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Estimating Markov TransitionsThis work has been accepted for publication in the Journal of Environmental Management (JEM) as of 9 November 2000. Copyright may be transferred without further notice, after which this version may no longer be accessible. AbstractA common technique for modeling and estimating changes between images (such as land cover or land use images) is a Markov process. In its simplest form it assumes each pixel changes its values randomly at constant rates determined by (a) the original pixel value and (b) the new value. The rates are interpreted in terms of land cover change. This short paper addresses two issues raised by work recently published in the JEM. To estimate Markov transition probabilities and to predict future image values currently requires a regular spacing of images over time. The paper completely solves the problem of interpolating transition rates to different time intervals. Second, the possibility of data error (specifically, image mis-registration and pixel mis-classification) creates uncertainty in the estimated transition probabilities. Recently, other researchers have proposed and used a natural method to account for these errors. This paper demonstrates that the natural method is incorrect. The paper suggests some ways to overcome this shortcoming. Investigations using simulated images show that these methods have promise. DownloadEstimating Markov Transitions (PDF format, 62 Kb). |
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