TRiP: Tracking Rhythms in Plants, an automated leaf movement analysis program for circadian period estimation
© Greenham et al.; licensee BioMed Central. 2015
Received: 10 November 2014
Accepted: 12 March 2015
Published: 3 May 2015
A well characterized output of the circadian clock in plants is the daily rhythmic movement of leaves. This process has been used extensively in Arabidopsis to estimate circadian period in natural accessions as well as mutants with known defects in circadian clock function. Current methods for estimating circadian period by leaf movement involve manual steps throughout the analysis and are often limited to analyzing one leaf or cotyledon at a time.
In this study, we describe the development of TRiP (Tracking Rhythms in Plants), a new method for estimating circadian period using a motion estimation algorithm that can be applied to whole plant images. To validate this new method, we apply TRiP to a Recombinant Inbred Line (RIL) population in Arabidopsis using our high-throughput imaging platform. We begin imaging at the cotyledon stage and image through the emergence of true leaves. TRiP successfully tracks the movement of cotyledons and leaves without the need to select individual leaves to be analyzed.
TRiP is a program for analyzing leaf movement by motion estimation that enables high-throughput analysis of large populations of plants. TRiP is also able to analyze plant species with diverse leaf morphologies. We have used TRiP to estimate period for 150 Arabidopsis RILs as well as 5 diverse plant species, highlighting the broad applicability of this new method.
The genomics era is transforming the way we form and test biological questions. With the decreasing cost of Next Generation Sequencing (NGS) technology the use of high-throughput experimentation on large plant populations is possible. This shift towards expanded genetic and phenotypic analysis has led to next generation mapping populations which include Nested Association Mapping (NAM) populations  and Multiparent Advanced Generation Inter-Cross (MAGIC) lines  for enhanced gene mapping and trait discovery. The availability of genome sequencing and the advancements in de novo genome assembly have stimulated research in important crop plants and the development of better model systems for studying biofuel production, photosynthesis, abiotic stress response and the impacts of climate change on yield . Many of the current techniques used for phenotyping are extremely labor intensive and often not feasible for the study of large populations. New methods for high-throughput phenotyping [4,5] are being developed to catch up with the mass of NGS data that is being generated.
It is well established that an output ofv the circadian clock in plants is the daily rhythmic movements of their leaves . This rhythmic movement can be used to estimate the period of the internal clock. To determine the timing of leaf movement, time-lapse photography is used to image every 10-20 min over a window of 5-10 days under constant light conditions. This generates large image series that are then analyzed for rhythmicity by tracking the position of the cotyledons or leaves in each image. Several methods have been developed to perform this analysis; however, they all require user input at several steps during the analysis [7-9]. For example, one commonly used method relies on MetaMorph®; software in combination with the Biological Rhythms Analysis Software System (BRASS), which analyzes individual cotyledon movement and fits period, phase and amplitude data using a Fast Fourier Transform Nonlinear Least Squares (FFT-NLLS) method . The input data for BRASS is generated in MetaMorph®;, or an equivalent image analysis software, and this step is a major bottleneck to the analysis. In MetaMorph®;, the region tool is used to select the region surrounding individual leaves. This region must be drawn large enough to surround the leaf across the image stack as it grows and moves over the course of the time series. The coordinates of the leaf are then recorded across the stack and exported to Excel for analyses with BRASS. The need to process each plant individually makes the analysis of a large population extremely labor intensive and time consuming. Another drawback to using a single cotyledon is that the movement of the cotyledon is dependent on active growth of the petiole and once growth ceases the movement dampens dramatically causing unreliable period detection . A more automated method was used to analyze leaf movement on Brassica oleracea seedlings; however it required glueing polystyrene balls to each cotyledon blade in order to track the movement in MetaMorph®; [10,11]. To overcome these constraints, we have developed a motion estimation algorithm  called Tracking Rhythms in Plants (TRiP) that tracks leaf movement of cotyledons and true leaves simultaneously.
Results and discussion
Period estimation using TRiP to analyze simulated data with different amplitude trends and noise levels
Noise level A 3
Noise level B 3
Noise level C 3
(h; mean ± sd)
(h; mean ± sd)
(h; mean ± sd)
20.00 ± 0.02
19.98 ± 0.06
19.99 ± 0.12
21.04 ± 0.07
21.07 ± 0.09
21.07 ± 0.12
22.08 ± 0.07
22.11 ± 0.09
22.10 ± 0.18
23.08 ± 0.07
23.09 ± 0.07
23.07 ± 0.18
23.99 ± 0.02
24.00 ± 0.04
24.06 ± 0.15
25.05 ± 0.06
25.05 ± 0.11
25.05 ± 0.26
26.09 ± 0.14
26.08 ± 0.24
25.98 ± 0.26
27.11 ± 0.12
27.20 ± 0.12
27.10 ± 0.34
28.13 ± 0.16
28.12 ± 0.22
28.14 ± 0.27
20.00 ± 0.03
20.00 ± 0.12
19.97 ± 0.10
21.06 ± 0.06
21.05 ± 0.09
21.06 ± 0.21
22.08 ± 0.09
22.10 ± 0.07
22.04 ± 0.14
23.08 ± 0.07
23.12 ± 0.12
23.05 ± 0.22
24.00 ± 0.04
23.98 ± 0.09
24.06 ± 0.19
25.07 ± 0.06
25.06 ± 0.13
25.07 ± 0.28
26.15 ± 0.11
26.07 ± 0.09
26.08 ± 0.27
27.16 ± 0.14
27.14 ± 0.14
26.99 ± 0.31
28.17 ± 0.15
28.19 ± 0.20
28.17 ± 0.31
20.00 ± 0.03
20.00 ± 0.07
20.06 ± 0.15
21.07 ± 0.05
21.08 ± 0.14
21.12 ± 0.20
22.09 ± 0.09
22.12 ± 0.09
22.02 ± 0.16
23.08 ± 0.08
23.04 ± 0.12
23.04 ± 0.18
24.00 ± 0.02
23.96 ± 0.12
24.08 ± 0.20
25.07 ± 0.05
25.08 ± 0.15
24.97 ± 0.19
26.18 ± 0.11
26.12 ± 0.19
26.22 ± 0.29
27.15 ± 0.14
27.18 ± 0.14
27.01 ± 0.17
28.18 ± 0.12
28.17 ± 0.17
28.16 ± 0.38
Circadian period of leaf movement on Arabidopsis clock mutants estimated using TRiP
(h; mean ± sem)
24.96 ± 0.15
19.92 ± 0.20
22.39 ± 0.21
23.09 ± 0.15
31.81 ± 0.87
Applying TRiP to an Arabidopsis RIL population
Summary of circadian period QTL detected in Jea x Col-0 RIL population
ELF3, CCR2, XCT, FIO1, LIP1, PHYB, LKP2
Applying TRiP to diverse plant species
Circadian period of cotyledon or leaf movement across diverse plant species
(h; mean ± sd)
23.58 ± 0.76
22.51 ± 0.54
25.67 ± 0.94
24.61 ± 0.25
25.02 ± 0.47
25.76 ± 0.64
The presence of circadian rhythms in plants was first documented in 1729 by the French astronomer Jean Jacques Ortous de Mairan following his observations of the daily leaf movements of the heliotrope plant (Mimosa) that persisted in constant darkness . This innate diurnal periodicity was measured a century later by de Candolle and others and found to be approximately 24 h in length . Darwin characterized and quantified these movements extensively in the 1880s , paving the way for the emergence of circadian biology. The development of transgenic technologies and the use of fluorescent reporter systems have increased the sensitivity and feasibility of more elaborate circadian clock studies in plants, in particular the model plant Arabidopsis [31,32]. However, with the advances in NGS technology and reduction in cost, the field of molecular ecology is transforming. The ability to sequence natural populations facilitates more directed study for evolutionary and ecological questions such as the genetic basis of local adaptation, speciation, species composition and species interactions . To complement these NGS studies, high-throughput phenotyping methods will need to be developed that can be applied to these natural populations. Understanding the genetic contributions to changes in flowering time in response to photoperiod, temperature and precipitation is critical towards expanding the geographical distribution of crops as well as their adaptability to the changing environment [34,35]. The circadian clock is an important integrator of environmental cues that coordinates the physiological response of the plant through a complex genetic network . The ability to asses circadian clock function and variation in these natural populations will lead to significant advances in our understanding of the interactions between the circadian clock and plant fitness. The automated nature of TRiP, as well as its utility on non-model organisms as demonstrated in this study, makes it an excellent platform for addressing these questions.
Material and methods
TRiP is a Matlab-based program. The source code can be run on the open source Octave software with slight modifications outlined in the readme file provided with the TRiP package. The TRiP code has been provided as a supplemental file (Additional file 15) and can also be found on GitHub (http://github.com/KTgreenham/TRiP). The first step of the TRiP analysis is generating individually cropped images of each plant. We have applied a grid-based cropping function that takes each camera image stack as input and crops the images using the grid coordinates given and outputs the cropped image files in a separate directory. We generate the grid coordinates in Matlab of each box drawn around the plant. It is important that the cells are drawn based on the first and last image of the time series to ensure that the entire plant is captured in the crop. Additional notes regarding the grid coordinates can be found in the readme file. Once the grid has been designed, all subsequent experiments can use the same crop function and requires no manual image processing.
Within the Computer Vision and Image Processing communities, differential motion estimation has proven highly effective at computing fine-grained and large-scale motion in video sequences [12,37,38]. We describe one such standard motion estimation algorithm.
where, f x , f y , and f t are the spatial and temporal image derivatives and where, for notational convenience, the spatial/temporal parameters on f and its derivatives are dropped.
This solution assumes that the 2×2 matrix M is invertible. This can usually be guaranteed by integrating over a large enough ROI Ω with sufficient image content.
and where d(y) and p(y) are the same filters oriented vertically instead of horizontally.
Circadian period estimation
The circadian period is estimated using a two-step process. Denote the plant’s vertical leaf motion over time as v y (t). In the first step, this time series is detrended to remove any linear trend. The Fourier transform of v y (t) is then computed and the circadian period τ 0 is taken to be the frequency with the maximal amplitude. In the second step, an iterative Nelder-Mead optimization is used to refine this estimate by searching for the frequency, phase and amplitude that best, in the root mean square sense, fits the motion data v y (t). This simple approach is similar to employing FFT-NLLS with only a single frequency. We have found that because the motion estimation is fairly accurate, a model based on only a single frequency suffices to extract accurate estimates of circadian period.
3-D Computer generated plant model
A 3-D computer generated (CG) model of a plant with a realistic and precisely known motion was used to validate TRiP. Top, front and side views of an Arabidopsis Col-0 seedling were taken every 10 minutes over a 5 day period under constant light conditions and 20 ∘C. This time series was used to build and animate a 3-D CG plant model (Figure 1). The modeling, texturing, and animation were done in Autodesk Maya®;. To verify the motion estimation algorithm of TRiP with known motion we used the first day of the 3-D CG model to generate simulated traces with a period of 24 h and 25 h. The resulting rendered video sequence could then be supplied to TRiP for validation of the motion estimation and circadian period estimation. We have also provided the raw images that were selected as key frames across the 5 day imaging along with movie files for the 24 h and 25 h simulations and the full 5 day model (Additional files 16, 17, 18, 19, 20, 21, 22, 23).
Camera and imaging set up
Our imaging system uses 14 cameras, both Canon PowerShot ELPH 300s and A2300 IS models, employing the CHDK (Canon Hacker Development Kit) software to set interval shooting to take a picture every 20 min. The CHDK software is installed on 4GB SIM cards that have been formatted to FAT32. The Ultimate Intervalometer script is used to run the time interval shooting. Details of the CHDK installation and use can be found on the CHDK wiki. A 4GB memory card can hold images from 3-4 weeks of 20 min interval shooting depending on the camera and image resolution. There are other methods for setting interval shooting on other camera platforms that have been described in previous studies [7,8,39]. Any of these camera systems can be used to generate the images; the new method described in this study was designed for any sequence of jpeg-formatted images. The cameras were mounted with a fixed focus and minimum per plant pixel count of 10,000 (100 × 100 pixels). Plants are placed in front of a black background for contrast. For all plant species tested except Glycine max, we built a step shaped structure to maximize the number of plants in one image frame. Each wood frame (L 18 cm × W 12 cm × H 6 cm) supports 6 shelves made of steel hollow sections cut in half lengthwise (L 24 cm × W 1.75 cm × H 0.75 cm). The edges were filed down and covered with electrical tape. Pieces of Plexiglass were glued to the ends using Aquarium safe silicone. The plants are placed in the stands with the tips of the cotyledons or true leaves pointing to either side, the first row holds 18 plants and the remaining rows have 20 for a total of 118 plants/camera (Additional file 1). Larger plants cannot be imaged on every shelf so we limit the imaging to 3 rows of 20 plants for each camera. The plants were watered daily to maintain soil saturation and prevent wilting or movement from soil swelling. To image Glycine max, we placed 10 plants in a plexiglass stand (L 45 cm × W 2.75 cm × H 2.5 cm) with 800 mL of water at the start of imaging and watered every day. Imaging for all plants began 24 h following transfer to constant light conditions.
QTL mapping and analysis
A total of 150 lines in the Col-0 x Jea population were assayed for leaf movement and circadian period estimation using TRiP. Model fit traces that gave period values above 32 h and below 18 h were removed. Standard error of the mean (SEM) was calculated for each line and lines with an SEM above 0.50 (corresponding to 30 min) were removed from the analysis (Additional file 2). Mean period values were used for QTL mapping. The markers and construction of the genetic map were previously described . Composite interval mapping (CIM) was performed with R/qtl  using 3 marker covariates and a window size of 20 cM to detect QTL. LOD threshold was calculated based on the averaged LOD following 1000 permutations. A two dimensional genome scan was performed using the “scantwo” function in R/qtl to test for QTL interactions. No significant interactions were detected.
Plant growth conditions
All plants were grown in Sunshine Redi-earth under ∼90 μmol s − 1 m − 2 light unless otherwise stated. All plant species described except Glycine max were grown in 0.5" pvc coupling purchased from Home Depot. The pots/pvc couplings were filled with damp soil wet with water. A day after transferring plants to the imaging chamber they were watered once with a 20-20-20 fertilizer. Plants were watered daily to prevent any movement due to water loss or uptake. Soil saturation must be maintained throughout the imaging.
Arabidopsis seeds were stratified in H 2O for 3 days at 4 ∘C in the dark. Seeds were germinated in soil and put in a 12 h light : 12 h dark (12L:12D) entrainment chamber at 20 ∘C for 7 days. On day 4 of entrainment the lights were turned off 4 h after dawn for 20 h to promote hypocotyl elongation and then returned to 12L:12D for 2 additional days. Following entrainment, seedlings were transferred to 24 h constant light (LL) and temperature (HH) for imaging.
Dry seeds were sown directly on soil. Plants were entrained for 7 days in a growth chamber at 20 ∘C under 12L:12D conditions and high light (∼350 μmol s − 1 m − 2) to limit hypocotyl elongation. Once cotyledons had expanded (7 days), plants were transferred to LLHH conditions for imaging.
Dry seeds were sown directly onto damp soil and entrained to 12L:12D at 20 ∘C until true leaves emerged. Plants were imaged in LLHH at 20 ∘C for 5 days.
Dry seeds were sown directly onto damp soil and entrained to 12L:12D at 20 ∘C for 7 days under low light. Cotyledons were imaged in LLHH at 20 ∘C for 5 days.
Dry seeds were sown directly onto damp soil in 2.25" square pots and put in a growth chamber at 12L:12D with a daytime temperature of 25 ∘C and night time temperature of 18 ∘C. Following emergence of the first trifoliate leaves, plants were transferred to LLHH at 25 ∘C for imaging.
Seeds were stratified in the dark at 4 ∘C in water for 1 week. Seeds were planted in soil and germinated in the entrainment chamber at 12L:12D with a daytime temperature of 20 ∘C and night time temperature of 16 ∘C. We observed more robust leaf movement from true leaves. Plants were moved into the imaging room at the emergence of the first set of true leaves and imaged in LLHH at 20 ∘C.
We would like to thank Qiguang Xie for providing prr5-1prr7-3prr9-1 mutant seed. This work was supported by the National Science Foundation (NSF) National Plant Genome Initiative Postdoctoral Fellowship (IOS-1202779) to K.G., and by grants from the NSF (IOS-0923752 and IOS-1025965) to C.R.M and (CNS-0708209) to H.F.
- McMullen MD, Kresovich S, Villeda HS, Bradbury P, Li H, Sun Q, et al. Genetic properties of the maize nested association mapping population. Science. 2009; 325:737–40.View ArticlePubMedGoogle Scholar
- Kover PX, Valdar W, Trakalo J, Scarcelli N, Ehrenreich IM, Purugganan MD, et al. A multiparent advanced generation inter-cross to fine-map quantitative traits in Arabidopsis thaliana. PLoS Genet. 2009; 5:1000551.View ArticleGoogle Scholar
- Bevan MW, Uauy C. Genomics reveals new landscapes for crop improvement. Genome Biol. 2013; 14:206.View ArticlePubMed CentralPubMedGoogle Scholar
- Yang W, Duan L, Chen G, Xiong L, Liu Q. Plant phenomics and high-throughput phenotyping: accelerating rice functional genomics using multidisciplinary technologies. Curr Opin Plant Biol. 2013; 16:180–7.View ArticlePubMedGoogle Scholar
- Araus JL, Cairns JE. Field high-throughput phenotyping: the new crop breeding frontier. Trends Plant Sci. 2014; 19:52–61.View ArticlePubMedGoogle Scholar
- Engelmann W, Simon K, Phen C. Leaf movement rhythm in Arabidopsis thaliana. Zeitschrift fur Naturforschung. 1992; 47c:925–8.Google Scholar
- Bours R, Muthuraman M, Bouwmeester H, van der Krol A. OSCILLATOR: a system for analysis of diurnal leaf growth using infrared photography combined with wavelet transformation. Plant Methods. 2012; 8:29.View ArticlePubMed CentralPubMedGoogle Scholar
- Edwards K, Millar A. Analysis of circadian leaf movement rhythms in Arabidopsis thaliana. Methods Mol Biol. 2007; 362:103–13.PubMedGoogle Scholar
- Onai K, Okamoto K, Nishimoto H, Morioka C, Hirano M, Kami-ike N, et al. Large-scale screening of Arabidopsis circadian clock mutants by a high-throughput real-time bioluminescence monitoring system. Plant J. 2004; 40:1–11.View ArticlePubMedGoogle Scholar
- Salathia N, Lynn JR, Millar AJ, King GJ. Detection and resolution of genetic loci affecting circadian period in Brassica oleracea. Theor Appl Genet. 2006; 114:683–92.View ArticlePubMedGoogle Scholar
- Plautz JD, Straume M, Stanewsky R, Jamison CF, Dowse HB, Hall JC, et al. Quantitative analysis of drosophila period gene transcription in living animals. J Biol Rhythms. 1997; 12:204–17.View ArticlePubMedGoogle Scholar
- Simoncelli EP. Bayesian multi-scale differential optical flow In: Jähne B, Haussecker H, Geissler P, editors. Handbook of Computer Vision and Applications vol. 2. 2nd edn. San Diego: Academic Press: 1999. p. 397–420.Google Scholar
- Zielinski T, Moore AM, Troup E, Halliday KJ, Millar AJ. Strengths and limitations of period estimation methods for circadian data. PLoS One. 2014; 9:96462.View ArticleGoogle Scholar
- Moore A, Zielinski T, Millar AJ. Online period estimation and determination of rhythmicity in circadian data, using the BioDare data infrastructure. Methods Mol Biol. 2014; 1158:13–44.PubMedGoogle Scholar
- Sanchez SE, Petrillo E, Beckwith EJ, Zhang X, Rugnone ML, Hernando CE, et al. A methyl transferase links the circadian clock to the regulation of alternative splicing. Nature. 2010; 468:112–6.View ArticlePubMedGoogle Scholar
- Hong S, Song H, Lutz K, Kerstetter RA, Michael TP, McClung CR. Type II protein arginine methyltransferase 5 (PRMT5) is required for circadian period determination in Arabidopsis thaliana. Proc Natl Acad Sci. 2010; 107:21211–1216.View ArticlePubMed CentralPubMedGoogle Scholar
- Zhang C, Xie Q, Anderson R, Ng G, Seitz N, Peterson T, et al. Crosstalk between the circadian clock and innate immunity in Arabidopsis. PLoS Pathog. 2014; 9:1003370.View ArticleGoogle Scholar
- Kikis E, Khanna R, Quail P. ELF4 is a phytochrome-regulated component of a negative-feedback loop involving the central oscillator components CCA1 and LHY. Plant J. 2005; 44:300–13.View ArticlePubMedGoogle Scholar
- Michael TP, Salomé PA, Yu HJ, Spencer TR, Sharp EL, McPeek MA, et al. Enhanced fitness conferred by naturally occurring variation in the circadian clock. Science. 2003; 302:1049–53.View ArticlePubMedGoogle Scholar
- Baudry A, Ito S, Song Y, Strait A, Kiba T, Lu S, et al. F-Box Proteins FKF1 and LKP2 act in concert with ZEITLUPE to control Arabidopsis clock progression. Plant Cell. 2010; 22:606–22.View ArticlePubMed CentralPubMedGoogle Scholar
- Nakamichi N, Kita M, Ito S, Sato E, Yamashino T, Mizuno T. PSEUDO-RESPONSE REGULATORS, PRR9, PRR7, and PRR5, together play essential roles close to the circadian clock of Arabidopsis thaliana. Plant Cell. 2005; 46:686–98.View ArticleGoogle Scholar
- Simon M, Loudet O, Durand S, Bérand A, Brunel D, Sennesal FX, et al. QTL mapping in five new large RIL populations of Arabidopsis thaliana genotyped with consensus SNP markers. Genetics. 2008; 178:2253–64.View ArticlePubMed CentralPubMedGoogle Scholar
- Swarup K, Alonso-Blanco C, Lynn JR, Michaels SD, Amasino RM, Koornneef M, et al. Natural allelic variation identifies new genes in the Arabidopsis circadian system. Plant J. 1999; 20:67–77.View ArticlePubMedGoogle Scholar
- Matsushika A, Makino S, Kojima M, Mizuno T. Circadian waves of expression of the APRR1/TOC1 family of pseudo-response regulators in Arabidopsis thaliana: insight into the plant circadian clock. Plant Cell Physiol. 2000; 41:1002–12.View ArticlePubMedGoogle Scholar
- Rawat R, Schwartz J, Jones MA, Sairanen I, Cheng Y, Andersson CR, et al. REVEILLE1, a Myb-like transcription factor, integrates the circadian clock and auxin pathways. Proc Natl Acad Sci. 2009; 106:16883–8.View ArticlePubMed CentralPubMedGoogle Scholar
- Covington MF, Panda S, Liu XL, Strayer CA, Wagner DR, Kay SA. ELF3 modulates resetting of the circadian clock in Arabidopsis. Plant Cell. 2001; 13:1305–16.View ArticlePubMed CentralPubMedGoogle Scholar
- Anwer MU, Boikoglou E, Herrero E, Hallstein M, Davis AM, James GV, et al. Natural variation reveals that intracellular distribution of ELF3 protein is associated with function in the circadian clock. eLife. 2014; 3:1–28.View ArticleGoogle Scholar
- de Mairan J. Observation botanique. Hist Acad Roy Sci. 1729; 1729:35–6.Google Scholar
- de Candolle AP. Physiologie Végétale. Paris: Bechet Jeune; 1832.Google Scholar
- Darwin CR, Darwin F. The Power of Movement in Plants. London: John Murray; 1880.View ArticleGoogle Scholar
- Hall A, Brown P. Monitoring circadian rhythms in Arabidopsis thaliana using luciferase reporter genes. Methods Mol Biol. 2007; 362:143–52.PubMedGoogle Scholar
- Millar AJ, Short SR, Chua NH, Kay SA. A novel circadian phenotype based on firefly luciferase expression in transgenic plants. Plant Cell. 1992; 4:1075–87.View ArticlePubMed CentralPubMedGoogle Scholar
- Tautz D, Ellegren H, Weigel D. Next generation molecular ecology. Mol Ecol. 2010; 19:1–3.View ArticlePubMedGoogle Scholar
- Henry LP, Watson RHB, Blackman BK. Transitions in photoperiodic flowering are common and involve few loci in wild sunflowers (Helianthus; asteraceae). Am J Bot. 2014; 101:1748–58.View ArticlePubMedGoogle Scholar
- Kooyers NJ, Greenlee AB, CJ M, Oh M, Blackman BK. Replicate altitudinal clines reveal that evolutionary flexibility underlies adaptation to drought stress in annual Mimulus guttatus. New Phytol. 2014; 206:152–65.View ArticlePubMedGoogle Scholar
- McClung CR. The genetics of plant clocks. Adv Genet. 2011; 74:105–38.PubMedGoogle Scholar
- Barron JL, Fleet DJ, Beauchemin SS. Performance of optical flow techniques. Int J Comput Vision. 1994; 12:43–77.View ArticleGoogle Scholar
- Horn BKP. Robot Vision. Cambridge, Massachusetts: MIT Press; 1986.Google Scholar
- Schaffer R, Samach A, Corden S, Putterill J, Carré IA, Coupland G. The late elongated hypocotyl mutation of Arabidopsis disrupts circadian rhythms and the photoperiodic control of flowering. Cell. 1998; 93:1219–29.View ArticlePubMedGoogle Scholar
- Broman KW, Sen S, Churchill GA. R/qtl: QTL mapping in experimental crosses. Bioinformatics. 2003; 19:889–90.View ArticlePubMedGoogle Scholar
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.