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We present a novel procedure aimed at unsupervised catheter reconstruction from CT images. The proposed procedure is performed in two steps: detection of catheters on CT images and 3D reconstruction. In the first step catheters are detected as curvilinear structures where the first derivative in the direction of the normal vanishes. In the second step, geometric constraints on the shape of catheters are used to reconstruct catheters and to eliminate noise yielding from imperfect detection. Multiple solutions are removed by a combinatorial optimization algorithm. The algorithm can be used for both prostate catheters (approximately perpendicular to image plane) and breast catheters nearly parallel to image plane. The algorithm is automatic, without human interaction involved. Results obtained by testing the algorithm on clinical data are presented.