The paper introduces a new parallel and efficient algorithm for the reinitialization of level set functions on unstructured finite element (FE) meshes in two and three dimensions. The originality of this implementation lies in the use of a direct method enhanced by a k-d tree space partitioning technique. Different test cases illustrate the potential of the method for typical metallurgical and micromechanical problems with isotropic and anisotropic meshes. Comparison with other classical reinitialization methods, such as Hamilton–Jacobi formulations, proves that the proposed method guarantees optimal accuracy together with importantly reduced computational costs.