3D RECONSTRUCTION OF PLANT ROOTS FROM MRI IMAGES

Hannes Schulz1, Johannes A. Postma2, Dagmar van Dusschoten2, Hanno Scharr2, and Sven Behnke1

1Computer Science VI: Autonomous Intelligent Systems, University Bonn, Friedrich-Ebert-Allee 144, 53113 Bonn, Germany2IBG-2: Plant Sciences, Forschungszentrum Julich, 52425 Julich, Germany

{schulz, behnke}@ais.uni-bonn.de, {j.postma, d.van.dusschoten, h.scharr}@fz-juelich.de

Keywords: root modeling, plant phenotyping, roots in soil, maize, barley

Abstract: We present a novel method for deriving a structural model of a plant root system from 3D Magnetic ResonanceImaging (MRI) data of soil grown plants. The structural model allows calculation of physiologically relevantparameters. Roughly speaking, MRI images show local water content of the investigated sample. The small,local amounts of water in roots require a relatively high resolution, which results in low SNR images. However,the spatial resolution of the MRI images remains coarse relative to the diameter of typical fine roots, causingmany gaps in the visible root system. To reconstruct the root structure, we propose a three step approach: 1)detect tubular structures, 2) connect all pixels to the base of the root using Dijkstra’s algorithm, and 3) prune thetree using two signal strength related thresholds. Dijkstra’s algorithm determines the shortest path of each voxelto the base of the plant root, weighing the Euclidean distance measure by a multi-scale vesselness measure. Asa result, paths running within good root candidates are preferred over paths in bare soil. We test this methodusing both virtually generated MRI images of Maize and real MRI images of Barley roots. In experiments onsynthetic data, we show limitations of our algorithm with regard to resolution and noise levels. In addition weshow how to use our reconstruction for root phenotyping on real MRI data of Barley roots in soil.

1 Introduction

In this paper, we present a method for deriving a struc-tural model of plant roots from MRI measurementsof roots in soil (cmp. Fig. 1). From this model, wethen derive local root mass and diameter together withsuitable statistics.

Plant roots are ‘the hidden half’ of plants (Waisel etal., 2002) because non-invasive root imaging in naturalsoils is hampered by a wide range of constrictions. Fora full, non-destructive 3D assessment of root structure,topology and growth, only two main techniques arecurrently available, Computer Tomography, using X-Rays or neutron (Ferreira et al., 2010; Nakanishi etal., 2003; Pierret et al., 2003) and Nuclear MagneticResonance Imaging (MRI) (Brown et al., 1990; Jahnkeet al., 2009; Southon and Jones, 1992). Both X-ray CTand MRI are volumetric 3D imaging techniques, whereCT is based on absorption and MRI is an emission-based technique.

For MRI, most signal stems from water in the rootsand to a lesser extend from soil water. Even thoughMRI contrast can be adapted such that discriminationbetween root water and soil water is maximized (seeSec. 3), signal-to-noise ratio (SNR) remains relatively

Figure 1: A simulated maize root MRI image at SNR 150(left) and its true and fitted structure model overlayed, withmissing/additional pieces marked in strong red/blue (right).

In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP), Rome, February 2012

low. In addition, contrast can be enhanced by manip-ulating the soil mixture such that mainly signal fromthe roots is detected.

With the same equipment, MRI measurements canbe done at different spatial resolutions, where lowerresolution results in a significant reduction in mea-surement time. This is relevant for root phenotypingstudies, where larger quantities of plants need to bemeasured repeatedly over a longer period. Thus, oneof our main concerns is in how far a diminishing res-olution and low SNR reduces the accuracy of a rootreconstruction algorithm. For plant root studies, thisalgorithm should produce from the MRI measurementsestimates for local and overall root mass, root length,and diameter. Here, we examine the capability of anovel root reconstruction algorithm to obtain these es-timates at different image resolutions and noise levels.

As root diameters may be of subvoxel size, voxel-wise segmentation would be brittle. We therefore re-construct a structural, i. e. zero-diameter model of theroot system and subsequently derive parameters like lo-cal root mass and diameter, without finding step edgesin the data. To construct the root structure, we firstfind tubular structures on multiple scales. We thendetermine the plant shoot position and connect everyroot candidate element to it by a shortest path algo-rithm. Finally, we prune the graph using two intuitivethresholds, and adjust node positions with subvoxelaccuracy by a mean-shift procedure. For root mass anddiameter estimation, we use the scale value σ givingmaximum response of the Frangi et al. (1998) tubular-ness measure V (σ) (see Eq. 1). Root mass can then bederived by locally summing image intensities within acylinder of the found diameter around the root center.

After reviewing related work, we start by giving ashort overview of the MRI method applied (Sec. 3), fol-lowed by a description of the novel root reconstructionalgorithm (Sec. 4) and how to use the reconstructedroot to derive root statistics (Sec. 5). Experiments inSec. 6 demonstrate the performance of our approach.

2 Related Work

Data similar to ours has been analyzed extensively inthe biomedical literature, e.g. using the multi-scale“vesselness” measure of Frangi et al. (1998). Of manysuggested approaches for finding and detecting vessels,Lo et al. (2010) is most similar to ours. Our approach isless heuristic, however, and uses knowledge of globalconnectedness. While the primary focus of most ap-proaches is visualization, we aim at fully automatedextraction of root statistics, such as length and waterdistribution, to model roots and biological processes

of roots.So far, only few image processing tools are avail-

able for plant root system analysis (Armengaud et al.,2009; Dowdy et al., 1998; Muhlich et al., 2008). Forthese tools, however, roots need to be well visible, e. g.by invasively digging them out, washing, and scanningthem or by cultivating plants in transparent agar (Nagelet al., 2006). Analysis is restricted to 2D data. Largeroot gaps, artifacts due to low SNR, or reconstructionin 3D have not yet been addressed.

Classical, non-invasive image-based root systemanalysis tools in biological studies are e. g. 2D rhi-zotrons (Pierret et al., 2003). 3D MRI has already beenused in root-soil-systems for the analysis of e. g. water-flow (Haber-Pohlmeier et al., 2009). Semi-automatedreconstruction of roots by 3D CT based on a multi-variate grey-scale analysis has recently been shownto work (Tracy et al., 2010). However, to the best ofthe authors knowledge, fully automatic root systemreconstruction in 3D data is new.

3 Imaging Roots in Soil by MRI

MRI is an imaging technique well-known from med-ical imaging and general background information isavailable in textbooks, see e. g. Haacke et al. (1999).The MRI signal is proportional to the proton densityper unit volume, modulated by an NMR relaxation phe-nomenon called T2 relaxation. It causes an exponentialsignal decrease after excitation that can be partiallyrefocused into an echo. Plant root analysis in soil wasso far hampered by a relatively poor contrast betweenroots and surrounding soil water. However, soil wa-ter contribution to the echo signal can be reduced toless than 1%, increasing contrast significantly. This isachieved by mixing small soil particles (a loamy sand)and larger ones and keeping the water saturation ofthe soil at moderate levels. Thus, the soil water T2 (re-laxation time) is only a few milliseconds whereas theroot water T2 is several tens of milliseconds. Using anecho time of 9 ms, the signal amplitude of soil water isdamped severely, whereas the root water signal inten-sity is only mildly affected. Additionally, as magneticparticles disturb MRI signals heavily, such particlesshould be removed from the soil beforehand to assurea high-fidelity 3D image reconstruction.

The MRI experiments were carried out on a verti-cal 4.7 Tesla spectrometer equipped with 300 mT/mgradients and a 100 mm r.f. coil (Varian, USA). 3Dimages were generated using a so-called single echomulti slice (SEMS) sequence, with a field of viewof 100 mm and a slice thickness of 1 mm. A barleyplant was grown in a 420 mm long 90 mm diameter

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Figure 2: Root diameter distribution of the root shown inFigure 1.

PVC tube with a perforated bottom to prevent waterclogging. Measurements where performed about 6weeks after germination. Because the tube is longerthan the homogeneous r.f. field, it was measured infive stages. The resulting image stacks were stitchedtogether without any further corrections. The final192×192×410 volumetric image has a lateral spatialresolution of 0.5 mm and a vertical resolution of 1 mm.

3.1 Synthetic MRI images

Synthetic MRI images were generated using SimRoot,a functional-structural model capable of simulatingthe architecture of plant roots (Postma and Lynch,2011a,b). Virtual root models of 15 day old maizeplants1 were converted into scalar valued images inwhich the pixel value corresponds to the root masswithin the 0.5 mm cubed pixels. Five images weregenerated from five runs, which only varied due tovariation in the model’s random number generators.We added variable amounts of Gaussian noise to theimages at SNRs of 10, 50, 100, 150, 200, and 500.Note that even images with high SNR cannot simplybe thresholded, since roots thinner than a voxel wouldnot be detected anymore. The resolution of the imageswith SNR of 150, i. e. an achievable SNR in real MRIdata, were scaled down in the two horizontal dimen-sion to voxel dimensions of 0.5, 0.67, 1, and 1.3 mm tosee how the resolution of the MRI image might affectthe results. Figure 1, left, shows one of the simulatedmaize root images, and Figure 2 its root diameter dis-tribution. Please note, that as for real roots not alldiameters are populated in the histogram.

1Barley plants are not yet available in SimRoot. 15 dayold maize roots come closest to the barley root data.

4 Reconstruction of Root Structure

We build a structural root model from volumetric MRImeasurements in four main steps. First, we find tubularstructures on multiple scales. Secondly, we determinethe shoot position (the horizontal position of the plantat ground level). Thirdly, we use a shortest path algo-rithm to determine connectivity. Finally, we prune thegraph using two intuitive thresholds.

Finding Tubular Structures We follow the ap-proach proposed by Frangi et al. (1998), which iswidely used in practice. MRI images typically donot contain isotropic voxels. The axes are thereforefirst scaled up using cubic spline interpolation. Theresult L(x) (Fig. 3b) is then convolved with a three-dimensional isotropic derivative of a Gaussian filterG(x,σ). The standard deviation σ determines the scaleof the tubes we are interested in:

∂

∂xL(x,σ) = σ

γL(x)∗ ∂

∂xG(x,σ).

In the factor σγ, introduced by Lindeberg (1996) forfair comparison of scales, γ is set to 0.78 (for a tubularroot model as in Krissian et al. (1998)). Differentiatingagain yields the Hessian matrix Ho(σ) for each pointxo of the image. The local second-order structure cap-tures contrast between inside and outside of tubes atscale σ as well as the tube direction. Let λ1,λ2,λ3(|λ1| ≤ |λ2| ≤ |λ3|) be the eigenvalues of Ho(σ). Fortubular structures in L holds: |λ1| ≈ 0, |λ1| � |λ2|,and |λ2| ≈ |λ3|. The signs and magnitudes of all threeeigenvalues are combined in the medialness measureVo(σ) proposed in Frangi et al. (1998) (Fig. 3c), de-termining how similar the local structure at xo is to atube at scale σ:

Vo(σ) =

0 if λ2 > 0 or λ3 > 0(

1−e−λ2

22α2λ2

3

)︸ ︷︷ ︸

RA

e−λ2

12β2 |λ2λ3 |︸ ︷︷ ︸

RB

(1−e

−∑i λ2i

2c2

)︸ ︷︷ ︸

S

.

Here, RA distinguishes between plate-like and line-like structures, RB is a measure of how similar thelocal structure is to a blob, and S is larger in regionswith more contrast. The relative weight of these termsis controlled by the parameters α and β, which weboth fixed at 0.5. Finally, we combine the responsesof multiple scales by selecting the maximum response

Vo = maxσ∈{σ0,...,σS}

Vo(σ). (1)

where σi = (σS/σ0)i/S ·σ0. For our experiments, we

select σ0 = 0.04mm, σS = 1.25mm, and S = 20.

Finding the shoot position In our model, we utilizethe fact that plant roots have a tree graph structure.The root node of this tree is a point at the base of theplant shoot, which has, due to its high water contentand large diameter, a high intensity in the image. Todetermine the position of the base of the plant shootxr, we find the maximum in the ground plane slice pconvolved with a Gaussian G(x,σ) with large σ,

xr = argmaxx{L(x,σ) |x3 = p} .

Determining connectivity So far, we have a localmeasure of vesselness V at each voxel and an initialroot position xr. What is lacking, is whether two neigh-boring voxels are part of the same root segment andhow root segments are connected. In contrast to somemedical applications, we can use the knowledge ofglobal tree connectedness. For this purpose, we firstdefine a graph on the voxel grid, where the verticesare the voxel centers and edges are inserted betweenall voxels in a 26-neighborhood. We further define anedge cost w for an edge between xs and xt as

w(xs,xt) = exp(−ω(Vs +Vt))

with ω� 0. For each voxel xo, we search for theminimum-cost path to xr. This can efficiently be doneusing the Dijkstra algorithm (Dijkstra, 1959), whichyields a predecessor for each node in the voxel graph,determining the connectivity.

Model construction Every voxel xo is now con-nected to xr, but we already know that not all voxelsare part of the root structure. The voxel graph needsto be pruned to represent only the roots. For this pur-pose, it is sufficient to select leaf node candidates thatexceed the two thresholds explained below. The nodesand edges on the path from leaf node xl to xr in thevoxel graph are then added to the root graph.

In a first step we cut away all voxels from the graphwith L(x)< Lmin, meaning that a leaf node candidateneeds to contain a minimum amount of water.

In a second step, we find leaf nodes of the tree,i. e. root tips. To do so, we search for high values ina median-based ‘upstream/downstream ratio’ D forvoxel xo

Do = medianu∈N+m (xo)

(L(u))/mediand∈N−m (xo)(L(d)),

where neighborhood N−m (xo) denotes the m predeces-sor voxels of x0 with highest V when following thegraph for m steps away from xr (i. e. into the soil),and N+

m (xo) are the m successor voxels with highestV when following the graph for m steps towards xr(i. e. into the root). Thus, Do is approx. 1 for voxelssurrounded by soil and voxels lying in a root since

there, the only variations of L(x) are due to noise. Dois largest and in the range of SNR for voxels indicat-ing a root tip as we encounter ‘signal’ on the one sideof the voxel and ‘noise’ on the other. Thus root tipsare voxels where Do > Dmin, where Dmin is a tuningparameter.

In roots with large diameter, there are still multiplepaths from the outer rim to the root center. In a finalstep, we remove segments which contain a leaf and areshorter than the maximum root radius from the rootgraph. This step is iterated as long as segments can beremoved from the graph.

5 Estimation of Root Parameters

In most biological contexts local and global parametersdescribing the phenotype of a root are needed, e. g. toderive species-specific models of roots. In this section,we show how to derive such parameters supported byour model.

Root lengths To determine the root lengths, high-precision positioning of vertices is essential. So far,vertices are positioned at voxel centers. We now applya mean-shift procedure to move the nodes to the centerof the root with subvoxel precision. At each node n atposition xn, we estimate the inertia tensor in a radiusof 3 mm and determine its eigenvalues λ1 ≤ λ2,≤ λ3as well as corresponding eigenvectors v1,v2,v3. Ifλ3 > 1.5λ2, we assume v3 to correspond to the localroot direction. We then move the node to the meanof a neighborhood in the voxel grid weighted by thevesselness measure V (Eq. 1). To do so, we choose a 4-neighborhood of xn in the plane spanned by v1 and v2,and evaluate V by linear interpolation. Nodes whereno main principal axis can be determined (λ3 < 1.5λ2)are moved to the mean of their immediate neighbors inthe root graph. We iterate these steps until convergence.The resulting structural model is shown in Fig. 3a.Finally, we can determine the total root lengths bysumming over all edge lengths.

Root Radius For estimation of the local root radiusr(x), we use the argument leading to the maximumresponse Vo in Eq. 1

ro = arg maxσ∈{σ0,...,σS}

Vo(σ) (2)

at location xo. The radius assigned to a node is calcu-lated by averaging r in each segment. A root segmentis a list of all vertices connected to each other by ex-actly two connections, meaning they are either endedby a junction or a root tip.

(a) (b) (c) (d) (e)

Figure 3: Root model reconstruction. (a) Raw data, tubeness-measure (Frangi et al., 1998), structural model. Volume renderingof (b) raw data and (c) tubeness-measure. (d) 3D rendering of model, edges weighted by estimated diameter. (e) Cylindricalprojection of model.

Root Mass Root mass is derived by sampling alongsegments in 0.2 mm steps. We mark for each samplinglocation xo all voxels within the local radius ro. Themass of a root segment is the sum of values L of allmarked voxels.

For constant water density ρ in the roots the massof a root slice of length l can be calculated from itsradius and vice versa

mo = ρπr2ol (3)

Thus especially for subvoxel roots mass estimate maybe used as a radius measure.

6 Experiments

6.1 Synthetic Maize Roots

Of the five synthetic root systems, one root systemis set aside to tune the two thresholding parametersfrom Sec. 4 so that they maximize the F0.5 measure(Rijsbergen, 1979)

F0.5 =1.25P ·R

0.25P+R. (4)

with precision P and recall R. Precision P is the frac-tion of true positives in all found positives (true andfalse positives), while recall is the fraction of true pos-itives in all elements that should have been found (truepositives and false negatives). The precision P hasdouble the weight of recall R in the F0.5 measure inorder to reduce the chance of false positives. As aresult the chance of false negatives increases, howeverthis error is relatively small compared to the currentdetection error of fine roots by the MRI.

To determine true/false positives and false nega-tives for precision and recall, we sample synthetic andreconstructed roots in 0.2 mm steps and determine theclosest edge of the respective other model. A ‘match’occurs when this distance is smaller than one voxelsize.

6.2 Sensitivity to Resolution and Noise

For quantitative analysis of our reconstruction algo-rithm, we use synthetic data of maize roots (see Sec. 3).Fig. 4 shows a typical detail view of such data atSNR 150. At this SNR Frangi’s tubularness mea-sure (Eq. (1), Fig. 4b) gives a reasonable indication ofwhere the root is. Figs. 4c, d show the found positions

(a) (b) (c)

(d) (e) (f)

Figure 4: Example of a reconstructed root (detail): false positives, false negatives, and diameter estimates. (a) Raw data at SNR150, (b) tubular structures enhanced using Eqn. (1), (c) extracted structure model before subvoxel positioning, (d) true andfitted structure model overlayed, with missing/additional pieces marked in strong red/blue, (e) diameter estimates, (f) massestimates.

before and after subvoxel positioning. In Fig. 4d wesee that most parts of the root system are correctlydetected, however, at junctions and crossings the algo-rithm sometimes prefers shortcuts over the true rootpath. For root length the effect has not much influence,however branching angles are slightly biased towards90◦. In addition, as short (< 3mm) root elements aresuppressed for the sake of robustness with respect tonoise and uncorrect skeletonization of thick roots, trueshort root elements are non-surprisingly missing.

Diameter and mass of the roots are shown inFig. 4e, f, where in Fig. 4e diameter is estimated fromthe Frangi scales (Eq. 2), and in Fig. 4f diameter is cal-culated from the estimated mass (by inverting Eq. 3).We observe that radius from mass, i. e. from the mea-sured image intensities, is much more reliable than thegeometry-based estimate—especially for smaller roots.However, this is only possible under the assumptionof constant water density in the root, being perfectlytrue for our synthetic data. While for healthy roots thisis also well fulfilled, the radius of drying roots willunavoidably be systematically underestimated by thismethod.

In the next sections we investigate the statisticalproperties of the found root systems with respect toroot length, volume, and diameter.

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Figure 5: Influence of image resolution: fraction of detectedoverall root length versus voxel size, for five individual datasets showing 15 day old maize roots at SNR 150. Matchedlength indicates true positives only, measured length alsoincludes false positives.

6.2.1 Root Length

Data acquisition time for MRI scales with image reso-lution. Therefore, image resolution should be selectedas low as possible with respect to the measurementtask at hand. In order to test sensitivity of our rootreconstruction algorithm with respect to image reso-lution, we calculated root length from the syntheticMRI data (see Sec. 3) with SNR = 150 and varyingimage resolution and compared to the known groundtruth. Fig. 5 shows how detected root length decreases

10 25 50 100 150200 500Signal/Noise Ratio (db)

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Figure 6: Influence of noise: fraction of detected overallroot length versus signal to noise ratio, for five individualdata sets showing 15 day old maize roots at 0.5 mm voxelsize. Matched length indicates true positives only, measuredlength also includes false positives.

with larger voxel sizes. For the highest resolution pro-vided (0.5 mm), 95.5% of the true overall root length isdetected with standard deviation 0.3%, which is wellacceptable for most plant physiological studies. In-creasing voxel size quickly decreases found root lengthto 80% at 1 mm voxel size and to ≈72% at 1.33 mmvoxel size. For larger voxels, false positives have ameasurable influence of about 2%. For highest resolu-tions, false positives have no significant influence. Weconclude, that voxel size should not be greater than0.5 mm.

As with other imaging modes, SNR of MRI dataincreases with acquisition time. Thus, to keep acqui-sition time short, image noise should be selected ashigh as possible with respect to the measurement taskat hand. We calculated root length from the syntheticMRI data (see Sec. 3) with 0.5 mm voxel size and vary-ing noise levels and compared to the known groundtruth (see Fig. 6). For the lowest SNR (10), only 50%of the roots are detected. Detection rate quickly in-creases with increasing SNR and levels off to 95% atan SNR of about 150. At the given resolution, an SNRof 150–200 seems to give the best balance betweendetection accuracy and measuring time.

6.2.2 Root Mass and Diameter

Root biologists commonly divide the root system intodiameter classes. The derived root diameter distribu-tion and the corresponding volume and mass distribu-tions give insight in the soil exploration strategy ofthe plant. In Fig. 7, we show scatter plots (i. e. 2Dhistograms) for true versus measured diameter and vol-ume for SNR 500, 150, and 50. The drawn slope 1line indicates perfect matches. In the high SNR case(Fig.7a) diameters between approx. 1 and 1.6 voxels

(0.5 mm to 0.8 mm) are reliably measured. Diametersbetween 0.5 and 1 voxel are slightly overestimated andsmaller diameters are strongly biased towards 1 voxel(0.5 mm) diameter. For diameters larger than 1.6 vox-els much less root elements are available (cmp. Fig. 2),thus the shown scatter plots are less populated there.We observe however, that diameters are slightly over-estimated there. Comparing Figs. 7a and 7b shows thatfor roots thicker than 1 voxel diameter estimates donot significantly change when increasing noise fromSNR 500 to SNR 150. Subvoxel diameters are morestrongly biased towards 1 voxel, meaning that suchroots are still found reliably but their diameter cannotbe estimated accurately. For SNR 50 overestimationbecomes even stronger and is also well visible for di-ameters up to approx. 0.75 mm. Root mass estimatesand diameters derived from them are much more robust(see Fig. 8). For SNR 500 and 150 almost no differ-ence is visible, while for SNR 50 results are slightlyworse, but still much better than the ones derived viathe Frangi scale σ, even at SNR 500.

6.3 Real MRI Measurements

We calculate statistical properties of barley roots inorder to demonstrate the usefulness of our algorithmon real MRI images of roots. Obviously, there are awealth of possibilities of how statistics on the modeledroot system may be built. In the following, we givetwo examples where1. the plausibility of the results can easily be checked

visually,2. results cannot be achieved from the MRI images

directly, and3. structural information on the roots is needed.

Length Distribution between Furcations Thismeasure cannot be derived from local root information,as connectedness between furcations needs to be en-sured. We define a segment as list of connected edges{ei(ni,ni+1)}, i ∈ {0, . . . ,N} where all intermediatenodes nk, k ∈ 1, . . . ,N−1 have indegree(nk) = 1 andoutdegree(nk) = 1. A segment is horizontal/verticalif the vector nN − n0 draws an angle smaller than45◦ with the horizontal/vertical axis. Here, we findthat horizontal segments have an average length of8.8±7.77 mm, whereas vertical segments have an av-erage length of 5.10±5.20 mm. Segments containinga root tip are excluded in this average. We conclude,that vertical roots have greater branching frequencythan the horizontal (higher order) roots.

Distribution of Mass The MRI voxel grid allows tocalculate the total mass of a plant. Using the model

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(c)Figure 7: Histograms of true versus measured diameter at resolution 0.5 mm and (a) SNR 500, (b) SNR 150, and (b) SNR 50.Diameter was measured using Eq. 2. For matching, each root was sampled in 0.2 mm steps and counted as “matched” if acorresponding line segment in the other root was closer than one voxel size.

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(c)Figure 8: Same as Fig. 7, however with diameter estimated from local mass (cmp. end of Sec. 5).

constructed above, this mass distribution can now beanalyzed in new ways, which may be useful whenbuilding statistical models of root growth. In Fig. 9,we show the distribution of mass under the model (asderived in Sec. 5) as a function of the depth and theroot angle. We distinguish between expected mass ofa root at a certain depth/angle and the total mass at thispoint. The data clearly shows that horizontal roots bindmost water (left), while vertical roots are less abundant,but are expected to be heavier (middle). These resultsagree with current biological understanding of the rootarchitecture of barley plants, which is characterizedby a small number of thick, vertically growing nodalroots and a large number of fine horizontally growinglateral roots, branching off the nodal roots.

6.4 Algorithm Runtime

On the 192×192×410 reference dataset, a complete,partially parallelized run currently takes less than 20minutes on a 12×2.67 GHz core Intel machine. Forthe sake of algorithmic simplicity, the dataset currentlyneeds to provide cubic voxels. Thus, the coarse ver-tical direction is upsampled resulting in a doublingof the number of voxels. Avoiding this and using thespeed up potential through further parallelization ofthe Hessian computation (across multiple computers)and later steps (across multiple cores) may reduce thecomputation time significantly.

7 Summary and Conclusions

In this paper, we showed how to derive a structuralmodel of root systems from 3D MRI measurementsand assign mass and radius to found root segments.

From our experiments on the dependence of foundroot length on image resolution and SNR, we concludethat root system reconstruction strongly depends onresolution, with better detection rates at higher reso-lution. This is in coherence with the naıve expecta-tion. Also sensitivity to noise is as expected. SNRbelow 100 severely effects detection accuracy of rootswith subvoxel diameters. Systematical errors of thederived root structure occur at junctions, where branch-ing angles are biased towards 90◦. A closer analysisof junctions should therefore be investigated in futureresearch. However other measures are already wellapplicable. Especially mass estimation (and radiusestimation when water density in roots is constant)turned out to be robust against SNR reduction, whilegeometry-based diameter estimates from Frangi scalesbecome less and less reliable. For healthy roots, ra-dius from mass is an excellent alternative to geometry-based measures, but in drying roots water density isnonconstant and more sophisticated radius measure-ments should be investigated.

For real data of barley roots we showed, how thederived structural and local quantities can readily beused for plant root phenotyping.

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horizontal verticalangle to vertical (rad)

Expected Mass

horizontal verticalangle to vertical (rad)

π/2 0 π/2 0

Figure 9: Mass distribution in root, w. r. t. depth and rootangle. Darker regions represent more mass. Left: Unnor-malized mass, shows that horizontal roots are prevalent andbind most of the water. Middle: Mass normalized by numberof roots, shows that vertical roots tend to have more massthan horizontal ones. Directly beneath the soil surface, rootstend to have more mass regardless of direction. Bottom plotsdepict the marginal mass distribution of angle. Right: Modelvisualization weighted by estimated mass (cmp. Fig. 3).

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