  Depth map super-resolution (DSR) has been a fundamental task for 3D computer
vision. While arbitrary scale DSR is a more realistic setting in this scenario,
previous approaches predominantly suffer from the issue of inefficient
real-numbered scale upsampling. To explicitly address this issue, we propose a
novel continuous depth representation for DSR. The heart of this representation
is our proposed Geometric Spatial Aggregator (GSA), which exploits a distance
field modulated by arbitrarily upsampled target gridding, through which the
geometric information is explicitly introduced into feature aggregation and
target generation. Furthermore, bricking with GSA, we present a
transformer-style backbone named GeoDSR, which possesses a principled way to
construct the functional mapping between local coordinates and the
high-resolution output results, empowering our model with the advantage of
arbitrary shape transformation ready to help diverse zooming demand. Extensive
experimental results on standard depth map benchmarks, e.g., NYU v2, have
demonstrated that the proposed framework achieves significant restoration gain
in arbitrary scale depth map super-resolution compared with the prior art. Our
codes are available at https://github.com/nana01219/GeoDSR.
