Modeling spatial context (e.g., autocorrelation) is a key challenge in classification problems that arise in geospatial domains. Markov random fields (MRF) is a popular model for incorporating spatial context into image segmentation and land-use classification problems. The spatial autoregression (SAR) model, which is an extension of the classical regression model for incorporating spatial dependence, is popular for prediction and classification of spatial data in regional economics, natural resources, and ecological studies. There is little literature comparing these alternative approaches to facilitate the exchange of ideas (e.g., solution procedures). We argue that the SAR model makes more restrictive assumptions about the distribution of feature values and class boundaries that MRF. The relationship between SAR and MRF is analogous to the relationship between regression and Bayesian classifiers. This paper provides comparisons between the two models using a probabilistic and an experimental framework.
Bibliographical noteFunding Information:
Manuscript received April 18, 2001; revised February 26, 2002. This work was supported in part by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory Cooperative Agreement DAAH04-95-2-0003/Contract DAAH04-95-C-0008. The associate editor coordinating the review of this paper and approving it for publication was Dr. Sankar Basu.
- Markov random fields (MRF)
- Spatial autoregression (SAR)
- Spatial context
- Spatial data mining