This thesis describes a system that, given approximately-centered images of spiral galaxies, produces quantitative descriptions of spiral galaxy structure without the need for per-image human input. This structure information consists of a list of spiral arm segments, each associated with a fitted logarithmic spiral arc and a pixel region. This list-of-arcs representation allows description of arbitrary spiral galaxy structure: the arms do not need to be symmetric, may have forks or bends, and, more generally, may be arranged in any manner with a consistent spiral-pattern center (non-merging galaxies have a sufficiently well-defined center). Such flexibility is important in order to accommodate the myriad structure variations observed in spiral galaxies. From the arcs produced from our method it is possible to calculate measures of spiral galaxy structure such as winding direction, winding tightness, arm counts, asymmetry, or other values of interest (including user-defined measures). In addition to providing information about the spiral arm "skeleton" of each galaxy, our method can enable analyses of brightness within individual spiral arms, since we provide the pixel regions associated with each spiral arm segment. For winding direction, arm tightness, and arm count, comparable information is available (to various extents) from previous efforts; to the extent that such information is available, we find strong correspondence with our output. We also characterize the changes to (and invariances in) our output as a function of modifications to important algorithm parameters. By enabling generation of extensive data about spiral galaxy structure from large-scale sky surveys, our method will enable new discoveries and tests regarding the nature of galaxies and the universe, and will facilitate subsequent work to automatically fit detailed brightness models of spiral galaxies.