Here, we mapped fMRI responses to incrementally changing shapes along a continuous 3D morph, ranging from a head ("face") to a house ("place"). The response to each shape was mapped independently by using single-stimulus imaging, and stimulus shapes were equated for lower-level visual cues. We measured activity in 2-mm samples across human inferior temporal cortex from the fusiform face area (FFA) (apparently selective for faces) to the parahippocampal place area (PPA) (apparently selective for places), testing for (i) incremental changes in the topography of FFA and PPA (predicted by the continuous-mapping model) or (ii) little or no response to the intermediate morphed shapes (predicted by the category model). Neither result occurred; instead, we found approximately linearly graded changes in the response amplitudes to graded-shape changes, without changes in topography-similar to visual responses in different lower-tier cortical areas.