In this paper, we address the problem of 3D object categorization for point cloud data. With the availability of inexpensive scanning devices and powerful computational resources, there is a rapid growth of point cloud data. This necessitates efficient classification techniques which form the basis for analysis and processing of 3D point cloud data. In order to address the classification problem, we propose a 3D object categorization framework for both rigid and non-rigid objects. Initially, the proposed approach extracts the feature descriptors using improved wave kernel signature by approximating Laplace-Beltrami operator on point cloud data for non-rigid objects. For rigid objects, our approach uses the geometric features, namely, metric tensor and Christoffel symbols by modifying the geodesic distance computation. These feature descriptors are then represented using bag-of-features and improved Fisher vector encoding techniques. Finally, the support vector machine classifies the 3D objects into predefined set of classes. We also provide an exhaustive performance evaluation of the proposed 3D object categorization framework on state-of-the-art datasets, namely, SHREC'10, SHREC'11, SHREC'12, SHREC'15 and Princeton Shape Benchmark. The evaluation results reveal that the proposed approach outperforms the existing object categorization methods for both rigid and non-rigid 3D objects.