While the structural complexity of cometary comae is already recognizable from telescopic observations, the innermost region, within a few radii of the nucleus, was not resolved until spacecraft exploration became a reality. The dust coma displays jet-like features of enhanced brightness superposed on a diffuse background . Some features can be traced to specific areas on the nucleus, and result conceivably from locally enhanced outgassing and/or dust emission. However, diffuse or even uniform activity over topographic concavity can converge to produce jet-like features. Therefore, linking observed coma morphology to the distribution of activity on the nucleus is difficult. Here, we study the emergence of dust activity at sunrise on comet 67P/Churyumov-Gerasimenko using high-resolution, stereo images from the OSIRIS camera onboard the Rosetta spacecraft, where the sources and formation of the jet-like features are resolved. We perform numerical simulations to show that the ambient dust coma is driven by pervasive but non-uniform water outgassing from the homogeneous surface layer. Physical collimations of gas and dust flows occur at local maxima of insolation and also via topographic focusing. Coma structures are projected to exhibit jet-like features that vary with the perspective of the observer. For an irregular comet such as 67P/Churyumov-Gerasimenko, near-nucleus coma structures can be concealed in the shadow of the nucleus, which further complicates the picture.