Abstract We present parallel single-pixel imaging (PSI), a photography technique that captures light transport coefficients and enables the separation of direct and global illumination, to achieve 3D shape reconstruction under strong global illumination. PSI is achieved by extending single-pixel imaging (SI) to modern digital cameras. Each pixel on an imaging sensor is considered an independent unit that can obtain an image using the SI technique. The obtained images characterize the light transport behavior between pixels on the projector and the camera. However, the required number of SI illumination patterns generally becomes unacceptably large in practical situations. We introduce local region extension (LRE) method to accelerate the data acquisition of PSI. LRE perceives that the visible region of each camera pixel accounts for a local region. Thus, the number of detected unknowns is determined by local region area, which is extremely beneficial in terms of data acquisition efficiency. PSI possesses several properties and advantages. For instance, PSI captures the complete light transport coefficients between the projector–camera pair, without making specific assumptions on measured objects and without requiring special hardware and restrictions on the arrangement of the projector–camera pair. The perfect reconstruction property of LRE can be proven mathematically. The acquisition and reconstruction stages are straightforward and easy to implement in the existing projector–camera systems. These properties and advantages make PSI a general and sound theoretical model to decompose direct and global illuminations and perform 3D shape reconstruction under global illumination.