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• HyM3D is an automatic algorithm for the digital 3D reconstruction of a defective neurocranium; the resulting model can be used as a reference for the preoperative design of devices for cranioplasty. • The innovative idea is to retrieve the full shape of the exocranial surface by using an external source to guide the reconstruction actually performed through a surface-interpolation method. • With respect to the existing alternatives, HyM3D does not require any user interaction except for the selection of a point on the edge of the gap to be reconstructed. • The external source used to guide the surface interpolation is attained by interpreting, through statistical methods, the shape information encoded in a set of healthy cranial vaults (according to statistical shape Analysis). • HyM3D has been tested on several test cases, both synthetic and real, proving to be robust and effective in providing consistent results also when facing large defects. The ability to accomplish a consistent restoration of a missing or deformed anatomical area is a fundamental step for defining a custom implant, especially in the maxillofacial and cranial reconstruction where the aesthetical aspect is crucial for a successful surgical outcome. At the same time, this task is also the most difficult, time-consuming, and complicated across the whole reconstruction process. This is mostly due to the high geometric complexity of the anatomical structures, insufficient references, and significant interindividual anatomical heterogeneity. Numerous solutions, specifically for the neurocranium, have been put forward in the scientific literature to address the reconstruction issue, but none of them has yet been persuasive enough to guarantee an easily automatable approach with a consistent shape reconstruction. This work aims to present a novel reconstruction method (named HyM3D) for the automatic restoration of the exocranial surface by ensuring both the symmetry of the resulting skull and the continuity between the reconstructive patch and the surrounding bone. To achieve this goal, the strengths of the Template-based methods are exploited to provide knowledge of the missing or deformed region and to guide a subsequent Surface Interpolation-based algorithm. HyM3D is an improved version of a methodology presented by the authors in a previous publication for the restoration of unilateral defects. Differently from the first version, the novel procedure applies to all kinds of cranial defects, whether they are unilateral or not. The presented method has been tested on several test cases, both synthetic and real, and the results show that it is reliable and trustworthy, providing a consistent outcome with no user intervention even when dealing with complex defects. HyM3D method proved to be a valid alternative to the existing approaches for the digital reconstruction of a defective cranial vault; furthermore, with respect to the current alternatives, it demands less user interaction since the method is landmarks-independent and does not require any patch adaptation. [ABSTRACT FROM AUTHOR]