Abstract

In precision agriculture, crop/weed discrimination is often based on image analysis but though several algorithms using spatial information have been proposed, not any has been tested on relevant databases. A simple model that simulates virtual fields is developed to evaluate these algorithms. Virtual fields are made of crops, arranged according to agricultural practices and represented by simple patterns, and weeds that are spatially distributed using a statistical approach. It ensures a user-defined Weed Infestation Rate (WIR). Then, experimental devices using cameras are simulated with a pinhole model. Its ability to characterize the spatial reality is demonstrated through different pairs (real, virtual) of pictures. Two spatial descriptors (nearest neighbor method and Besag’s function) have been set up and tested to validate the spatial realism of the crop field model, comparing a real image to the homologous virtual one.

© 2010 OSA

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References

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  1. L. Streit, P. Federl, and M. Costa Sousa, “Modelling Plant Variation Through Growth,” Comput. Graph. Forum 24, 497–506 (2005).
    [CrossRef]
  2. J. Bossu, C. Gée, and F. Truchetet, “Development of a machine vision system for a real time precision sprayer,” Electron. Lett. Comput. Vision 7, 54–66 (2008).
  3. J. Bossu, C. Gée, G. Jones, and F. Truchetet, “Wavelet transform to discriminate between crop and weed in perspective agronomic images,” Comput. Electron. Agric. 65(1), 133–143 (2009).
    [CrossRef]
  4. C. Onyango, J. Marchant, A. Grundy, K. Phelps, and R. Reader, “Image Processing Performance Assessment using Crop Weed Competition Models,” Precis. Agric. 6(2), 183–192 (2005).
    [CrossRef]
  5. G. Jones, C. Gée, and F. Truchetet, “Modelling agronomic images for weed detection and comparison of crop/weed discrimination algorithm performance,” Precis. Agric. 10(1), 1–15 (2009).
    [CrossRef]
  6. G. Jones, C. Gée, and F. Truchetet, “Assessment of an inter-row weed infestation rate on simulated agronomic images,” Comput. Electron. Agric. 67(1-2), 43–50 (2009).
    [CrossRef]
  7. J. Cardina, G. Johnson, and D. Sparrow, “The nature and consequence of weed spatial distribution,” Weed Sci. 43, 364–373 (1997).
  8. R. A. Fisher and R. E. Miles, “The role of spatial pattern in the competition between plants and weeds. A theoretical analysis,” Math. Biosci. 18(3-4), 335–350 (1973).
    [CrossRef]
  9. F. Goreaud, “Apports de l’analyse de la structure spatiale en fôret tempérée à l’étude et la modélisation des peuplements complexes,” (Clermont-Ferrand, 2000).
  10. O. Faugeras, Three-Dimensional Computer Vision (MIT Press, 1993).
  11. D. M. Woebbecke, G. E. Meyer, K. Von Bargen, and D. A. Mortensen, “Color indices for weed identification under various soil, residue, and lightning conditions,” Trans. ASAE 38, 259–269 (1995).
  12. J.-Y. Bouguet, (juin 2008), retrieved juillet 2009, http://www.vision.caltech.edu/bouguetj/calib_doc/index.html .
  13. J. G. Skellam, “Studies in statistical ecology I. Spatial pattern,” Biometrica 39(3/4), 346–362 (1952).
    [CrossRef]
  14. B. D. Ripley, Spatial statistics (Wiley, New-York, 1981).
  15. P. J. Diggle, “Statistical analysis of spatial point patterns,” (Academic Press, 1983).
  16. F. Goreaud, M. Loreau, and C. Millier, “Spatial structure and the survival of an inferior competitor: a theoretical model of neighbourhood competition in plants,” Ecol. Modell. 158(1-2), 1–19 (2002).
    [CrossRef]
  17. J. E. Besag, “Comments on Ripley’s paper,” J. R. Stat. Soc., B 39, 193–195 (1977).
  18. B. D. Ripley, “Modelling spatial patterns,” J. Royal Stat. Soc. Ser. B (Methodol.), 172–212 (1977).
  19. H. A. Gleason, “Some applications of the quadrat method,” Bull. Torrey Bot. Club 47(1), 21–33 (1920).
    [CrossRef]
  20. N. A. C. Cressie, Statistics for spatial data, Wiley Series in Probability and Mathematical Statistics (John Wiley and and Sons, New York, 1993).
  21. S. Jacquemoud, S. L. Ustin, J. Verdebout, G. Schmuck, G. Andreoli, and B. Hosgood, “Estimating leaf biochemistry using the PROSPECT leaf optical properties model,” Remote Sens. Environ. 56(3), 194–202 (1996).
    [CrossRef]
  22. B. Hapke, “Bidirectional Reflectance Spectroscopy,” J. Geophys. Res. 86(B4), 3039–3054 (1981).
    [CrossRef]

2009 (3)

J. Bossu, C. Gée, G. Jones, and F. Truchetet, “Wavelet transform to discriminate between crop and weed in perspective agronomic images,” Comput. Electron. Agric. 65(1), 133–143 (2009).
[CrossRef]

G. Jones, C. Gée, and F. Truchetet, “Modelling agronomic images for weed detection and comparison of crop/weed discrimination algorithm performance,” Precis. Agric. 10(1), 1–15 (2009).
[CrossRef]

G. Jones, C. Gée, and F. Truchetet, “Assessment of an inter-row weed infestation rate on simulated agronomic images,” Comput. Electron. Agric. 67(1-2), 43–50 (2009).
[CrossRef]

2008 (1)

J. Bossu, C. Gée, and F. Truchetet, “Development of a machine vision system for a real time precision sprayer,” Electron. Lett. Comput. Vision 7, 54–66 (2008).

2005 (2)

L. Streit, P. Federl, and M. Costa Sousa, “Modelling Plant Variation Through Growth,” Comput. Graph. Forum 24, 497–506 (2005).
[CrossRef]

C. Onyango, J. Marchant, A. Grundy, K. Phelps, and R. Reader, “Image Processing Performance Assessment using Crop Weed Competition Models,” Precis. Agric. 6(2), 183–192 (2005).
[CrossRef]

2002 (1)

F. Goreaud, M. Loreau, and C. Millier, “Spatial structure and the survival of an inferior competitor: a theoretical model of neighbourhood competition in plants,” Ecol. Modell. 158(1-2), 1–19 (2002).
[CrossRef]

1997 (1)

J. Cardina, G. Johnson, and D. Sparrow, “The nature and consequence of weed spatial distribution,” Weed Sci. 43, 364–373 (1997).

1996 (1)

S. Jacquemoud, S. L. Ustin, J. Verdebout, G. Schmuck, G. Andreoli, and B. Hosgood, “Estimating leaf biochemistry using the PROSPECT leaf optical properties model,” Remote Sens. Environ. 56(3), 194–202 (1996).
[CrossRef]

1995 (1)

D. M. Woebbecke, G. E. Meyer, K. Von Bargen, and D. A. Mortensen, “Color indices for weed identification under various soil, residue, and lightning conditions,” Trans. ASAE 38, 259–269 (1995).

1981 (1)

B. Hapke, “Bidirectional Reflectance Spectroscopy,” J. Geophys. Res. 86(B4), 3039–3054 (1981).
[CrossRef]

1977 (2)

J. E. Besag, “Comments on Ripley’s paper,” J. R. Stat. Soc., B 39, 193–195 (1977).

B. D. Ripley, “Modelling spatial patterns,” J. Royal Stat. Soc. Ser. B (Methodol.), 172–212 (1977).

1973 (1)

R. A. Fisher and R. E. Miles, “The role of spatial pattern in the competition between plants and weeds. A theoretical analysis,” Math. Biosci. 18(3-4), 335–350 (1973).
[CrossRef]

1952 (1)

J. G. Skellam, “Studies in statistical ecology I. Spatial pattern,” Biometrica 39(3/4), 346–362 (1952).
[CrossRef]

1920 (1)

H. A. Gleason, “Some applications of the quadrat method,” Bull. Torrey Bot. Club 47(1), 21–33 (1920).
[CrossRef]

Andreoli, G.

S. Jacquemoud, S. L. Ustin, J. Verdebout, G. Schmuck, G. Andreoli, and B. Hosgood, “Estimating leaf biochemistry using the PROSPECT leaf optical properties model,” Remote Sens. Environ. 56(3), 194–202 (1996).
[CrossRef]

Besag, J. E.

J. E. Besag, “Comments on Ripley’s paper,” J. R. Stat. Soc., B 39, 193–195 (1977).

Bossu, J.

J. Bossu, C. Gée, G. Jones, and F. Truchetet, “Wavelet transform to discriminate between crop and weed in perspective agronomic images,” Comput. Electron. Agric. 65(1), 133–143 (2009).
[CrossRef]

J. Bossu, C. Gée, and F. Truchetet, “Development of a machine vision system for a real time precision sprayer,” Electron. Lett. Comput. Vision 7, 54–66 (2008).

Cardina, J.

J. Cardina, G. Johnson, and D. Sparrow, “The nature and consequence of weed spatial distribution,” Weed Sci. 43, 364–373 (1997).

Costa Sousa, M.

L. Streit, P. Federl, and M. Costa Sousa, “Modelling Plant Variation Through Growth,” Comput. Graph. Forum 24, 497–506 (2005).
[CrossRef]

Federl, P.

L. Streit, P. Federl, and M. Costa Sousa, “Modelling Plant Variation Through Growth,” Comput. Graph. Forum 24, 497–506 (2005).
[CrossRef]

Fisher, R. A.

R. A. Fisher and R. E. Miles, “The role of spatial pattern in the competition between plants and weeds. A theoretical analysis,” Math. Biosci. 18(3-4), 335–350 (1973).
[CrossRef]

Gée, C.

J. Bossu, C. Gée, G. Jones, and F. Truchetet, “Wavelet transform to discriminate between crop and weed in perspective agronomic images,” Comput. Electron. Agric. 65(1), 133–143 (2009).
[CrossRef]

G. Jones, C. Gée, and F. Truchetet, “Modelling agronomic images for weed detection and comparison of crop/weed discrimination algorithm performance,” Precis. Agric. 10(1), 1–15 (2009).
[CrossRef]

G. Jones, C. Gée, and F. Truchetet, “Assessment of an inter-row weed infestation rate on simulated agronomic images,” Comput. Electron. Agric. 67(1-2), 43–50 (2009).
[CrossRef]

J. Bossu, C. Gée, and F. Truchetet, “Development of a machine vision system for a real time precision sprayer,” Electron. Lett. Comput. Vision 7, 54–66 (2008).

Gleason, H. A.

H. A. Gleason, “Some applications of the quadrat method,” Bull. Torrey Bot. Club 47(1), 21–33 (1920).
[CrossRef]

Goreaud, F.

F. Goreaud, M. Loreau, and C. Millier, “Spatial structure and the survival of an inferior competitor: a theoretical model of neighbourhood competition in plants,” Ecol. Modell. 158(1-2), 1–19 (2002).
[CrossRef]

Grundy, A.

C. Onyango, J. Marchant, A. Grundy, K. Phelps, and R. Reader, “Image Processing Performance Assessment using Crop Weed Competition Models,” Precis. Agric. 6(2), 183–192 (2005).
[CrossRef]

Hapke, B.

B. Hapke, “Bidirectional Reflectance Spectroscopy,” J. Geophys. Res. 86(B4), 3039–3054 (1981).
[CrossRef]

Hosgood, B.

S. Jacquemoud, S. L. Ustin, J. Verdebout, G. Schmuck, G. Andreoli, and B. Hosgood, “Estimating leaf biochemistry using the PROSPECT leaf optical properties model,” Remote Sens. Environ. 56(3), 194–202 (1996).
[CrossRef]

Jacquemoud, S.

S. Jacquemoud, S. L. Ustin, J. Verdebout, G. Schmuck, G. Andreoli, and B. Hosgood, “Estimating leaf biochemistry using the PROSPECT leaf optical properties model,” Remote Sens. Environ. 56(3), 194–202 (1996).
[CrossRef]

Johnson, G.

J. Cardina, G. Johnson, and D. Sparrow, “The nature and consequence of weed spatial distribution,” Weed Sci. 43, 364–373 (1997).

Jones, G.

G. Jones, C. Gée, and F. Truchetet, “Modelling agronomic images for weed detection and comparison of crop/weed discrimination algorithm performance,” Precis. Agric. 10(1), 1–15 (2009).
[CrossRef]

J. Bossu, C. Gée, G. Jones, and F. Truchetet, “Wavelet transform to discriminate between crop and weed in perspective agronomic images,” Comput. Electron. Agric. 65(1), 133–143 (2009).
[CrossRef]

G. Jones, C. Gée, and F. Truchetet, “Assessment of an inter-row weed infestation rate on simulated agronomic images,” Comput. Electron. Agric. 67(1-2), 43–50 (2009).
[CrossRef]

Loreau, M.

F. Goreaud, M. Loreau, and C. Millier, “Spatial structure and the survival of an inferior competitor: a theoretical model of neighbourhood competition in plants,” Ecol. Modell. 158(1-2), 1–19 (2002).
[CrossRef]

Marchant, J.

C. Onyango, J. Marchant, A. Grundy, K. Phelps, and R. Reader, “Image Processing Performance Assessment using Crop Weed Competition Models,” Precis. Agric. 6(2), 183–192 (2005).
[CrossRef]

Meyer, G. E.

D. M. Woebbecke, G. E. Meyer, K. Von Bargen, and D. A. Mortensen, “Color indices for weed identification under various soil, residue, and lightning conditions,” Trans. ASAE 38, 259–269 (1995).

Miles, R. E.

R. A. Fisher and R. E. Miles, “The role of spatial pattern in the competition between plants and weeds. A theoretical analysis,” Math. Biosci. 18(3-4), 335–350 (1973).
[CrossRef]

Millier, C.

F. Goreaud, M. Loreau, and C. Millier, “Spatial structure and the survival of an inferior competitor: a theoretical model of neighbourhood competition in plants,” Ecol. Modell. 158(1-2), 1–19 (2002).
[CrossRef]

Mortensen, D. A.

D. M. Woebbecke, G. E. Meyer, K. Von Bargen, and D. A. Mortensen, “Color indices for weed identification under various soil, residue, and lightning conditions,” Trans. ASAE 38, 259–269 (1995).

Onyango, C.

C. Onyango, J. Marchant, A. Grundy, K. Phelps, and R. Reader, “Image Processing Performance Assessment using Crop Weed Competition Models,” Precis. Agric. 6(2), 183–192 (2005).
[CrossRef]

Phelps, K.

C. Onyango, J. Marchant, A. Grundy, K. Phelps, and R. Reader, “Image Processing Performance Assessment using Crop Weed Competition Models,” Precis. Agric. 6(2), 183–192 (2005).
[CrossRef]

Reader, R.

C. Onyango, J. Marchant, A. Grundy, K. Phelps, and R. Reader, “Image Processing Performance Assessment using Crop Weed Competition Models,” Precis. Agric. 6(2), 183–192 (2005).
[CrossRef]

Ripley, B. D.

B. D. Ripley, “Modelling spatial patterns,” J. Royal Stat. Soc. Ser. B (Methodol.), 172–212 (1977).

Schmuck, G.

S. Jacquemoud, S. L. Ustin, J. Verdebout, G. Schmuck, G. Andreoli, and B. Hosgood, “Estimating leaf biochemistry using the PROSPECT leaf optical properties model,” Remote Sens. Environ. 56(3), 194–202 (1996).
[CrossRef]

Skellam, J. G.

J. G. Skellam, “Studies in statistical ecology I. Spatial pattern,” Biometrica 39(3/4), 346–362 (1952).
[CrossRef]

Sparrow, D.

J. Cardina, G. Johnson, and D. Sparrow, “The nature and consequence of weed spatial distribution,” Weed Sci. 43, 364–373 (1997).

Streit, L.

L. Streit, P. Federl, and M. Costa Sousa, “Modelling Plant Variation Through Growth,” Comput. Graph. Forum 24, 497–506 (2005).
[CrossRef]

Truchetet, F.

J. Bossu, C. Gée, G. Jones, and F. Truchetet, “Wavelet transform to discriminate between crop and weed in perspective agronomic images,” Comput. Electron. Agric. 65(1), 133–143 (2009).
[CrossRef]

G. Jones, C. Gée, and F. Truchetet, “Modelling agronomic images for weed detection and comparison of crop/weed discrimination algorithm performance,” Precis. Agric. 10(1), 1–15 (2009).
[CrossRef]

G. Jones, C. Gée, and F. Truchetet, “Assessment of an inter-row weed infestation rate on simulated agronomic images,” Comput. Electron. Agric. 67(1-2), 43–50 (2009).
[CrossRef]

J. Bossu, C. Gée, and F. Truchetet, “Development of a machine vision system for a real time precision sprayer,” Electron. Lett. Comput. Vision 7, 54–66 (2008).

Ustin, S. L.

S. Jacquemoud, S. L. Ustin, J. Verdebout, G. Schmuck, G. Andreoli, and B. Hosgood, “Estimating leaf biochemistry using the PROSPECT leaf optical properties model,” Remote Sens. Environ. 56(3), 194–202 (1996).
[CrossRef]

Verdebout, J.

S. Jacquemoud, S. L. Ustin, J. Verdebout, G. Schmuck, G. Andreoli, and B. Hosgood, “Estimating leaf biochemistry using the PROSPECT leaf optical properties model,” Remote Sens. Environ. 56(3), 194–202 (1996).
[CrossRef]

Von Bargen, K.

D. M. Woebbecke, G. E. Meyer, K. Von Bargen, and D. A. Mortensen, “Color indices for weed identification under various soil, residue, and lightning conditions,” Trans. ASAE 38, 259–269 (1995).

Woebbecke, D. M.

D. M. Woebbecke, G. E. Meyer, K. Von Bargen, and D. A. Mortensen, “Color indices for weed identification under various soil, residue, and lightning conditions,” Trans. ASAE 38, 259–269 (1995).

Biometrica (1)

J. G. Skellam, “Studies in statistical ecology I. Spatial pattern,” Biometrica 39(3/4), 346–362 (1952).
[CrossRef]

Bull. Torrey Bot. Club (1)

H. A. Gleason, “Some applications of the quadrat method,” Bull. Torrey Bot. Club 47(1), 21–33 (1920).
[CrossRef]

Comput. Electron. Agric. (2)

J. Bossu, C. Gée, G. Jones, and F. Truchetet, “Wavelet transform to discriminate between crop and weed in perspective agronomic images,” Comput. Electron. Agric. 65(1), 133–143 (2009).
[CrossRef]

G. Jones, C. Gée, and F. Truchetet, “Assessment of an inter-row weed infestation rate on simulated agronomic images,” Comput. Electron. Agric. 67(1-2), 43–50 (2009).
[CrossRef]

Comput. Graph. Forum (1)

L. Streit, P. Federl, and M. Costa Sousa, “Modelling Plant Variation Through Growth,” Comput. Graph. Forum 24, 497–506 (2005).
[CrossRef]

Ecol. Modell. (1)

F. Goreaud, M. Loreau, and C. Millier, “Spatial structure and the survival of an inferior competitor: a theoretical model of neighbourhood competition in plants,” Ecol. Modell. 158(1-2), 1–19 (2002).
[CrossRef]

Electron. Lett. Comput. Vision (1)

J. Bossu, C. Gée, and F. Truchetet, “Development of a machine vision system for a real time precision sprayer,” Electron. Lett. Comput. Vision 7, 54–66 (2008).

J. Geophys. Res. (1)

B. Hapke, “Bidirectional Reflectance Spectroscopy,” J. Geophys. Res. 86(B4), 3039–3054 (1981).
[CrossRef]

J. R. Stat. Soc., B (1)

J. E. Besag, “Comments on Ripley’s paper,” J. R. Stat. Soc., B 39, 193–195 (1977).

Math. Biosci. (1)

R. A. Fisher and R. E. Miles, “The role of spatial pattern in the competition between plants and weeds. A theoretical analysis,” Math. Biosci. 18(3-4), 335–350 (1973).
[CrossRef]

Precis. Agric. (2)

C. Onyango, J. Marchant, A. Grundy, K. Phelps, and R. Reader, “Image Processing Performance Assessment using Crop Weed Competition Models,” Precis. Agric. 6(2), 183–192 (2005).
[CrossRef]

G. Jones, C. Gée, and F. Truchetet, “Modelling agronomic images for weed detection and comparison of crop/weed discrimination algorithm performance,” Precis. Agric. 10(1), 1–15 (2009).
[CrossRef]

Remote Sens. Environ. (1)

S. Jacquemoud, S. L. Ustin, J. Verdebout, G. Schmuck, G. Andreoli, and B. Hosgood, “Estimating leaf biochemistry using the PROSPECT leaf optical properties model,” Remote Sens. Environ. 56(3), 194–202 (1996).
[CrossRef]

Trans. ASAE (1)

D. M. Woebbecke, G. E. Meyer, K. Von Bargen, and D. A. Mortensen, “Color indices for weed identification under various soil, residue, and lightning conditions,” Trans. ASAE 38, 259–269 (1995).

Weed Sci. (1)

J. Cardina, G. Johnson, and D. Sparrow, “The nature and consequence of weed spatial distribution,” Weed Sci. 43, 364–373 (1997).

Other (7)

F. Goreaud, “Apports de l’analyse de la structure spatiale en fôret tempérée à l’étude et la modélisation des peuplements complexes,” (Clermont-Ferrand, 2000).

O. Faugeras, Three-Dimensional Computer Vision (MIT Press, 1993).

J.-Y. Bouguet, (juin 2008), retrieved juillet 2009, http://www.vision.caltech.edu/bouguetj/calib_doc/index.html .

B. D. Ripley, Spatial statistics (Wiley, New-York, 1981).

P. J. Diggle, “Statistical analysis of spatial point patterns,” (Academic Press, 1983).

B. D. Ripley, “Modelling spatial patterns,” J. Royal Stat. Soc. Ser. B (Methodol.), 172–212 (1977).

N. A. C. Cressie, Statistics for spatial data, Wiley Series in Probability and Mathematical Statistics (John Wiley and and Sons, New York, 1993).

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Figures (6)

Fig. 1
Fig. 1

Results of pixel integration and grey-level appearance.

Fig. 2
Fig. 2

a) Wheat picture: inter-row width = 16cm, camera’s height = 1.20m, pitch angle = 65°, roll angle = 0° and WIR = 20% with a mixture of both distributions. b) Sunflower picture: inter-row width = 45cm, intra-row frequency = 10cm, camera’s height = 15m, pitch angle = 0°, roll angle = 20° and WIR = 10% with a punctual distribution.

Fig. 3
Fig. 3

(a) Pre-processed sunflower field picture from a drone. (b) Virtual picture from initial parameters deduced from the real one.

Fig. 4
Fig. 4

Structure of the local moving window (example for the pattern 1) centered on a pixel of intensity equals one. The window size d varies from 1 to (image width)/2 allowing a spatial study at different scales.

Fig. 5
Fig. 5

Comparison of the evolution of the crop spatial information at different length scales in the real picture (line) and the virtual picture (dots) for every pattern. The width ([σsimulated, σsimulated]) of error bars characterizes the standard deviation of a virtual data set composed of 2000 images.

Fig. 6
Fig. 6

(a) and (b) represent the real and the virtual weed patterns. The pictures are composed of a number of 177 weed plants. The figures (c) and (d) are the point weed distributions associated to each weed plant pattern for both real and virtual pictures. The figures (e) and (f) are Besag’s functions deduced for both real and virtual pictures. These functions are calculated with a confidence interval of 1%. In both case, they reveal that weed plant pattern is a homogeneous point distribution.

Tables (1)

Tables Icon

Table 1 RMSE values for all the nine patterns deduced from real picture and its virtual homologous one presented in Fig. 3.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

WIR(%)=weedpixels*100(crop+weed)pixels
Pk(λS)=P(X=k)=(λS)kk!eλS
RMSE=1Nn=1N(ρsimulated(Xn)ρreal(Xn))2
K^(r)=1λ^.1N.i=1Njikij
L^(r)=K^(r)πr

Metrics