Abstract
Image segmentation persists as a major statistical problem, with the volume and complexity of data expanding alongside new technologies. Land cover classification, one of the largest problems in Remote Sensing, provides an important example of image segmentation whose needs transcend the choice of a particular classification method. That is, the challenges associated with land cover classification pervade the analysis process from data pre–processing to estimation of a final land cover map. Multispectral, multitemporal data with inherent spatial relationships have hardly received adequate treatment due to the large size of the data and the presence of missing values. In this chapter we propose a novel, concerted application of methods which provide a unified way to estimate model parameters, impute missing data, reduce dimensionality, and classify land cover. This comprehensive analysis adopts a Bayesian approach which incorporates prior subject matter knowledge to improve the interpretability, efficiency, and versatility of land cover classification. We explore a parsimonious parametric model whose structure allows for a natural application of principal component analysis to the isolate important spectral characteristics while preserving temporal information. Moreover, it allows us to impute missing data and estimate parameters via expectation-maximization. We employ a spanning tree approximation to a lattice Potts model prior to incorporating spatial relationships in a judiciousway and more efficiently access the posterior distribution of the pixel labels. We achieve exact inference of the labels via the centroid estimator. We demonstrate this series of analysis on a set of MODIS data centered on Montreal, Canada.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Besag, J.: On the statistical analysis of dirty pictures. J. R. Stat. Soc. 48(3), 259–302 (1986). (With discussions).
Bonan, G.B., Oleson, K.W., Vertenstein, M., Levis, S., Zeng, X., Dai, Y., Dickinson, R.E., Yang, Z.L.: The land surface climatology of the community land model coupled to the NCAR community climate model*. J. Clim. 15(22), 3123–3149 (2002)
Carvalho, L.E., Lawrence, C.E.: Centroid estimation in discrete high-dimensional spaces with applications in biology. Proc. Natl. Acad. Sci. 105(9), 3209–3214 (2008)
Crist, E.P., Cicone, R.C.: A physically-based transformation of Thematic Mapper data—The TM Tasseled Cap. IEEE Trans. Geosci. Remote Sens. 22(3), 256–263 (1984)
DeFries, R., Townshend, J.: NDVI-derived land cover classifications at a global scale. Int. J. Remote Sens. 15(17), 3567–3586 (1994)
Dempster, A., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm. J. Royal Stat. Soc. Series B (Methodological) 39(1), 1–38 (1977)
Ek, M., Mitchell, K., Lin, Y., Rogers, E., Grunmann, P., Koren, V., Gayno, G., Tarpley, J.: Implementation of Noah land surface model advances in the National Centers for Environmental Prediction operational mesoscale Eta model. J. Geophys. Res. 108(D22), 885–1 (2003)
Friedl, M.A., Sulla-Menashe, D., Tan, B., Schneider, A., Ramankutty, N., Sibley, A., Huang, X.: MODIS collection 5 global land cover: Algorithm refinements and characterization of new datasets. Remote Sens. Environ. 114, 168–182 (2010)
Glanz, H., Carvalho, L.: An expectation-maximization algorithm for the matrix normal distribution. arXiv preprint arXiv:1309.6609 (2013)
Glanz, H., Carvalho, L., Sulla-Menashe, D., Friedl, M.: A parsimonious model for land cover classification and characterization of training data using multitemporal remotely sensed imagery. Submitted (2014)
Hansen, M., Defries, R., Townshend, J., Sohlberg, R.: Global land cover classification at 1km spatial resolution using a classification tree approach. Int. J. Remote Sens. 21(6–7), 1331–1364 (2000).
Jolliffe, I.: Principal Component Analysis. Wiley, Hoboken (2005)
Lobser, S., Cohen, W.: MODIS tasselled cap: land cover characteristics expressed through transformed MODIS data. Int. J. Remote Sens. 28(22), 5079–5101 (2007)
Moser, G., Serpico, S.B., Benediktsson, J.A.: Land-cover mapping by Markov modeling of spatial–contextual information in very-high-resolution remote sensing images. Proc. IEEE 101(3), 631–651 (2013)
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover, New York (1998)
Potts, R.: Some generalized order-disorder transformations. Proc. Camb. Philos. Soc. 48, 106–109 (1952)
Running, S.W., Coughlan, J.C.: A general model of forest ecosystem processes for regional applications I. Hydrologic balance, canopy gas exchange and primary production processes. Ecol. Model. 42(2), 125–154 (1988)
Schaaf, C., Gao, F., Strahler, A., Lucht, W., Li, X., Tsang, T., Strugnell, N., Zhang, X., Jin, Y., Muller, J., Lewis, P., Barnsley, M., Hobson, P., Disney, M., Roberts, G., Dunderdale, M., Doll, C., d’Entremont, R., Hu, B., Liang, S., J.L., P., Roy, D.: First operational BRDF, Albedo Nadir reflectance products from MODIS. Remote Sens. Environ. 83(1), 135–148 (2002)
Srivastava, M., Khatri, C.: An Introduction to Multivariate Statistics. North Holland, New York (1979)
Acknowledgements
Hunter Glanz was supported by funding from NASA under grant number NNX11AG40G. Luis Carvalho was supported by NSF grant DMS-1107067.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Glanz, H., Carvalho, L. (2015). A Spanning Tree Hierarchical Model for Land Cover Classification. In: Polpo, A., Louzada, F., Rifo, L., Stern, J., Lauretto, M. (eds) Interdisciplinary Bayesian Statistics. Springer Proceedings in Mathematics & Statistics, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-12454-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-12454-4_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12453-7
Online ISBN: 978-3-319-12454-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)