Modern remote sensing technologies such as three-dimensional (3D) laser scanners and image-based 3D scene reconstruction are in increasing demand for applications in civil infrastructure design, maintenance, operation, and as-built construction verification. The complex nature of the 3D point clouds these technologies generate, as well as the often massive scale of the 3D data, make it inefficient and time consuming to manually analyze and manipulate point clouds, and highlights the need for automated analysis techniques. This paper presents one such technique, a new region growing algorithm for the automated segmentation of both planar and non-planar surfaces in point clouds. A core component of the algorithm is a new point normal estimation method, an essential task for many point cloud processing algorithms. The newly developed estimation method utilizes robust multivariate statistical outlier analysis for reliable normal estimation in complex 3D models, considering that these models often contain regions of varying surface roughness, a mixture of high curvature and low curvature regions, and sharp features. An adaptation of Mahalanobis distance, in which the mean vector and covariance matrix are derived from a high-breakdown multivariate location and scale estimator called Deterministic MM-estimator (DetMM) is used to find and discard outlier points prior to estimating the best local tangent plane around any point in a cloud. This approach is capable of more accurately estimating point normals located in highly curved regions or near sharp features. Thereafter, the estimated point normals serve a region growing segmentation algorithm that only requires a single input parameter, an improvement over existing methods which typically require two control parameters. The reliability and robustness of the normal estimation subroutine was compared against well-known normal estimation methods including the Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) estimators, along with Maximum Likelihood Sample Consensus (MLESAC). The overall region growing segmentation algorithm was then experimentally validated on several challenging 3D point clouds of real-world infrastructure systems. The results indicate that the developed approach performs more accurately and robustly in comparison with conventional region growing methods, particularly in the presence of sharp features, outliers and noise.