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This paper presents a scheme that addresses the practical issues associated with producing a geometric model of a scene using a passive sensing technique. The proposed image-based scheme comprises a recursive structure recovery method and a recursive surface reconstruction technique. The former method employs a robust corner-tracking algorithm that copes with the appearance and disappearance of features and a corner-based structure and motion estimation algorithm that handles the inclusion and expiration of features. The novel formulation and dual extended Kalman filter computational framework of the estimation algorithm provide an efficient approach to metric structure recovery that does not require any prior knowledge about the camera or scene. The newly developed surface reconstruction technique employs a visibility constraint to iteratively refine and ultimately yield a triangulated surface that envelops the recovered scene structure and can produce views consistent with those of the original image sequence. Results on simulated data and synthetic and real imagery illustrate that the proposed scheme is robust, accurate, and has good numerical stability, even when features are repeatedly absent or their image locations are affected by extreme levels of noise.