In recent years a number of researchers have found scaling power spectra in natural images (i.e., the spectrum takes the form of a power-law). This result is surprisingly robust given the variety in each team's choice of image calibration and subject matter. We propose that the salient universal structure present in natural images is their composition of independent occluding objects. In such a world the correlation function, and thus the power spectrum, is generated by two underlying causes: the distribution of object to object transitions, and the correlations present within objects. We show that a power-law distribution of apparent object sizes combined with strongly correlated intra-object structure gives rise to the ubiquitous power-law spectrum in natural scenes. By generating images from occluding square objects we can show definitively that it is not the 1/k2 spectrum of individual edges but rather the distribution of object sizes which causes the scaling in natural images. We demonstrate also that recent measurements of spatio-temporal natural image spectra can be reproduced by such a segmentation of images into independent moving objects.