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Probabilistic classification of forest structures by hierarchical modelling of the remote sensing process

Satellite sensors observe upwelling radiant flux from the Earth's surface. Classification of forest structures from these measurements is a statistical inference problem. A hierarchical model has been developed by linking several sub-models which represent the image acquisition process and the spatial interaction of the classes. The model for blur assumes the underlying, unobserved image is degraded according to the system point spread function. The model for topographic effects assumes the unblurred pixel values are determined by the corresponding bidirectional reflectance distribution function (BRDF) and the mean spectral reflectance of each class. A discrete Markov random field (MRF) model provides information about the spatial contiguity of the classes. Prior distributions are specified for the mean and covariance parameters. Bayes theorem is used to construct a posterior probability distribution for the classification given the data. Due to the high dimensionality of the resulting MRF, estimates of image attributes are obtained using a Markov chain Monte Carlo technique. The marginal posterior modes (MPM) point estimate minimizes the expected number of misclassifications by maximizing the marginal probability with which each pixel is classified. The advantages of this approach include the ability to specify a unique BRDF for each class and to have posterior probability estimates provide spatially explicit information about the certainty of the MPM estimate. Limitations of the model include the assumptions necessary for modeling bidirectional reflectance, the difficulty of defining classes as an appropriate scale, and assessing the accuracy of probabilistic classifications. Specimen results using Landsat TM data are presented.