We propose a robust method for surface mesh reconstruction from unorganized, unoriented, noisy and outlier-ridden 3D point data. A kernel-based scale estimator is introduced to estimate the scale of inliers of the input data. The best tangent planes are computed for all points based on mean shift clustering and adaptive scale sample consensus, followed by detecting and removing outliers. Subsequently, we estimate the normals for the remaining points and smooth the noise using a surface fitting and projection strategy. As a result, the outliers and noise are removed and filtered, while the original sharp features are well preserved. We then adopt an existing method to reconstruct surface meshes from the processed point data. To preserve sharp features of the generated meshes that are often blurred during reconstruction, we describe a two-step approach to effectively recover original sharp features. A number of examples are presented to demonstrate the effectiveness and robustness of our method.