Use of the Bradley–Terry Model to Quantify Association in Remotely Sensed Images

Thematic maps prepared from remotely sensed images require a statistical accuracy assessment. For this purpose, the -statistic is often used. This statistic does not distinguish between whether one unit is classified as another, or vice versa. In this paper, the Bradley–Terry (BT) model is applied for accuracy assessment. This model compares categories pairwise. The probability of one class over another class is estimated as well as the expected values of class pixels. The study is illustrated with an Advanced Spaceborne Thermal Emission and Reflection Radiometer image from the Netherlands, to which a maximum-likelihood classification with the Euclidean distance is applied. An error matrix is generated using an IKONOS image from the same area as ground truth. It is shown to which degree the BT model extends the -statistic. A comparison with the Mahalanobis distance is made. Standardization is carried out to overcome problems emerging from the fact that a common BT model does not include the number of correctly classified pixels. The study shows how the BT model serves as an alternative to the usual -statistic.