  We describe algorithms that detect 21cm line HI self-absorption (HISA) in
large data sets and extract it for analysis. Our search method identifies HISA
as spatially and spectrally confined dark HI features that appear as negative
residuals after removing larger-scale emission components with a modified CLEAN
algorithm. Adjacent HISA volume-pixels (voxels) are grouped into features in
(l,b,v) space, and the HI brightness of voxels outside the 3-D feature
boundaries is smoothly interpolated to estimate the absorption amplitude and
the unabsorbed HI emission brightness. The reliability and completeness of our
HISA detection scheme have been tested extensively with model data. We detect
most features over a wide range of sizes, linewidths, amplitudes, and
background levels, with poor detection only where the absorption brightness
temperature amplitude is weak, the absorption scale approaches that of the
correlated noise, or the background level is too faint for HISA to be
distinguished reliably from emission gaps. False detection rates are very low
in all parts of the parameter space except at sizes and amplitudes approaching
those of noise fluctuations. Absorption measurement biases introduced by the
method are generally small and appear to arise from cases of incomplete HISA
detection. This paper is the third in a series examining HISA at high angular
resolution. A companion paper (Paper II) uses our HISA search and extraction
method to investigate the cold atomic gas distribution in the Canadian Galactic
Plane Survey.
