When photographers and other editors of image material produce an image, they make a statement about what matters by situating some objects in the foreground and others in the background. While this prominence of objects is a key analytical category to qualitative scholars, recent quantitative approaches to automated image analysis have not yet made this important distinction but treat all areas of an image similarly. We suggest carefully considering objects' prominence as an essential step in analyzing images as data. Its modeling requires defining an object and operationalizing and measuring how much attention a human eye would pay. Our approach combines qualitative analyses with the scalability of quantitative approaches. Exemplifying object prominence with different implementations -- object size and centeredness, the pixels' image depth, and salient image regions -- we showcase the usefulness of our approach with two applications. First, we scale the ideology of eight US newspapers based on images. Second, we analyze the prominence of women in the campaign videos of the U.S. presidential races in 2016 and 2020. We hope that our article helps all keen to study image data in a conceptually meaningful way at scale.