Depth maps are used in many applications, e.g. 3D television, stereo matching, segmentation, etc. Often, depth maps are
available at a lower resolution compared to the corresponding image data. For these applications, depth maps must be
upsampled to the image resolution. Recently, joint bilateral filters are proposed to upsample depth maps in a single step.
In this solution, a high-resolution output depth is computed as a weighted average of surrounding low-resolution depth
values, where the weight calculation depends on spatial distance function and intensity range function on the related
image data. Compared to that, we present two novel ideas. Firstly, we apply anti-alias prefiltering on the high-resolution
image to derive an image at the same low resolution as the input depth map. The upsample filter uses samples from both
the high-resolution and the low-resolution images in the range term of the bilateral filter. Secondly, we propose to
perform the upsampling in multiple stages, refining the resolution by a factor of 2×2 at each stage. We show
experimental results on the consequences of the aliasing issue, and we apply our method to two use cases: a high quality
ground-truth depth map and a real-time generated depth map of lower quality. For the first use case a relatively small
filter footprint is applied; the second use case benefits from a substantially larger footprint. These experiments show that
the dual image resolution range function alleviates the aliasing artifacts and therefore improves the temporal stability of
the output depth map. On both use cases, we achieved comparable or better image quality with respect to upsampling
with the joint bilateral filter in a single step. On the former use case, we feature a reduction of a factor of 5 in
computational cost, whereas on the latter use case, the cost saving is a factor of 50.