Acta Biotheoretica

, Volume 66, Issue 1, pp 17–60 | Cite as

Quaternion-Based Texture Analysis of Multiband Satellite Images: Application to the Estimation of Aboveground Biomass in the East Region of Cameroon

  • Cedrigue Boris Djiongo Kenfack
  • Olivier Monga
  • Serge Moto Mpong
  • René Ndoundam
Regular Article


Within the last decade, several approaches using quaternion numbers to handle and model multiband images in a holistic manner were introduced. The quaternion Fourier transform can be efficiently used to model texture in multidimensional data such as color images. For practical application, multispectral satellite data appear as a primary source for measuring past trends and monitoring changes in forest carbon stocks. In this work, we propose a texture-color descriptor based on the quaternion Fourier transform to extract relevant information from multiband satellite images. We propose a new multiband image texture model extraction, called FOTO++, in order to address biomass estimation issues. The first stage consists in removing noise from the multispectral data while preserving the edges of canopies. Afterward, color texture descriptors are extracted thanks to a discrete form of the quaternion Fourier transform, and finally the support vector regression method is used to deduce biomass estimation from texture indices. Our texture features are modeled using a vector composed with the radial spectrum coming from the amplitude of the quaternion Fourier transform. We conduct several experiments in order to study the sensitivity of our model to acquisition parameters. We also assess its performance both on synthetic images and on real multispectral images of Cameroonian forest. The results show that our model is more robust to acquisition parameters than the classical Fourier Texture Ordination model (FOTO). Our scheme is also more accurate for aboveground biomass estimation. We stress that a similar methodology could be implemented using quaternion wavelets. These results highlight the potential of the quaternion-based approach to study multispectral satellite images.


Discrete quaternion Fourier transform Quaternion-based texture indices Multiband satellite images Aboveground biomass Cameroon 



The authors would like to thank Pierre Ploton for his important contribution to data collection and for fruitful discussions on tropical forest structures. Many thanks go also to Nicolas Barbier, Nicolas Picard and Bonaventure Sonke for their expertise about tropical forest trees, dendrometric properties, forest dynamic processes and radiometric properties of trees, and to the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. Finally, they thank all the members of the SAM’s team of UMMISCO-Cameroon. The BIOFORAC Project and the PDI (Programme Doctoral International) of IRD and Paris 6 University have funded this research.


  1. Barbier N, Couteron P, Proisy C, Malhi Y, Gastellu-Etchegorry J-P (2010) The variation of apparent crown size and canopy heterogeneity across lowland Amazonian forest”. Glob Ecol Biogeogr 19:72–84CrossRefGoogle Scholar
  2. Barbier N, Couteron P, Gastellu-Etchegorry J-P, Proisy C (2012) Linking canopy images to forest structural parameters: potential of a modeling framework. Ann For Sci 69:305–311. CrossRefGoogle Scholar
  3. Basak D, Pal S, Patranabis DC (2007) Support vector regression. Neural Inf Process Lett Rev 11:203–224Google Scholar
  4. Basuki TM, Van Laake PE, Skidmore AK, Hussin YA (2009) Allometric equations for estimating the above-ground biomass in tropical lowland Dipterocarp forests. For Ecol Manag 257:1684–1694. CrossRefGoogle Scholar
  5. Chave J, Condit R, Aguilar S, Hernandez A, Lao S, Perez R (2004) Error propagation and scaling for tropical forest biomass estimates. Philos Trans R Soc Biol Sci 359:409–420CrossRefGoogle Scholar
  6. Chave J, Rejou-Mechain M, Burquez A, Chidumayo E, Colgan MS, Delitti WBC, Duque A, Eid T, Fearnside PM, Goodman RC, Henry M, Martinez-Yrizar A, Mugasha WA, Muller-Landau HC, Mencuccini M, Nelson BW, Ngomanda A, Nogueira EM, Ortiz-Malavassi E, Pelissier R, Ploton P, Ryan CM, Saldarriaga JG, Vieilledent G (2014) Improved allometric models to estimate the above ground biomass of tropical trees. Glob Change Biol. Google Scholar
  7. Chen CH, Pau LF, Wang PSP (1998) The handbook of pattern recognition and computer vision, 2nd edn. World Scientific Publishing Co, Singapore, pp 207–248Google Scholar
  8. Cheng HD, Jiang XH, Sun Y, Wang Jing Li (2001) Color images segmentation: advances and prospects. Pattern Recogn 34:2259–2281. CrossRefGoogle Scholar
  9. Couteron P (2002) Quantifying change in patterned semi-arid vegetation by Fourier analysis of digitized aerial photographs. Remote Sens 23:3407–3425CrossRefGoogle Scholar
  10. Couteron P, Raphael P, Eric A, Domonique P (2005) Predicting tropical forest stand structure parameters from Fourier transform of very high-resolution remotely sensed canopy images. J Appl Ecol 42:1121–1128CrossRefGoogle Scholar
  11. Dengsheng L (2006) The potential and challenge of remote sensing-based biomass estimation. Int J Remote Sens 27:297–1328Google Scholar
  12. Dial G, Bowen H, Gerlach F, Grodecki J, Oleszczuk R (2003) IKONOS satellite imagery, and products. Remote Sens Environ 88:23–36CrossRefGoogle Scholar
  13. Ekoungoulou R, Liu X, Loumeto JJ, Ifo SA, Bocko YE, Koula FE, Niu S (2014) Tree allometry in tropical forest of Congo for carbon stocks estimation in aboveground biomass. Open J For 4(05):481Google Scholar
  14. Ekoungoulou R, Niu S, Loumeto JJ, Ifo SA, Bocko YE, Mikieleko FEK, Liu X (2015) Evaluating the carbon stock in above-and below-ground biomass in a moist Central African forest. Sci Educ 2:51–59Google Scholar
  15. Ell TA, Sangwine SJ (2007) Hypercomplex Fourier transforms of color images. IEEE Trans Image Process 16:22–35CrossRefGoogle Scholar
  16. Ell TA, Le Bihan N, Sangwine SJ (2014) Quaternion Fourier transforms for signal and image processing. Wiley, New York. ISBN 978-1-84821-478-1CrossRefGoogle Scholar
  17. Fayolle A, Doucet JL, Gillet JF, Bourland N, Lejeune P (2013) Tree allometry in Central Africa: testing the validity of pantropical multi-species allometric equations for estimating biomass and carbon stocks. For Ecol Manag 305:29–37CrossRefGoogle Scholar
  18. Feldpausch TR, Lloyd J, Lewis SL, Brienen RJ, Gloor M, Monteagudo Mendoza A, Lopez-Gonzalez G, Banin L, Abu Salim K, Affum-Baffoe K, Alexiades M (2012) Tree height integrated into pantropical forest biomass estimates. Biogeosciences 9:3381–3403. CrossRefGoogle Scholar
  19. Fernandez-Maloigne C, Robert-Inacio F, Macaire L (2012) Digital color imaging. Wiley, New York. ISBN 978-1-84821-347-0CrossRefGoogle Scholar
  20. Gaia VL, Qi C, Jeremy AL, David AC, Del Frate Fabio, Leila G, Francesco P, Riccardo V (2014) Aboveground biomass estimation in an African tropical forest with lidar and hyperspectral data. J Photogramm Remote Sens 89:49–58CrossRefGoogle Scholar
  21. Gastellu-Etchegorry JP (2008) 3D modeling of satellite spectral images, radiation budget and energy budget of urban landscapes. Meteorol Atmos Phys 102:187–207CrossRefGoogle Scholar
  22. Goetz SJ, Alessandro B, Nadine TL, Tracy J, Wayne W, Josef K, Richard AH, Mindy S (2009) Mapping and monitoring carbon stocks, with satellite observations: a comparison of methods. Carbon Balance Manag 4(2):1–7Google Scholar
  23. Gong Z, Sangram G, Ramakrishna RN, Michael AW, Cristina M, Hirofumi H, Weile W, Sassan S, Yifan Yu, Myneni Ranga B (2014) Estimation of forest aboveground biomass in California using canopy height and leaf area index estimated from satellite data. Remote Sens Environ 151:44–56CrossRefGoogle Scholar
  24. Hamey Leonord GC (2015) A functional approach to border handling in image processing. In: 2015 international conference on digital image computing techniques and application, DICTA 2015, pp 15–22.
  25. Hamilton William R (1866) Elements of quaternions. Longmans, Green and Co., LondonGoogle Scholar
  26. Hunter MO, Keller M, Victoria D, Morton DC (2013) Tree height and tropical forest biomass estimation. Biogeosciences 10:8385–8399CrossRefGoogle Scholar
  27. Karush W (1939) Minima of functions of several variables with inequalities as side constraints. Master’s thesis, Department of Mathematics, University of ChicagoGoogle Scholar
  28. Kearsley E, De Haulleville T, Hufkens K, Kidimbu A, Toirambe B, Baert G, Verbeeck H (2013) Conventional tree height–diameter relationships significantly overestimate aboveground carbon stocks in the Central Congo Basin. Nat Commun. Google Scholar
  29. Keerthi SS, Shevade SK, Bhattacharyya C, Murthy KRK (2001) Improvements to Platt’s SMO algorithm for SVM classifier design. Neural Comput 13:637–649CrossRefGoogle Scholar
  30. Ketterings QM, Coe R, van Noordwijk M, Palm CA (2001) Reducing uncertainty in the use of allometric biomass equations for predicting above-ground tree biomass in mixed secondary forests. For Ecol Manag 146:199–209CrossRefGoogle Scholar
  31. Kuhn HW, Tucker AW (1951) Nonlinear programming. In: Proceedings 2nd Berkeley symposium on mathematical statistics and probabilities. University of California Press, Berkeley, pp 481–492Google Scholar
  32. Luccheseyz L, Mitray SK (2001) Color image segmentation: a state-of-the-art survey. Proc Indian Natl Sci Acad 67:207–221Google Scholar
  33. Meister L, Schaeben H (2005) A concise quaternion geometry of rotations. Math Methods Appl Sci 28:101–126CrossRefGoogle Scholar
  34. Mitchard ET, Saatchi SS, Baccini A, Asner GP, Goetz SJ, Harris NL, Brown S (2013) Uncertainty in the spatial distribution of tropical forest biomass: a comparison of pan-tropical maps. Carbon Balance Manag 8:1–13CrossRefGoogle Scholar
  35. Moxey CE, Sangwine SJ, Ell T (2003) Hypercomplex correlation techniques for vector images. IEEE Trans Signal Process 51:1941–1953CrossRefGoogle Scholar
  36. Mugglestone MA, Renshaw E (1996) A practical guide to the spectral analysis of spatial point processes. Comput Stat Data Anal 21:43–65CrossRefGoogle Scholar
  37. Nagao M, Matsuyama T (1979) Edge preserving smoothing. Comput Graph Image Process 9:394–407CrossRefGoogle Scholar
  38. Noor AI, Mokhtar MH, Rafiqul ZK, Pramod KM (2012) Understanding color model: a review. J Sci Technol 2(265):275Google Scholar
  39. Pei S, Cheng CM (1996) A novel block truncation coding of color images by using quaternion-moment preserving principle. IEEE Int Symp Circuits Syst Atlanta 2:684–687Google Scholar
  40. Pei S, Ding J, Chang J (2001) Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2D complex FFT. IEEE Trans Signal Process 49:2783–2797. CrossRefGoogle Scholar
  41. Picard N, Bosela FB, Rossi V (2014) Reducing the error in biomass estimates strongly depends on model selection. Ann For Sci 72:811–823CrossRefGoogle Scholar
  42. Ploton P, Pélissier R, Proisy C, Flavenot T, Barbier N, Rai SN, Couteron P (2012) Assessing aboveground tropical forest biomass using Google Earth canopy images. Ecol Appl 22:993–1003CrossRefGoogle Scholar
  43. Proisy C, Couteron P, Fromard F (2007) Predicting and mapping mangrove biomass from canopy grain analysis using Fourier-based textural ordination of IKONOS images. Remote Sens Environ 109:379–392CrossRefGoogle Scholar
  44. Re DS, Engel VL, Sousa OLM, Blanco JLA (2015) Tree allometric equations in mixed forest plantations for the restoration of seasonal semi deciduous forest. CERNE 21:133–140. CrossRefGoogle Scholar
  45. Roy PS, Shirish A (1996) Biomass estimation using satellite remote sensing data an investigation on possible approaches for natural forest. J Biosci 21:535–561CrossRefGoogle Scholar
  46. Saatchi SS, Harris NL, Brown S, Lefsky M, Mitchard ET, Salas W, Morel A (2011) Benchmark map of forest carbon stocks in tropical regions across three continents. Proc Natl Acad Sci 108:9899–9904CrossRefGoogle Scholar
  47. Sangwine SJ (1996) Fourier transforms of colour images using quaternions or hypercomplex, numbers. Electron Lett 32:1979–1989CrossRefGoogle Scholar
  48. Sangwine SJ, Ell TA (1999) Hypercomplex auto-and cross- correlation of color images. In: IEEE international conference on image processing (ICIP’99), Kobe, Japan, pp 319–322Google Scholar
  49. Sangwine SJ, Le Bihan N (2013) Quaternion toolbox for Matlab®, Ver.2 with support for octonions, Software Library downloaded 03 June 2013 from
  50. Shi L, Funt B (2005) Quaternion colour texture. In: Proceedings 10th congress of the international color association, GranadaGoogle Scholar
  51. Shuy MJ, Parkkinen J (2012) Fundamentals of color. In: C. Fernandez-Maloigne (ed) Advanced color images processing and analysis, chapter 1. Springer, New YorkGoogle Scholar
  52. Smola AJ, Schölkopf B (1998) A tutorial on support vector regression. Stat Comput 14:199–222CrossRefGoogle Scholar
  53. Tapamo H, Mfopou A, Ngonmang B, Couteron P, Monga O (2014) Linear versus non-linear methods: a comparative study for forest above ground biomass estimation from texture analysis of satellite image. ARIMA 18:114–131Google Scholar
  54. Thenkabail PS, Enclona EA, Ashton MS, Legg C, Minko JDD (2004) Hyperion, IKONOS, ALI, and ETM+ sensors in the study of African rainforests. Remote Sens Environ 90:23–43CrossRefGoogle Scholar
  55. Ustin SL, Gamon JA (2010) Remote sensing of plant functional types. New Phytol. Google Scholar
  56. Vapnik VN (1995) The nature of statistic learning theory. Springer, BerlinCrossRefGoogle Scholar
  57. Vapnik V, Golowich SE, Smola A (1997) Support vector method for function approximation regression estimation and signal processing. Adv Neural Inf Process Syst 9:281–289Google Scholar
  58. Verhegghen A, Mayaux P, De Wasseige C, Defourny P (2012) Mapping Congo basin vegetation types from 300 m and 1 km multi-sensor time series for carbon stocks and forest areas estimation. Biogeosciences 9:5061–5079CrossRefGoogle Scholar
  59. Vieilledent G, Vaudry R, Andriamanohisoa SF, Rakotonarivo OS, Randrianasolo HZ, Razafindrabe HN, Rakotoarivony CB, Ebeling J, Rasamoelina M (2012) A universal approach to estimate biomass and carbon stock in tropical forests using generic allometric models. Ecol Appl 22:572–583CrossRefGoogle Scholar
  60. Willmot CJ, Robeson SM, Matsuura K, Ficklin DL (2015) Assessment of three dimensionless measures of model performance. Environ Model Softw 73:167–173CrossRefGoogle Scholar
  61. Willmott CJ, Robeson SM, Matsuura K (2012) A refined index of model performance. Int J Climatol 32:2088–2094. CrossRefGoogle Scholar
  62. Xu Z, Gao Y, Jin Y (2014) Application of an optimized SVR model of machine learning. J Multimed Ubiquitous Eng 9:67–80CrossRefGoogle Scholar

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.UMMISCO, SAM TeamUniversity of Yaoundé 1YaoundéCameroon
  2. 2.UMI 209, UMMISCOIRDBondyFrance
  3. 3.UMI 209, UMMISCOSorbonne Université, Univ. Paris 06ParisFrance

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