We present a high-performance, graphics processing unit (GPU)-based framework for the efficient analysis and visualization of (nearly) terabyte (TB)-sized 3-dimensional images. Using a cluster of 96 GPUs, we demonstrate for a 0.5 TB image: (1) volume rendering using an arbitrary transfer function at 7--10 frames per second; (2) computation of basic global image statistics such as the mean intensity and standard deviation in 1.7 s; (3) evaluation of the image histogram in 4 s; and (4) evaluation of the global image median intensity in just 45 s. Our measured results correspond to a raw computational throughput approaching one teravoxel per second, and are 10--100 times faster than the best possible performance with traditional single-node, multi-core CPU implementations. A scalability analysis shows the framework will scale well to images sized 1 TB and beyond. Other parallel data analysis algorithms can be added to the framework with relative ease, and accordingly, we present our framework as a possible solution to the image analysis and visualization requirements of next-generation telescopes, including the forthcoming Square Kilometre Array pathfinder radiotelescopes.