corresponding to the black area are set to 0.
Step 5: Thresholding the image
Thresholding is applied to extract the vein segments of the
leaf from the rest of the image. Since leaves harvested on the
same day showed uneven illumination in the same image, it
was difficult to find a standard value for the threshold value
that could be applicable to all images. Thus, adaptive
thresholding is used by automatically calculating the
discriminative threshold from the corresponding image
histogram. The histogram of any leaf image shows three
main gray scale level ranges: a lower one that corresponds to
the background of the image, a middle one that corresponds
to the leaf blade, and a higher one that corresponds to the leaf
veins. Therefore, the higher gray scale level region is of
interest for our thresholding. Since the histogram showed
additional peaks corresponding to the small variations
resulting from high frequency noise, histogram smoothing is
performed by applying a weighted averaging filter that acts as
a low-pass filter for the histogram. As a result, the smoothed
histogram shows three peaks that are separated by two main
valley points. The value of the lowest valley point is
computed by finding the gray scale level that corresponds to
the first local minimum of the histogram function. After
excluding the gray scale level values that are lower than the
computed valley point, the resulting histogram (consisting
now of two peaks) is used to find the optimal threshold
separating the gray level values of the leaf blade from the
gray level values of the leaf veins. Global thresholding using
Otsu’s method [8] is thus applied to the new histogram. The
final thresholded image represents the venation pattern of the
leaf.
Step 6: Skeletonizing and processing the image
Thinning is then performed by skeletonizing the resulting
leaf venation structure. Skeletons represent a powerful tool
for qualitative shape matching as they can effectively
represent both the object shape and its topology. A thinning
process is used in our approach to guarantee the condition of
obtaining one-pixel thick and connected skeletons. If the
skeleton is considered as a connected graph, each vertex can
then be labeled as an end point or a branching point. A pixel
is defined as an end point if it has a single connected pixel
among its 8 neighborhood pixels. A pixel is defined as a
branching point if it has more than two connected pixels
among its 8 neighborhood pixels. A segment connecting two
adjacent vertices is defined as a branch. Skeletonization is
followed by image cleaning, which consists of removing
unwanted connected blogs below a certain size threshold. For
instance, all connected blog regions smaller than 10 pixels
are removed.
In order to reinforce our algorithm as a fully automated
technique, we need to avoid any broken contour that might
result from thresholding and any extraneous spurs that might
occurr after skeletonization. A gap filling function was
developed to join all the disconnected edges that are supposed
to be connected. The function consists of considering all end
points of the skeleton and check if they were connected in the
original image of the leaf before thresholding by calculating
the average intensity of the pixels joining the two end points
in the prethresholded image. If the computed value is lower
than a preset threshold, the two end point pixels are
considered not initially connected and the gap is not filled. If
the computed value is higher than the threshold, then the gap
between the two end point pixels is filled. This step is
followed by cleaning all connected objects that are smaller
than the largest connected object (venation structure). This
guarantees to clean any other concomitant unwanted leaves
or intruders present with the main leaf in the image, which in
turn avoids the time-wasting step of manually removing any
extraneous features.
On the other hand, extraneous spurs are pruned by
considering all branch segments having an end point and a
branching point as its vertices. If the branch segment length
is smaller than a preset threshold, it is removed.
Step 7: Extracting and quantifying the venation pattern
features
Using the known coordinates of the branching points and end
points along each vein segment, we could record segment
parameters. We could also automatically record the number
and position of branching points and free-vein endings.
Loops could also be identified by automatically counting the
number of closed elements. The latter correspond to elements
starting at one node and ending at the same visited node. The
area of the blade is computed by finding the area of the white
blog resulting from the aforementioned Step 4. As for the
length of the venation structure, it is computed by summing
the number of pixels of the final processed skeleton.
3
Results and discussion
Software was developed in the lab to extract venation
patterns from leaf images. Fig. 1 shows the different images
resulting from the processing steps described above. The case
of a leaf harvested at DAS 16 was selected on purpose to
highlight the efficiency of our algorithm when applied to a
complex venation structure. Fig. 2 displays a comparison of
the results between the manual and the proposed techniques.
The first rosette leaves of Arabidopsis from the [3] data set
grew throughout the period analyzed (from 8 to 16 days after
sowing), with a decrease in growth rate after 14 days from
sowing for both non-automated and automated methods (Fig.
2a). The vein density for each leaf was calculated as the total
vein length across the leaf divided by the whole leaf area. The
average leaf vein density is shown in Fig. 2b and shows that
venation decreases over the period analyzed. The vein density
has an obvious decreasing rate starting 12 days after sowing,
which is consistent with the results of the non-automated
approach. The mean loop number per leaf and the mean
segment number per leaf for each day are shown in Figs. 2c,
d. Both techniques showed similar plots where loop numbers
from day 12 till day 16 and segment numbers from day 13 till
day 16 were not significantly different. Free vein ending and
branching point densities were calculated as number of free
vein endings and branching points per unit leaf area (mm-2)
(Figs. 2e,f). Free vein endings showed significant similarities
in mean densities of free vein endings between the plots of
the non-automated and automated methods. Both techniques
showed that free vein ending densities varied considerably
between days. We observed comparable results for the
branching point densities where the observed increase in
branching point densities between day 8 and day 10 in the
automated plot (Fig. 2f) was consistent with the nonautomated results.
d
a
e
b
c
f
Figure 2. Plots of automated and non-automated temporal analysis of veins patterns in first rosette leaf of Arabidopsis.
4
Conclusions
We developed a method to automatically process and
quantify leaf vein patterns using a series of image processing
techniques and applied it to the analysis of vein pattern
formation during leaf development in the first rosette leaf of
Arabidopsis. Our work has the advantage of fully automating
the extraction and analysis of leaf venation patterns without
any user assistance. Therefore, it speeds up the analysis and
allows large scale comparative analyses of vein patterning.
To our knowledge, there is no available software that allows
for an efficient extraction and analysis of the leaf venation
pattern using fully automated programs. Therefore, our
algorithm might be considered a reliable tool that can be used
by plant biologists to assess their manual results rapidly and
under various conditions.
5
Acknowledgments
We would like to thank Prof. Anne-Gaëlle RollandLagan for kindly providing us with the dataset of the
Arabidopsis leaves and for her helpful comments on the draft
of this paper.
6
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