The standard approach to signal difference-to-noise ratio (SDNR) analysis requires a region of interest (ROI) positioned within the object to measure signal-difference, restricting this metric to flat-topped objects with large, sharply delineated areas. This work develops a generalized expression for SDNR (SDNR _g ) calculated from a ROI encompassing the object. Signal power, defined as the deviation of pixel values from the mean background due to the object, is used instead of signal-difference. Comparison was first made by simulating ideal flat-topped discs with sharp edges and diameters between 1 and 80 pixels, into a uniformly noisy background using a known signal-difference. For discs covering more than 20 pixels, SDNR _g and standard SDNR (SDNR _st ) were within 3%, while for discs of less than 20 pixels, SDNR _g was within 26% of the truth compared to 58% for SDNR _st . Generalized and standard SDNR were compared for radiography images of three different phantoms with microcalcification-like objects (MTM-100 phantom), hemispheric objects of different thicknesses with a Gaussian intensity distribution and mammography quality control (QC) images. Applied to Gaussian details, SDNR _g was between 20% and 45% higher than SDNR _st , depending on object thickness, while for the QC images, SDNR _g was with 1.7% of the standard SDNR. Compared to the standard SDNR, SDNR _g is applicable to non-uniform signals, where an explicit contrast measurement is not suitable, and has improved accuracy when assessing SDNR of small objects.