  Disk galaxies are typically in a stable configuration where matter moves in
almost closed circular orbits. However, non-circular motions caused by
distortions, warps, lopsidedness, or satellite interactions are common and
leave distinct signatures on galaxy velocity maps. We develop an algorithm that
uses an ordinary least square method for fitting a non-axisymmetric model to
the observed two-dimensional line-of-sight velocity map of an external galaxy,
which allows for anisotropic non-circular motions. The method approximates a
galaxy as a flat disk, which is an appropriate assumption for spiral galaxies
within the optical radius where warps are rare. In the outer parts of HI
distributions, which may extend well into the warp region, we use this method
in combination with a standard rotating tilted ring model to constrain the
range of radii where the flat disk assumption can be conservatively considered
valid. Within this range, the transversal and radial velocity profiles,
averaged in rings, can be directly reconstructed from the velocity map. The
novelty of the algorithm consists in using arc segments in addition to rings:
in this way spatial velocity anisotropies can be measured in both components,
allowing for the reconstruction of angularly resolved coarse-grained
two-dimensional velocity maps. We applied this algorithm to 25 disk galaxies
from the THINGS sample for which we can provide 2D maps of both velocity
components.
