A Comparison of Projective Reconstruction Methods for Pairs of Views

Abstract Recently, different approaches for uncalibrated stereo have been suggested which permit projective reconstructions from multiple views. These use weak calibration which is represented by the epipolar geometry, and so we require no knowledge of the intrinsic or extrinsic camera parameters. In this paper we consider projective reconstructions from pairs of views and compare a number of the available methods. Projective stereo algorithms can be categorized by the way in which the 3D coordinates are computed. The first class is similar to traditional stereo algorithms in that the 3D world geometry is made explicit; the initial phase of the processing always involves the estimation of the camera matrices from which the 3D coordinates are computed. We show how the camera matrices can be computed either from point correspondences, or how they are constrained by the fundamental matrices. The second class of algorithms are based on implicit image measurements which are used to compute projective invariants from image correspondences. The invariants are based on the Cayley algebra and on cross ratios. In all cases, the invariants are functionally dependent on the 3D coordinates. We report on the stabilities of the different methods using a range of meaningful synthetic and real images. From these we can conclude which methods are most likely to be of use in applications that are dependent on 3D uncalibrated reconstructions.

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