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Optical Remote Sensing pp 171–206Cite as

A Review of Kernel Methods in Remote Sensing Data Analysis

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Part of the book series: Augmented Vision and Reality ((Augment Vis Real,volume 3))

Abstract

Kernel methods have proven effective in the analysis of images of the Earth acquired by airborne and satellite sensors. Kernel methods provide a consistent and well-founded theoretical framework for developing nonlinear techniques and have useful properties when dealing with low number of (potentially high dimensional) training samples, the presence of heterogenous multimodalities, and different noise sources in the data. These properties are particularly appropriate for remote sensing data analysis. In fact, kernel methods have improved results of parametric linear methods and neural networks in applications such as natural resource control, detection and monitoring of anthropic infrastructures, agriculture inventorying, disaster prevention and damage assessment, anomaly and target detection, biophysical parameter estimation, band selection, and feature extraction. This chapter provides a survey of applications and recent theoretical developments of kernel methods in the context of remote sensing data analysis. The specific methods developed in the fields of supervised classification, semisupervised classification, target detection, model inversion, and nonlinear feature extraction are revised both theoretically and through experimental (illustrative) examples. The emergent fields of transfer, active, and structured learning, along with efficient parallel implementations of kernel machines, are also revised.

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Notes

  1. 1.

    In v-fold, the training set is divided in v subsets, then during v times v − 1 subsets are used for training, and the remaining subset is used for validation. At the end, the parameters that have worked the best in the v subsets are selected.

  2. 2.

    In our case, nearby points are those pixels spectrally similar and thus the assumption is applied to the (high) dimensional space of image pixels.

  3. 3.

    \(\log p(\mathbf{y}|\mathbf{x}) \equiv \log p(\mathbf{y}|\mathbf{x},\varvec{\theta}) = -{\frac{1}{2}}\mathbf{y}^\top(\mathbf{K} + \sigma_n^2\mathbf{I})^{-1}\mathbf{y} - {\frac{1}{2}}\log(det(\mathbf{K} +\sigma_n^2 \mathbf{I})) - {\frac{n}{2}}\log(2\pi).\)

  4. 4.

    More information about the data can be obtained from http://seabass.gsfc.nasa.gov/seabam/seabam.html.

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Acknowledgments

This work was partially supported by projects CICYT-FEDER TEC2009-13696, AYA2008-05965-C04-03, and CSD2007-00018. Valero Laparra acknowledges the support of a Ph.D grant from the Spanish Government BES-2007-16125. The authors would like to thank a number of colleagues and collaborators in the field of kernel methods, and whose insight and points of view are at some extent reflected in this chapter: Dr. Devis Tuia from the University of Lausanne (Switzerland), Dr. Frédéric Ratle from Nuance Communications (Belgium), Dr. Jerónimo Arenas from the University Carlos III de Madrid (Spain), and Prof. Lorenzo Bruzzone from the University of Trento (Italy).

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  1. Image Processing Laboratory, Universitat de València, Catedrático José Beltrán, 2. Paterna, 46980, Valencia, Spain

    Luis Gómez-Chova, Jordi Muñoz-Marí, Valero Laparra, Jesús Malo-López & Gustavo Camps-Valls

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  1. Luis Gómez-Chova
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  1. Geosystems Research Inst., Dept. Electrical & Computer Engineering, Mississippi State University, Mississippi State, 39762, Mississippi, USA

    Saurabh Prasad

  2. Geosystems Research Inst., Dept. Electrical & Computer Engineering, Mississippi State University, Mississippi State, 39762, Mississippi, USA

    Lori M. Bruce

  3. Institut Polytechnique de Grenoble, av. Félix Viallet 46, Grenoble CX 1, 38000, France

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Gómez-Chova, L., Muñoz-Marí, J., Laparra, V., Malo-López, J., Camps-Valls, G. (2011). A Review of Kernel Methods in Remote Sensing Data Analysis. In: Prasad, S., Bruce, L., Chanussot, J. (eds) Optical Remote Sensing. Augmented Vision and Reality, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14212-3_10

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