  Extended radio sources are an important minority population in modern deep
radio surveys, because they enable detailed investigation of the physics
governing radio-emitting regions such as active galaxies and their
environments. Cross-identification of radio sources with optical host galaxies
is challenging for this extended population, due to their morphological
complexity and multiple potential counterparts. In the first data release of
the Low-frequency array (LOFAR) Two-metre Sky Survey (LoTSS DR1) the automated
likelihood ratio for compact sources was supplemented by a citizen science
visual identification process for extended sources. In this paper we present a
novel method for automating the host identification of extended sources by
using ridgelines, which trace the assumed direction of fluid-flow through the
points of highest flux density. Applying a new code, RL-Xid, to LoTSS DR1, we
demonstrate that ridgelines are versatile; by providing information about
spatial structure and brightness distributions, they can be used both for
optical host identification and morphological studies in radio surveys. RL-Xid
draws ridgelines for 85 per cent of sources brighter than 10 mJy and larger
than 15 arcsec, with an improved performance of 96 per cent for the subset >30
mJy and >60 arcsec. Using a sample of sources with known hosts from LoTSS DR1,
we demonstrate that RL-Xid successfully identifies the host for 98 per cent of
the sources with successfully drawn ridgelines, and performs at a comparable
level to visual identification via citizen science. We also demonstrate that
ridgeline brightness profiles provide a promising automated technique for
morphological classification.
