A 'region' is an important concept in interpreting 3D point cloud data since regions may correspond to objects in a scene. To correctly interpret 3D point cloud data, we need to partition the dataset into regions that correspond to objects or parts of an object. In this paper, we present a region growing approach that combines global (topological) and local (color, surface normal) information to segment 3D point cloud data. Using ideas from persistent homology theory, our algorithm grows a simplicial complex representation of the point cloud dataset. At each step in the growth process we compute the zeroth homology group of the complex, which corresponds to the number of connected components, and use color and surface normal statistics to build regions. Lastly, we extract out the segmented regions of the dataset. We show that this method provides a stable segmentation of point cloud data in the presence of noise and poorly sampled data, thus providing advantages over contemporary region-based segmentation techniques.