Hovens, H.L.E.

Polder, G.

Zweers, A.J.

English

Name not available

Measuring shoot length of submerged aquatic plants using graph analysis

Wageningen Yield 

Measuring shoot length of submerged aquatic plants using
graph analysis
G. Poldera, H.L.E. Hovensb and A.J. Zweersc
aBiometris, Wageningen University, PO Box 100, 6700 AC, Wageningen, The Netherlands;
bEindhoven University of Technology, Eindhoven, The Netherlands;
cAlterra, Wageningen University, PO Box 47, 6700 AA, Wageningen, The Netherlands
Reprinted from:
Proceedings of the ImageJ User and Developer Conference
2010
27-29 October 2010, Luxembourg
edited by
Centre de Recherche Public Henri Tudor
Andreas Jahnen, Christian Moll
29, Avenue John F. Kennedy
L-1855 Luxembourg
ISBN: 2-919941-11-9
EAN: 978291994117
Measuring shoot length of submerged aquatic plants using
graph analysis
G. Poldera, H.L.E. Hovensb and A.J. Zweersc
aBiometris, Wageningen University, PO Box 100, 6700 AC, Wageningen, The Netherlands;
bEindhoven University of Technology, Eindhoven, The Netherlands;
cAlterra, Wageningen University, PO Box 47, 6700 AA, Wageningen, The Netherlands
ABSTRACT
The fate of herbicides in experimental studies can be observed by measuring the total shoot lenght of submerged
aquatic plants, such as M. spicatum and E. canadensis. Manual measurement of the shoot lengths takes a lot
of time and is difficult to trace. An ImageJ application has been developed to measure the individual shoot
length of the plants taken by a digital picture. After thresholding the picture, the binary image is transferred
to a skeleton and the skeleton to a weighted graph using the ImageJ plug-in Analyze-Skeleton. The nodes in
the graph are the junction pixels and the edges are the slab pixels. The weight of the edges corresponds with
their length. In computer science, the FloydWarshall algorithm is a graph analysis algorithm for finding shortest
paths in a weighted graph. A single execution of the algorithm will find the lengths (summed weights) of the
shortest paths between all pairs of nodes. The longest length can be considered as a good estimation of the
total length of the plant. The warshall algorithm was implemented in the Analyze-Skeleton plugin and used to
measure the length of a large number of plants of both specimens. The lengths measured this way were compared
with manual measurements. The R2 was 0.94 for E. canadensis and 0.91 for M. spicatum. From those high R2
values we can conclude that the algorithm works very well.
Keywords: plants, shoot length, skeleton, pruning, nodes, edges, Floyd-Warshall, shortest path.
1. INTRODUCTION
In aquatic risk assessment procedures for herbicides within the context of EU Regulation 1109/2009/EC, tests
with rooted submerged macrophytes may be required. The ecotoxicological impact of herbicides in experimental
studies can be observed by measuring concentration-response relationships for the endpoint total shoot length of
submerged aquatic plants, such as Myriophyllum spicatum L. (Eurasian Watermilfoil) (Figure 1(a)) and Elodea
canadensis (American Waterweed)(Figure 1(b)), as recommended by the HARAP workshop.1
Traditionally these lengths are measured manually, but this takes a lot of time and is difficult to trace. Auto-
matic measurements using a digital photograph and ImageJ was researched. In first instance after thresholding
the image lengths were measured with standard measures from ’Analyze Particles’. Unfortunately none of those
measures gave good correlation with the manual measures. Therefore a new approach was developed using the
skeleton of the binary objects.
2. EXPERIMENTAL SETUP
After harvesting, the plants are cut in pieces and placed on a back illumination table. In order to be able to
measure the plant color accurately also front illumination was used. The object was coded with a QR-Code
placed on the table and a calibration disk with a fixed size of 50 mm diameter (figure 1). Images are recorded
with a Nikon D90 Camera equipped with a Nikon AF-S DX NIKKOR 16-85mm objective lens. Before recording
the images the total shoot length was measured manually. One to three images were needed per plant to hold
all the pieces. The images were analyzed using the procedure described in section 3. Finally the manual and
automated measurements were compared.
Further author information: (Send correspondence to G. Polder)
G. Polder: E-mail: gerrit.polder@wur.nl, Telephone: +31 317 480751
172
(a) M. spicatum
(b) E. canadensis
Figure 1. Example image of M. spicatum (a) and E. canadensis (b). The upper-left corners shows the QR-Coded object
information along with a calibration disk.
173
(a) Color (b) Binary (c) Skeleton (d) Tagged (e) Longest shortest
path
Figure 2. Processing steps for a piece of E. canadensis. An color image (a) is thresholded to a binary image (b). From
the binary image a skeleton (c) is calculated. The skeleton is tagged (d) and the longest shortest path (e) is calculated.
3. PROCEDURE
3.1 Skeleton
In binary image processing repeatably removing pixels from the edges of objects, while keeping the connectivity
of the object intact, results in single pixel wide skeletons. These skeletons can be used to measure shape
parameters. Van Eck et. al. (1998)2 used the skeleton for measuring the length of cucumber fruits. This was
easily accomplished since cucumber fruits are smooth objects and the constructed skeleton did not have any
side branches. In our case the plants have lots of leaves and side branches which results in a very complicated
skeleton. Figure 2 shows the steps which were carried out on a small example image of E. canadensis. First a
fixed threshold was applied on the color image 2(a) resulting in a binary image (2(b)). Figure 2(c) shows the
skeleton of the binary image. Thresholding and skeletonizing were applied using standard ImageJ functions.
Using the Analyze Skeleton plugin3 the skeleton is annotated. This plugin tags all pixels in the skeleton
image and then counts all its junctions, triple and quadruple points and branches, and measures their average
and maximum length. Although the plugin is suitable to annotate 3D skeletons (26-connected pixels) in our case
it is used in 2D only.
The pixels are classified into three different categories depending on their 8 neighbors:
• End-point pixels: if they have less than 2 neighbors.
• Junction pixels: if they have more than 2 neighbors.
• Slab pixels: if they have exactly 2 neighbors.
174
Figure 3. Tagged skeleton, zoomed into top portion of figure 2(e).
Figure 2(d) shows the result. The end-point pixels are colored yellow, the junction pixels purple and the slab
pixels cyan.
3.2 Longest shortest path
The tagged skeleton can be described as an undirected and weighted graph. The nodes are the end-point and
junction pixels, the weighted edges are the summed euclidian distances between every slab pixel and its neighbor
in the edge. From graph theory it is known that there always is a shortest path between two nodes of a connected
graph. So, in a graph there always exists a longest, shortest path, which is the best approximation for the plant
length in our case. Dijkstra’s algorithm, conceived by Dutch computer scientist Edsger Dijkstra in 1956 and
published in 19594 is a well known graph search algorithm that solves the single-source shortest path problem for
a graph with nonnegative edge path costs, producing a shortest path tree. The Floyd–Warshall algorithm5 is a
graph analysis algorithm for finding shortest paths in a weighted graph (with positive or negative edge weights).
A single execution of the algorithm will find the lengths (summed weights) of the shortest paths between all pairs
of nodes though it does not return details of the paths themselves. The algorithm uses an adjacency matrix to
determine the shortest path from every node to every other node. Initially this adjacency matrix contains the
weight of the edge from node i to node j which respectively correspond to the row and column of the matrix, if
there is no edge from i to j the weight is set to infinity. During these iterations the algorithm will check if there
exists a shorter path between nodes. If this is the case it replaces the old value in the matrix with the new. In
this way, after (n)3 iterations we get all the shortest paths, where n is the number of nodes.
The Warshall algorithm was implemented in the AnalyzeSkeleton plugin. The maximum length of all shortest
paths was used as output of the algorithm.
The Warshall algorithm does not return details about the paths, but in order to be able to verify the results
it is nice when the shortest path is visualized. Therefore we reconstructed the found shortest path using the
predecessor matrix which is computed at the same time as the adjacency matrix. In the predecessor matrix all
the shortest paths going from node i to any other node are coded in row i. The column j then contains the
predecessor node (hence the name) in the shortest path going from i to j. In this way we can reconstruct the
longest path as drawn in the final image (figure 2(e)). In figure 3 we zoomed in on the upper part of figure 2(e).
The longest shortest path is colored green.
4. RESULTS AND CONCLUSION
In order to test our approach the longest shortest path shoot lengths of 60 E. canadensis and 66 M. spicatum
plants were compared with manual measurements. Figure 4(a) shows the manual measured versus automated
measured shoot length of M. spicatum. The R2 is 0.91 The results for E. canadensis are depicted in figure 4(b),
with a R2 of 0.94. From those high R2 values we can conclude that the algorithm works very well.
175
1000 2000 3000 4000 5000 6000 7000 8000 9000
1000
2000
3000
4000
5000
6000
7000
8000
9000
Manual length measure [mm]
S
h
o
rt
e
s
t 
p
a
th
 m
e
a
s
u
re
 [
m
m
]
M. spicatum
(a)
0 0.5 1 1.5 2 2.5 3
x 10
4
0
0.5
1
1.5
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2.5
3
x 10
4
Manual length measure [mm]
S
h
o
rt
e
s
t 
p
a
th
 m
e
a
s
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 [
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m
]
E. canadensis
(b)
Figure 4. Manual measured versus automated measured shoot length for M. spicatum (a) and E. canadensis (b).
176
M. spicatum shows one outlier which is possibly caused by a lost plant piece or segmentation error in case
the plant touches the border of the image.
The total shoot length per plant is calculated by summing of the shoot lengths of all plant pieces in all
images which were analyzed per plant. For each small piece a longest shortest path is determined. If there is a
systematic error in the calculated length, this error will contribute more to the total error when the plant is cut
in a large number of small pieces. Therefore it is advised to keep the plant pieces as long as possible.
The proposed procedure is a cost-effective approach to study concentration-response relationships of herbi-
cides (and other relevant pesticides) on shoot length growth of submerged rooted macrophytes, as required in
the test procedures underlying EU Regulation 1109/2009/EC.
REFERENCES
[1] Maltby, L., Arnold, D., Arts, G., Davies, J., Heimbach, F., Pickl, C., and Poulsen, V., [Aquatic Macrophyte
Risk Assessment for Pesticides. ], SETAC Press & CRC Press, Taylor and Francis Group, Boca Raton,
London, New York. (2010).
[2] van Eck, J. W., van der Heijden, G. W. A. M., and Polder, G., “Accurate measurement of size and shape of
cucumber fruits with image analysis,” J Agr Eng Res 70, 335–343 (Jan 1998).
[3] Arganda-Carreras, I., “Analyzeskeleton [imagej documentation wiki].” http://imagejdocu.tudor.lu/
doku.php?id=plugin:analysis:analyzeskeleton:start (Aug. 2010).
[4] Dijkstra, E. W., “A note on two problems in connexion with graphs,” Numerische mathematik 1(1), 269–271
(1959).
[5] Wikipedia, “Floydwarshall algorithm - wikipedia, the free encyclopedia.” http://en.wikipedia.org/wiki/
FloydWarshall_algorithm (Aug. 2010).
177


A note on two problems in connexion with graphs,”

Accurate measurement of size and shape of cucumber fruits with image analysis,”

Analyzeskeleton [imagej documentation wiki].” http://imagejdocu.tudor.lu/ doku.php?id=plugin:analysis:analyzeskeleton:start

Aquatic Macrophyte Risk Assessment for Pesticides.

Floydwarshall algorithm - wikipedia, the free encyclopedia.” http://en.wikipedia.org/wiki/ FloydWarshall_algorithm

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Measuring shoot length of submerged aquatic plants using graph analysis

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