Signals acquired by sensors in the real world are non-linear combinations, requiring non-linear mixture models to describe the resultant mixture spectra for the endmember’s (pure pixel’s) distribution. This communication discusses inferring class fraction through a novel hybrid mixture model (HMM). HMM is a three-step process, where the endmembers are first derived from the images themselves using the N-FINDR algorithm. These endmembers are used by the linear mixture model (LMM) in the second step that provides an abundance estimation in a linear fashion. Finally, the abundance values along with the training samples representing the actual ground proportions are fed into neural network based multi-layer perceptron (MLP) architecture as input to train the neurons. The neural output further refines the abundance estimates to account for the non-linear nature of the mixing classes of interest. HMM is first implemented and validated on simulated hyper spectral data of 200 bands and subsequently on real time MODIS data with a spatial resolution of 250 m. The results on computer simulated data show that the method gives acceptable results for unmixing pixels with an overall RMSE of 0.0089 ± 0.0022 with LMM and 0.0030 ± 0.0001 with the HMM when compared to actual class proportions. The unmixed MODIS images showed overall RMSE with HMM as 0.0191 ± 0.022 as compared to the LMM output considered alone that had an overall RMSE of 0.2005 ± 0.41, indicating that individual class abundances obtained from HMM are very close to the real observations.
References
[1]
Guilfoyle, K.J.; Althouse, M.L.; Chang, C.-I. A quantitative and comparative analysis of linear and nonlinear spectral mixture models using radial basis neural networks. IEEE Trans. Geosci. Remote Sens. 2001, 39, 2314–2318, doi:10.1109/36.957296.
[2]
Atkinson, P.M.; Cutler, M.E.J.; Lewis, H. Mapping sub-pixel proportional land cover with AVHRR imagery. Int. J. Remote Sens. 1997, 18, 917–935, doi:10.1080/014311697218836.
Kumar, U.; Kerle, N.; Ramachandra, T.V. Constrained linear spectral unmixing technique for regional land cover mapping using MODIS data. In Innovations and Advanced Techniques in Systems, Computing Sciences and Software Engineering; Elleithy, K., Ed.; Springer: Berlin, Germany, 2008; pp. 87–95.
[5]
Foody, G.M.; Cox, D.P. Subpixel land cover composition estimation using a linear mixture model and fuzzy membership functions. Int. J. Remote Sens. 1994, 15, 619–631, doi:10.1080/01431169408954100.
[6]
Kanellopoulos, I.; Varfis, A.; Wilkinson, G.G.; Megier, J. Land-cover discrimination in SPOT imagery by artificial neural network-a twenty class experiment. Int. J. Remote Sens. 1992, 13, 917–924, doi:10.1080/01431169208904164.
Ju, J.; Kolaczyk, E.D.; Gopal, S. Gaussian mixture discriminant analysis and sub-pixel and sub-pixel land cover characterization in remote sensing. Remote Sens. Environ. 2003, 84, 550–560, doi:10.1016/S0034-4257(02)00172-4.
[9]
Arai, K. Non-linear mixture model of mixed pixels in remote sensing satellite images based in Monte Carlo simulation. Adv. Space Res. 2008, 42, 1715–1723, doi:10.1016/j.asr.2007.04.096.
[10]
Mustard, J.F.; Sunshine, J.M. Spectral analysis for Earth science: investigations using remote sensing data. In Remote Sensing for the Earth Sciences: Manual of Remote Sensing, 3rd; Rencz, A.N., Ed.; John Wiley & Sons: New York, NY, USA, 1999; Volume 3, pp. 251–306.
[11]
Adams, J.B.; Gillespie, A.R. Remote Sensing of Landscapes with Spectral Images: A Physical Modeling Approach; Cambridge University Press: New York, NY, USA, 2006.
[12]
Plaza, J.; Martinez, P.; Pérez, R.; Plaza, A. Nonlinear neural network mixture models for fractional abundance estimation in AVIRIS Hyperspectral Images. In Proceedings of the NASA Jet Propulsion Laboratory AVIRIS Airborne Earth Science Workshop, Pasadena, CA, USA, 31 March–2 April 2004; pp. 1–12.
[13]
Carpenter, G.A.; Gopal, S; Macomber, S.; Martens, S.; Woodcock, C.E. A neural network method for mixture estimation for vegetation mapping. Remote Sens. Environ. 1999, 70, 138–152.
[14]
Cantero, M.C.; Pérez, R.; Martínez, P.; Aguilar, P.L.; Plaza, J.; Plaza, A. Analysis of the behaviour of a neural network model in the identification and quantification of hyperspectral signatures applied to the determination of water quality. In Chemical and Biological Standoff Detection II, Proceedings of SPIE Optics East Conference, Philadelphia, PA, USA, 25–28 October 2004; Jensen, J.O., Thériault, J.-M., Eds.; SPIE: Bellingham, WA, USA, 2004; pp. 174–185.
[15]
Shimabukuro, Y.E.; Smith, A.J. The least-squares mixing models to generate fraction images derived from remote sensing multispectral data. IEEE Trans. Geosci. Remote Sens. 1991, 29, 16–20, doi:10.1109/36.103288.
[16]
Liu, W.; Gopal, S.; Woodcock, C. ARTMAP Multisensor-resolution framework for land cover characterization. In Proceedings 4th Annual Conference information fusion, Montreal, Canada, 7–10 August, 2001; pp. 11–16.
[17]
Liu, W.; Seto, K.; Wu, E.; Gopal, S.; Woodcock, C. ART-MMAP: A neural network approach to subpixel classification. IEEE Trans. Geosci. Remote Sens. 2004, 42, 1976–1983, doi:10.1109/TGRS.2004.831893.
[18]
Winter, M.E. N-FINDR: An algorithm for fast autonomous spectral end-member determination in hyperspectral data. In Proceedings of the SPIE: Imaging Spectrometry V; Descour, M.R., Shen, S.S., Eds.; SPIE: Bellingham, WA, USA, 1999; Volume 3753, pp. 266–275.
[19]
Chang, C.-I. Orthogonal Subspace Projection (OSP) Revisited: A comprehensive study and analysis. IEEE Trans. Geosci. Remote Sens. 2005, 43, 502–518, doi:10.1109/TGRS.2004.839543.
Crippen, R.E.; Bloom, R.G. Unveiling the lithology of vegetated terrains in remotely sensed imagery via forced decorrelation. In Proceedings of the Thirteenth International Conference on Applied Geologic Remote Sensing, Vancouver, Canada, 1–3 March 1999; p. 150.
[22]
Tu, T.-M.; Chen, C.-H.; Chang, C.-I. A noise subspace projection approach to target signature detection and extraction in an unknown background for hyperspectral images. IEEE Trans. Geosci. Remote Sens. 1998, 36, 171–181, doi:10.1109/36.655327.
[23]
Settle, J.J. On the relationship between spectral unmixing and subspace projection. IEEE Trans. Geosci. Remote Sens. 1996, 34, 1045–1046, doi:10.1109/36.508422.
[24]
Nielsen, A.A. Spectral mixture analysis: Linear and semi-parametric full and iterated partial unmixing in multi-and hyperspectral image data. Int. J. Comput. Vis. 2001, 42, 17–37, doi:10.1023/A:1011181216297.
[25]
Haykin, S. Neural Networks: A Comprehensive Foundation; Macmillan: New York, NY, USA, 1998.
[26]
Duda, R.O.; Hart, P.E.; Stork, D.G. Pattern Classification; Wiley: Indianapolis, IN, USA, 2000; pp. 517–598.
[27]
Kavzoglu, T.; Mather, P.M. The use of backpropagating artificial neural networks in land cover classification. Int. J. Remote Sens. 2003, 24, 4907–4938, doi:10.1080/0143116031000114851.
[28]
Mas, J.F. Mapping land use/cover in a tropical coastal area using satellite sensor data, GIS and artificial neural networks. Estuar. Coast. Shelf Sci. 2003, 59, 219–230.
Kumar, U.; Raja, K.S.; Mukhopadhyay, C.; Ramachandra, T.V. A Multi-layer Perceptron based Non-linear Mixture Model to estimate class abundance from mixed pixels. In Proceedings of the 2011 IEEE Students’ Proceedings of the 2011 IEEE Students’ Technology Symposium, Indian Institute of Technology, Kharagpur, India, 14–16 January 2011; pp. 148–153.
[31]
Jet Propulsion Laboratory (JPL) Homepage. Available online: http://speclib.jpl.nasa.gov/ (accessed on 27 July 2009).
[32]
Plaza, J.; Plaza, A.; P’erez, R.; Martinez, P. Joint linear/nonlinear spectral unmixing of hyperspectral image data. In Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS'07), Barcelona, Spain, 23–27 July 2007; pp. 4037–4040.
[33]
Plaza, J.; Plaza, A.; Perez, R.; Martinez, P. On the use of small training sets for neural network-based characterization of mixed pixels in remotely sensed hyperspectral images. Pattern Recognition 2009, 42, 3032–3045.
