This study investigates whether an automatic anonymization algorithm that takes as input a 3D model of a human face can produce an output model exempt from General Data Protection Regulation (GDPR) biometric data definition. The algorithm first uses Random Sample Consensus (RANSAC) for registering the source point cloud globally to an oriented template. Next, the alignment is refined using an Iterative Closest Point (ICP) technique. Secondly, a subset of the source point cloud is created using a fixed radius vector on each template point resulting in the corresponding face contour. Finally, the algorithm uses a point cloud template to remove the unnecessary facial features and converts the point cloud to a mesh. The quality of the anonymization has been evaluated using a survey assessment of 100 participants. The latter resulted in half of the participants failing to recognize any of the anonymized models, one-fifth scoring one out of four correct. Only 2% correctly associated all the models to the right individual.