Quality assessment of 3D medical images is becoming increasingly important, because of clinical practice rapidly moving
in the direction of volumetric imaging. In a recent publication, three multi-slice channelized Hotelling observer (msCHO)
models are presented for the task of detecting 3D signals in multi-slice images, where each multi-slice image is inspected
in a so called stack-browsing mode. The observer models are based on the assumption that humans observe multi-slice
images in a simple two stage process, and each of the models implement this principle in a different way.
In this paper, we investigate the theoretical performance, in terms of detection signal-to-noise-ratio (SNR) of msCHO
models, for the task of detecting a separable signal in a Gaussian background with separable covariance matrix. We
find that, despite the differences in architecture of the three models, they all have the same asymptotical performance in
this task (i.e., when the number of training images tends to infinity). On the other hand, when backgrounds with nonseparable
covariance matrices are considered, the third model, msCHOc, is expected to perform slightly better than the
other msCHO models (msCHOa and msCHOb), but only when sufficient training images are provided. These findings
suggest that the choice between the msCHO models mainly depends on the experiment setup (e.g., the number of available
training samples), while the relation to human observers depends on the particular choice of the "temporal" channels that
the msCHO models use.