Three-dimensional (3D) imaging has recently been applied to human gesture recognition using depth maps from RGB-D sensors. An alternative which has been scarcely explored is 3D Integral Imaging, which has shown to give very competitive results in object reconstruction and recognition tasks, even under challenging conditions (e.g. low illumination, occlusions). Integral Imaging has some remarkable advantages over other sensors that may give 3D information (like RGB-D sensors). One of the most important ones is its long range working capability, which stands out even more when compared against other sensors that lose their capabilities for depths of 2m or more. In this paper we present results corresponding to the application of the integral imaging 3D acquisition technique for the recognition of human gestures, when there are occlusions that may hinder the recognition capability. We also present results comparing its capability against that given by an RGB-D sensor (Kinect) and that obtained when only one of the cameras in the camera array is used. Our results show that Integral Imaging compares more or less similarly to Kinect and the monocular case when there are not occlusions, but much more favorably when there are. We also show that the camera spatial resolution may be an issue to account for, when we refer to gesture recognition under occlusions, for the monocular case, but it is less sensitive for the Integral Imaging case, because the features that are extracted from Integral Imaging seem to be more descriptive and discriminative than for the monocular counterpart case.