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It has been shown, in previous work, that the 3D position of a line can be reconstructed from a single image in vision systems that do not possess a single viewpoint. We present a new method that, in a non-central axial catadioptric system, can achieve line spacial reconstruction from 3 or more image points, given the distance ratio of 3 points in the line (a fair assumption in, for example, structured environment with repetitive architectural features). We use cross-ratio as an invariant to constrain the line localization and perform the reconstruction from a set of image points through non-linear optimization. Experimental results are presented.