The innermost astronomical unit in protoplanetary disks is a key region for stellar and planet formation, as exoplanet searches have shown a large occurrence of close-in planets that are located within the first au around their host star. We aim to reveal the morphology of the disk inner rim using near-infrared interferometric observations with milli-arcsecond resolution provided by infrared interferometry. We provide reconstructed images of 15 objects selected from the Herbig AeBe survey carried out with PIONIER at the VLTI, using SPARCO. We find that 40% of the systems are centrosymmetric at the angular resolution of the observations. For the rest of the objects, we find evidence for asymmetric emission due to moderate-to-strong inclination of a disk-like structure for 30% of the objects and noncentrosymmetric morphology due to a nonaxisymmetric and possibly variable environment (30%). Among the systems with a disk-like structure, 20% show a resolved dust-free cavity. The image reconstruction process is a powerful tool to reveal complex disk inner rim morphologies. At the angular resolution reached by near-infrared interferometric observations, most of the images are compatible with a centrally peaked emission (no cavity). For the most resolved targets, image reconstruction reveals morphologies that cannot be reproduced by generic parametric models. Moreover, the nonaxisymmetric disks show that the spatial resolution probed by optical interferometers makes the observations of the near-infrared emission sensitive to temporal evolution with a time-scale down to a few weeks. The evidence of nonaxisymmetric emission that cannot be explained by simple inclination and radiative transfer effects requires alternative explanations, such as a warping of the inner disks. Interferometric observations can, therefore, be used to follow the evolution of the asymmetry of those disks at a sub-au scale.
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