Psychophysical validation of the Hotelling trace criterion as a metric for system performance

The Hotelling trace criterion (HTC) is a measure of class separability used in pattern recognition to find a set of linear features that optimally separate two classes of objects. We use the HTC here not as a figure of merit for features, but as a figure of merit for characterizing imaging systems. In an earlier study, a set of images, created by overlapping ellipses, was used to simulate images of livers, with and without tumors, with noise and blur added to each image. Using the ROC parameter d_a as our measure, we found that the ability of the HTC to separate these images into their correct classes, by detecting the presence or absence of a tumor, has a correlation of 0.988 with the ability of humans to separate the same two classes of objects. In our most recent observer study, we used a mathematical model of normal and diseased livers, and of the imaging system to generate a realistic set of liver images. These images simulate those a physician would use in making a diagnosis, yet we have control over the disease state of the liver, and hence the object class it belongs to, as well as the amount of degradation added to the image from the imaging system. When an observer study was performed with these images we found the performance of the HTC to have a correlation of 0.829 with the performance of the human observers, with d_a as our measure of performance.