Abstract: Empty-space skipping is an essential acceleration technique for volume rendering. Image-order empty-space skipping is not well suited to GPU implementation, since it must perform checks on, essentially, a per-sample basis, as in kd-tree traversal, which can lead to a great deal of divergent branching at runtime, which is very expensive in a modern GPU pipeline. In contrast, object-order empty-space skipping is extremely fast on a GPU and has negligible overheads compared with approaches without empty-space skipping, since it employs the hardware unit for rasterisation. However, previous object-order algorithms have been able to skip only exterior empty space and not the interior empty space that lies inside or between volume objects.In this paper, we address these issues by proposing a multi-layer depth-peeling approach that can obtain all of the depth layers of the tight-fitting bounding geometry of the isosurface by a single rasterising pass. The maximum count of layers peeled by our approach can be up to thousands, while maintaining 32-bit float-point accuracy, which was not possible previously. By raytracing only the valid ray segments between each consecutive pair of depth layers, we can skip both the interior and exterior empty space efficiently.In comparisons with 3 state-of-the-art GPU isosurface rendering algorithms, this technique achieved much faster rendering across a variety of data sets.