Abstract: In this paper we propose a denoising algorithm based on L₁ median filtering for noisy sets of points.The proposed algorithm improves the traditional methods to better preserve the surface features and handle well the outliers.Based on the kernel regression theory,we establish a framework for normal mollification.The framework utilizes the Hessian matrix and predicates more accurate normals.Using the framework we present a novel iterative denoising method for point-sampled model based on the classic L₁ median theory.The comparison of our method to the classical mean-shift denoising method and bilateral filtering method are discussed.The experimental results are presented which show the efficiency of the algorithm and the simplicity of implementation.