Purpose: In the early development of new imaging modalities - such as tomosynthesis and cone-beam CT (CBCT) - an accurate predictive model for imaging performance is particularly valuable in identifying the physical factors that govern image quality and guiding system optimization. In this work, a task-based cascaded systems model for detectability index is proposed that describes not only the signal and noise propagation in the 2D (projection) and 3D (reconstruction) imaging chain but also the influence of background anatomical noise. The extent to which generalized detectability index provides a valid metric for imaging performance was assessed through direct comparison to human observer experiments. Methods: Detectability index (d') was generalized to include anatomical background noise in the same manner as the generalized noise-equivalent quanta (NEQ) proposed by Barrett et al. (Proc. SP1E Med. Imaging, Vol. 1090, 1989). Anatomical background noise was measured from a custom phantom designed to present power-law spectral density comparable to various anatomical sites (e.g., breast and lung). Theoretical calculations of d' as a function of the source-detector orbital extent (θtot) was obtained from a 3D cascaded systems analysis model for tomosynthesis and cone-beam CT (CBCT). Four model observers were considered in the calculation of d': prewhitcning (PW), non-prewhitcning (NPW), prewhitcning with eye filter and internal noise (PWE), and non-prcwhitening with eye filter and internal noise (NPWE). Human observer performance was measured from 9AFC tests for a variety of idealized imaging tasks presented within a clutter phantom. Theoretical results (d') were converted to area under the ROC curve (Az) and compared directly to human observer performance as a function of imaging task and orbital extent. Results: Theoretical results demonstrated reasonable correspondence with human observer response for all tasks across the continuum in θtot ranging from low-angle tomosynthesis (θ tot ∼10°) to CBCT (θtot ∼180°). Both theoretical and experimental Az were found to increase with acquisition angle, consistent with increased rejection of out-of-plane clutter for larger tomosynthesis angle. Of the four theoretical model observers considered, the prewhitening models tended to overestimate real observer performance, while the non-prewhitening models demonstrated reasonable agreement. Conclusions: Generalized detectability index was shown to provide a meaningful metric for imaging performance, helping to bridge the gap between real observer performance and prevalent Fourier-based metrics based in first principles of spatial-frequency-dcpendent NEQ and imaging task.