In recent years, implicit functions have drawn attention in the field of 3D reconstruction and have successfully been applied with Deep Learning. However, for incremental reconstruction, implicit function-based registrations have been rarely explored. Inspired by the high precision of deep learning global feature registration, we propose to combine this with distance fields. We generalize the algorithm to a non-Deep Learning setting while retaining the accuracy. Our algorithm is more accurate than conventional models while, without any training, it achieves a competitive performance and faster speed, compared to Deep Learning-based registration models. The implementation is available on github for the research community.