The endoscope is a popular imaging modality used in many preevaluations and surgical treatments, and is also one of the essential tools in minimally invasive surgery. However, regular endoscopes provide only 2-D images. Even though stereoendoscopy systems can display 3-D images, the real anatomical structure of the observed lesion is unavailable and can only be judged by the surgeon's imagination. In this paper, we present a constraint-based factorization method for reconstructing 3-D structures registered to the patient, from 2-D endoscopic images. The proposed method incorporates the geometric constraints from the tracked surgical instrument into the traditional factorization method based on frame-to-frame feature motion on the endoscopically viewed scene. Experiments with real and synthetic data demonstrate good real-scale 3-D extraction, with greater accuracy than is available from traditional methods. The reconstruction process can also be accomplished in a few seconds, making it suitable for on-line surgical applications to provide surgeons with additional 3-D shape information, critical distance monitoring and warnings.
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