Typical time intervals between acquisitions of 3D images of the same cell in live cell imaging are in the orders of minutes. In the meantime the live cell can move in a water basin on the stage. This movement can hamper the studies of intranuclear processes. We propose a fast point-based image registration method for the suppression of the movement of a cell as a whole in the image data. First, centroids of certain intracellular objects are computed for each image in a time-lapse series. Then, a matching between the centroids, which have the maximal number of pairs, is sought between consecutive point-sets by a 3D extension of a 2D fast point pattern matching method, which is invariant to rotation, translation, local distortion and extra/missing points. The proposed 3D extension assumes rotations only around the z-axis to retain the complexity of the original method. The final step involves computing the optimal fully 3D transformation between images from corresponding points in the least squares manner. The robustness of the method was evaluated on generated data. The results of simulations show that the method is very precise and its correctness can be estimated. This article also presents two practical application examples, namely the registration of images of HP1 domains, and the registration of images of telomeres. More than 97% of time-consecutive images were successfully registered. The results show that the method is very well suited to live cell imaging.