FUZZY SUPER-RESOLUTION MAPPING BASED ON MARKOV RANDOM FIELD V.A. Tolpekin and N.A.S. Hamm (presenting author) International Institute for Geo-Information Science and Earth Observation Department of Earth Observation Science P.O. Box 6, 7500 AA Enschede, The Netherlands. e-mail:
[email protected],
[email protected] 1. ABSTRACT Super resolution mapping is a land cover classification technique that produces thematic maps at a finer spatial resolution than the input image [1, 2]. Several super resolution mapping techniques have been proposed. Tatem et al. [3, 4] presented a Hopfield neural network that predicted the location and spatial pattern of class proportions within each pixel. Mertens et al. [5] provided a genetic algorithm for sub-pixel mapping. Mertens et al. [6] developed a spatial attraction models for super resolution mapping. Thornton et al. [7] used pixel swapping technique, based on mathematical morphology, to predict the location of linear sub-pixel features. Kasetkasem et al. [8] proposed using Markov Random Field (MRF) together with simulated annealing for supervised super-resolution mapping. A common assumption of the above mentioned methods is that the pixels at the fine resolution are pure; hence they can be described with a single land cover class. This assumption simplifies the solution of super-resolution mapping problem and results in a crisp land-cover map. However, the super-resolution mapping problem is underdetermined, meaning that it allows multiple plausible solutions that satisfy the problem constrains. It is necessary for users to be informed of the uncertainty in the resulting super-resolution thematic maps. Kasetkasem et al. [8] simulated multiple realizations of the super-resolution map and studied the variance of the resulting kappa statistic. However, this method does not guarantee that all plausible solutions have been found and requires much more computational time. We investigated a fuzzy super-resolution mapping technique where the possibility for each pixel in the resulting land-cover map to belong to each land cover class was expressed as a membership value. We chose a Markov Random Field (MRF) based super resolution mapping. We assigned a membership value equal to the posterior probability that a pixel belongs to a specific class. The advantage of this is twofold. First, it informs the user about the uncertainty in the resulting super-resolution thematic map in the same way as in conventional fuzzy classification. Second, the result presented in fuzzy form allows the opportunity to realize multiple possible outcomes of the super-resolution map. This is of particular value where multiple realizations are required for evaluation of uncertainty in the output of environmental models. We applied the proposed technique to the super-resolution mapping of a synthetic image that incorporated boundary subpixels (as defined in [9]). First, we generated a land cover map with five classes and a pixel size of 0.1 m. Next, this was aggregated to form a fuzzy reference land cover map with a pixel size of 1 m. Here fuzziness results from mixed pixels. Next we generated a multi-spectral image from the reference map through sampling from the multivariate normal distribution with known parameters. This image was aggregated to spatial resolution of 10 m. Next we applied super-resolution mapping on the 10 m resolution multi-spectral images, setting the spatial resolution of the result to 1 m. This result was compared to the reference map at 1 m resolution in terms of mean square error and fuzzy kappa statistic. Crisp super-resolution mapping was performed on the same multi-spectral images for comparison with the fuzzy super-resolution mapping. The fuzzy super resolution mapping yielded a mean square error two times lower than that of the crisp super resolution map. 2. REFERENCES [1] P.M. Atkinson, Remote sensing image analysis : including the spatial domain, chapter Resolution manipulation and subpixel mapping, pp. 51–70, Kluwer Academic, 2004. [2] A. J. Tatem, H. G. Lewis, P. M. Atkinson, and M. S. Nixon, Uncertainty in Remote Sensing and GIS, chapter SuperResolution Land Cover Mapping from Remotely Sensed Imagery using a Hopfield Neural Network, pp. 77–98, John Wiley & Sons, 2003.
[3] A. J. Tatem, H. G. Lewis, P. M. Atkinson, and M. S. Nixon, “Super-resolution target identification from remotely sensed images using a Hopfield neural network,” IEEE Transactions on Geoscience and Remote Sensing, vol. 39, pp. 781–796, 2001. [4] A. J. Tatem, H. G. Lewis, P. M. Atkinson, and M. S. Nixon, “Super-resolution land cover pattern prediction using a Hopfield neural network,” Remote Sensing of Environment, vol. 79, pp. 1–14, 2002. [5] K.C. Mertens, L.P.C. Verbeke, E.I. Ducheyne, and R.R. De Wulf, “Using genetic algorithms in sub-pixel mapping,” International Journal of Remote Sensing, vol. 24, no. 21, pp. 4241–4247, 2003. [6] K.C. Mertens, B. De Baets, L.P.C. Verbeke, and R.R. De Wulf, “A sub-pixel mapping algorithm based on sub-pixel/pixel spatial attraction models,” International Journal of Remote Sensing, vol. 27, no. 15, pp. 3293–3310, 2006. [7] M.W. Thornton, P.M. Atkinson, and D.A. Holland, “Sub-pixel mapping of rural land cover objects from fine spatial resolution satellite sensor imagery using super-resolution swapping,” International Journal of Remote Sensing, vol. 27, no. 3, pp. 473–491, 2006. [8] Teerasit Kasetkasem, Manoj K. Arora, and Pramod K. Varshney, “Super-resolution land cover mapping using a Markov random field based approach,” Remote Sensing of Environment, vol. 96, pp. 302–314, 2005. [9] P. Fisher, “The pixel: a snare and a delusion,” International Journal of Remote Sensing, vol. 18, pp. 679–685, 1997.
