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We revisit the problem of matching a set of lines in the 2D image to a set of corresponding lines in the 3D model for the following reasons. (a) Existing algorithms that treat lines as infinitely long contain a flaw, namely, the solutions found are not invariant with respect to the choice of the coordinate frame. The source of this flaw is in the way lines are represented. We propose a frame-independent representation for sets of infinite lines that removes the non-invariance flaw. (b) Algorithms for finding the best rigid transform are nonlinear optimizations that are sensitive to initialization and may result in unreliable and expensive solutions. We present a new recipe for initialization that exploits the 3D geometry of the problem and is applicable to all algorithms that perform the matching in the 3D scene. Experiments show that with this initialization all algorithms find the best transform. (c) We present a new efficient matching algorithm that is significantly faster than existing alternatives, since it does not require explicit evaluation of the cost function and its derivatives.