We introduce a robust and high order strategy to perform the reinitialization in a level set framework. The reinitialization by closest-points (RCP) method is based on geometric considerations. It relies on a gradient descent to find the closest points at the interface in order to solve the eikonal equation and thus reinitializing the level set field. Furthermore, a new algorithm, also based on a similar geometric approach, is introduced to detect precisely all the ill-defined points of the level set. These points, also referred to as kinks, can mislead the gradient descent and more widely impact the accuracy of level set methods. This algorithm coupled with the precise computation of the closest points of the interface, permits the novel method to be robust and accurate even when performing the reinitialization every time step after solving the advection equation. Furthermore, they both require very few given parameters with the advantage of being based on a geometrical approach and independent of the application. The proposed method was tested on various benchmarks, and demonstrated equivalent or even better results compared to solving the Hamilton-Jacobi equation.< Leer menos