Sequential updating of projective and affine structure from motion

We present a new formulation of sequential least-squares applied to scene and motion reconstruction from image features.

In this paper, sequences of camera motions that lead to inherent ambiguities in uncalibrated Euclidean reconstruction or self-calibration are studied.

Our main contribution is a complete, detailed classification of these critical motion sequences (CMS).

The algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and subsequently finding its roots.

It is the first algorithm well suited for numerical implementation that also corresponds to the inherent complexity of the problem.

Recently, we have shown (Zhang 1996a) that even in the case where images are calibrated, more reliable results can be obtained if we use the... A structure from motion algorithm is described which recovers structure and camera position, modulo a projective ambiguity.

Camera calibration is not required, and camera parameters such as focal length can be altered freely during motion.

The performance is compared to that of the well known 8 and 7-point methods and a 6-point scheme.

The algorithm is used in a robust hypothesize-and-test framework to estimate structure and motion in real-time with low delay.

We investigate the numerical precision of the algorithm.

We also study its performance under noise in minimal as well as over-determined cases.

The real-time system uses solely visual input and has been demonstrated at major conferences. Two images of a single scene/object are related by the epipolar geometry, which can be described by a 3×3 singular matrix called the essential matrix if images' internal parameters are known, or the fundamental matrix otherwise.

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