Volume and isosurface rendering are methods of projecting volumetric images to two dimensions for visualisation. These methods are common in medical imaging and scientific visualisation. Head-mounted optical see-through displays have recently become an affordable technology and are a promising platform for volumetric image visualisation. Images displayed on a head-mounted display must be presented at a high frame rate and with low latency to compensate for head motion. High latency can be jarring and may cause cybersickness which has similar symptoms to motion sickness. Volumetric images can be very computationally expensive to render as they often have hundreds of millions of scalar values. Fortunately, certain materials in images such as air surrounding an object boundary are often made transparent and need not be sampled, which improves rendering e?ciency. In our previous work we introduced a novel ray traversal technique for rendering large sparse volumetric images at high frame rates. The method relied on the computation of an occupancy and distance map to speed up ray traversal through empty regions. In this work we achieve higher frame rates than our previous work with an improved method of resuming empty space skipping and the use of anisotropic Chebyshev distance maps. An optimised algorithm for computing Chebyshev distance maps on a graphical processing unit is introduced supporting real-time transfer function editing.