Many lines in a typical cluttered image incur a size explosion when invariants from every combination of the extracted lines are calculated. To solve this problem, we propose a new method of reducing the search space by introducing not only a line convex hull (LCH) but also an indexing logic filter (ILF). The LCH arranges five lines in a unique order and classifies a set of five lines into topological types. The ILF produces an integer indexing key from the acquired LCHs. The LCH and ILF are incorporated into a hierarchical database so that the model features can be retrieved efficiently. We achieved satisfactory results for synthetic welding panels used in shipbuilding.