Extraction of vegetation from Landsat satellite images using rationalized Haar wavelet algorithm

Document Type : علمی - پژوهشی

Authors

1 Instructor of Geographical Sciences and Social Studies Research Center, Hakim Sabzevari University

2 Assistant Professor, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University

Abstract

This study aims to provide a computational-approximate algorithm based on Rationalized Haar (RH) to estimate the vegetation of the Landsat image using reflecting this phenomenon in the near-infrared band. This band is in the RGB color combination and located in the R section.This algorithm, using Digital Number (DN) vegetation in 200 selected pixels of R band (infrared band) from the study area, tries to extract the features and vegetation of the whole study area. The number of selected pixels is distributed uniformly and only covers the vegetation.Due to using the matrix format in the input data, first vegetation reflection matrices for 4 and 8 wavelets are constructed using the assumed 200 pixels. Then, these matrices are extended to 16 and 64 parts respectively, through blocking the Landsat image of the region.Each matrix element represents the average vegetation of the area in its corresponding block. Then, by introducing an efficient mathematical equation, the vegetation of the entire study area is extracted. In addition, each pixel is reconstructed. Due to matrix calculations, speed and accuracy of calculations at the pixel scale will be listed as advantage of this approach.In this study, vegetation extraction with 4 and 8 RH Wavelets was performed with 75 and 87.5% accuracy, respectively. As the number of wavelets increases, the accuracy of the RH wavelet algorithm increases. However, rounding error and the increase in computational cost in high number of wavelet can be listed as disadvantage of this method. Such that, time and space memory will be increased exponentially. In remote sensing, extraction techniques such as classification have been proposed by remote sensing software. The accuracy of vegetation pixel extracted using this approach will be as advantage in comparison with those common methods. In processing and analytical techniques (for vegetation extraction and classification) in remote sensing, many pixels contain vegetation depicted as single or clustered (but in small numbers) while, in other classes such as barren or Urban land will be merged, which RH wavelet overcomes this shortcoming.

Keywords


باغانی، ا.، 1392، کاربرد قضیه نقطه ثابت در معادلات انتگرالی و تحلیل خطای آن، پایان نامه دکتری، دانشگاه فردوسی مشهد.  
قاسمیان یزدی، م.ح.، 1381، پردازش و تفسیر تصاویر دیجیتال در سنجش از دور، انتشارات دانشگاه تربیت مدرس، تهران.
رضائی، ی. و فاطمی، س.ب.، 1385، مبانی سنجش از دور، انتشارات آزاده، تهران.
Atkinson K.E., 1997, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge.
Aziz, I. & Islam, S., 2013, New Algorithms for the Numerical Solution of Nonlinear Fredholm and Volterra Integral Equations Using Haar Wavelets, Journal of Computational and Applied Mathematics, 239: 333–345.
 
Babolian, E. & Shahsavaran, A., 2009, Numerical Solution of Nonlinear Fredholm Integral Equations of the Second Kind Using Haar Wavelets, Journal of Computational and Applied Mathematics, 225: 87–95.
Berenguer, M.I., Gamez, D., Garralda Guillem, A.I. & Serrano Perez, M.C., 2010, Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems, Abstract and Applied Analysis, Article ID 135216.
Daubechies, I., Orthonormal Bases of Compactly Supported Wavelets, 1988, Communications on Pure and Applied Mathematics, 41: 909–996.
Daubechies, I., 1992, Ten Lectures on Wavelets, SIAM Publications, Philadelphia.
Grossmann, A. & Morlet, J., 1984, Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape, SIAM Journal on Mathematical Analysis, 15: 723–736.
Haar, A., 1910, Zur Theorie der orthogonalen funktionen systeme, Mathematische Annalen, 69: 331–371.
Maleknejad, K. & Aghazadeh, N., 2005, Numerical Solution of Volterra Integral Equations of the Second Kind with Convolution Kernel by Using Taylor-Series Expansion Method, Applied Mathematics and Computation, 161: 915–922.
Maleknejad, K. & Mirzaee, F., 2005, Using Rationalized Haar Wavelet for Solving Linear Integral Equations, Applied Mathematics and Computation, 160: 579–587.
Mallat, S., 1988, Multiresolution Representation and Wavelets, Ph.D. Thesis, University of Pennsylvania.
Mallat, S., 1989, A Theory for Multiresolution Signal Decomposition: The Wavelet Representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11: 678–693.
Meyer, Y., 1993, Wavelets, Algorithms and Applications, SIAM Publications, Philadelphia.
Meyer, Y., 1993, Wavelets and Operators, Cambridge University Press, Cambridge.
J. Morlet, J., Arens, G., Fourgeau, E. & Giard, D., 1982, Wave Propagation and Sampling Theory, Part I: Complex Signal Land Scattering in Multilayer Media, Journal of Geophysical Research, 47: 203–221.   
Ordokhani, Y., 2006, Solution of Nonlinear Volterra-Fredholm-Hammerstein Integral Equations via Rationalized Haar Functions, Applied Mathe-matics and Computation,180: 436–443.
Saeedi, H., Mollahasani, N., Moghadam, M.M. & Chuev, G.N., 2011, An Operational Harr Wavelet Method for Solving Fractional Volterra Integral Equations, International Journal of Applied Mathematics and Computer Science, 21: 535–547.