Predicting individual pixel error in remote sensing soft classification

Accuracy assessment of remote sensing soft (sub-pixel) classifications is a challenging topic. Previous efforts have focused on constructing a soft classification error matrix and producing summary measures to describe overall and per-class map accuracy. However, these summary assessments do not provide information on the spatial distribution of the soft classification error as distributed at the individual pixel level. This is important because the map error of a given class may vary considerably over different regions. Spatial interpolation has been previously used for predicting soft classification error at the pixel level. Here, we propose two alternative domains for soft classification error interpolation, the spectral and mapped class proportion domains. In the spectral domain we interpolate errors in the classification feature space, whereas in the mapped class proportion domain interpolation takes place in a space with dimensions defined by the mapped class proportions (i.e., the output of the soft classification). The two newly proposed prediction methods (spectral domain and mapped class proportion domain), spatial interpolation, and a summary measure method were evaluated using 23 test regions, each 10 km x 10 km, distributed throughout the United States. These 10 km x 10 km blocks had complete coverage reference data (where the reference classification was determined by manual interpretation) and the predicted error maps were then evaluated by comparing them to these complete coverage reference error maps. Mean absolute error was used to quantify the agreement of the predicted error maps to the reference error maps. The spectral and mapped class proportion methods generally outperformed the spatial interpolation and the summary measure methods both in terms of smaller mean absolute error and visual similarity of predicted error maps to the reference error maps. The superiority of the new methods over spatial interpolation is an important result because spatial interpolation is a familiar method analysts would commonly consider for modeling spatial variation of classification error. The predicted soft classification error maps provide a straightforward visual assessment of the spatial patterns of error that can accompany the original classification products to enhance their value in subsequent analysis and modeling tasks. Furthermore, from the standpoint of implementation, our methods do not require additional datasets; the same test dataset currently used for confusion/error matrix construction can be used for our error interpolation methods.