A new 3-dimensional receiver operating characteristic curve for detection performance analysis

Target detection for remotely sensed imagery has been invasively researched for decades. Many detection algorithms are designed and claimed to be outperform others. In order to make an objective comparison, two issues need to be solved. The first one is to have standardized data sets with accurate ground truth, and the second one is to use objective performance analysis techniques. The Receiver Operating Characteristic (ROC) curve is one of the most recognized tools for detection performance analysis. It is based on binary hypothesis test approach. First it constructs two hypothesis distributions (null and alternative hypotheses) and then draws the ROC curve by calculating all the possible detection probability and false-alarm probability pairs. The larger area under the curve means the better detection performance of the algorithm. But one issue is rarely discussed. In ROC analysis, the alternative hypothesis means target exists, but we seldom discuss how much target is presented. In this paper, we include target abundance as the third dimension to form 3-Dimension ROC. The proposed technique can be used to analyze the performance of detection algorithms or the sensor instruments from the different point of views. It can perform the detection probability versus false-alarm probability test as the original ROC, and it can also be use to estimate the minimum target abundance the algorithm can detect.