1. A computer-implemented method for monitoring a characteristic of a specimen, comprising: determining a property of individual pixels on the specimen using output generated by inspecting the specimen with an inspection system; determining a characteristic of individual regions on the specimen using the properties of the individual pixels in the individual regions, wherein the characteristic of the individual regions comprises a statistic of the properties of the individual pixels within the individual regions; determining the characteristic of the specimen, wherein the characteristic of the specimen comprises a specimen-level signature in the statistics for the individual regions; monitoring the characteristic of the specimen based on the characteristics of the individual regions; and performing correlation analysis of the properties of the individual pixels in two or more die on the specimen to identify portions of the two or more die on the specimen in which the properties of the individual pixels are correlated as locations of a potential systematic defect causing mechanism on the specimen, wherein locations in the two or more die on the specimen at which the properties of the individual pixels vary indicate that geometries at the locations are not susceptible to a systematic defect causing mechanism.