We describe a hierarchical structure-from-motion pipeline.No information is needed beside images themselves.The pipeline proved successful in real-world tasks. This paper addresses the structure-and-motion problem, that requires to find camera motion and 3D structure from point matches. A new pipeline, dubbed Samantha, is presented, that departs from the prevailing sequential paradigm and embraces instead a hierarchical approach. This method has several advantages, like a provably lower computational complexity, which is necessary to achieve true scalability, and better error containment, leading to more stability and less drift. Moreover, a practical autocalibration procedure allows to process images without ancillary information. Experiments with real data assess the accuracy and the computational efficiency of the method.
A great deal of published methods rely on equations involving the dual image of the absolute quadric (DIAQ), introduced by Triggs in @cite_63 . Earlier approaches for variable focal lengths were based on linear, weighted systems @cite_34 @cite_14 , solved directly or iteratively @cite_24 . Their reliability has been improved by more recent algorithms, such as @cite_61 , solving super-linear systems while directly forcing the positive definiteness of the DIAQ. Such enhancements were necessary because of the structural non-linearity of the task: for this reason the problem has also been approached using branch and bound schemes, based either on the Kruppa equations @cite_35 , dual linear autocalibration @cite_79 or the modulus constraint @cite_42 .
@cite_61 @cite_35 @cite_14 @cite_42 @cite_24 @cite_79 @cite_63 @cite_34
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We present a practical, stratified autocalibration algorithm with theoretical guarantees of global optimality. Given a projective reconstruction, the first stage of the algorithm upgrades it to affine by estimating the position of the plane at infinity. The plane at infinity is computed by globally minimizing a least squares formulation of the modulus constraints. In the second stage, the algorithm upgrades this affine reconstruction to a metric one by globally minimizing the infinite homography relation to compute the dual image of the absolute conic (DIAC). The positive semidefiniteness of the DIAC is explicitly enforced as part of the optimization process, rather than as a post-processing step. For each stage, we construct and minimize tight convex relaxations of the highly non-convex objective functions in a branch and bound optimization framework. We exploit the problem structure to restrict the search space for the DIAC and the plane at infinity to a small, fixed number of branching dimensions, independent of the number of views. Experimental evidence of the accuracy, speed and scalability of our algorithm is presented on synthetic and real data. MATLAB code for the implementation is made available to the community. The author describes a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structure is formulated in terms of the absolute quadric-the singular dual 3D quadric (4 spl times 4 rank 3 matrix) giving the Euclidean dot-product between plane normals. This is equivalent to the traditional absolute conic but simpler to use. It encodes both affine and Euclidean structure, and projects very simply to the dual absolute image conic which encodes camera calibration. Requiring the projection to be constant gives a bilinear constraint between the absolute quadric and image conic, from which both can be recovered nonlinearly from m spl ges 3 images, or quasi-linearly from m spl ges 4. Calibration and Euclidean structure follow easily. The nonlinear method is stabler, faster, more accurate and more general than the quasi-linear one. It is based on a general constrained optimization technique-sequential quadratic programming-that may well be useful in other vision problems. We investigate the problem of finding the metric structure of a general 3D scene viewed by a moving camera with square pixels and constant unknown focal length. While the problem has a concise and well-understood formulation in the stratified framework thanks to the absolute dual quadric, two open issues remain. The first issue concerns the generic Critical Motion Sequences, i.e. camera motions for which self-calibration is ambiguous. Most of the previous work focuses on the varying focal length case. We provide a thorough study of the constant focal length case. The second issue is to solve the nonlinear set of equations in four unknowns arising from the dual quadric formulation. Most of the previous work either does local nonlinear optimization, thereby requiring an initial solution, or linearizes the problem, which introduces artificial degeneracies, most of which likely to arise in practice. We use interval analysis to solve this problem. The resulting algorithm is guaranteed to find the solution and is not subject to artificial degeneracies. Directly using interval analysis usually results in computationally expensive algorithms. We propose a carefully chosen set of inclusion functions, making it possible to find the solution within few seconds. Comparisons of the proposed algorithm with existing ones are reported for simulated and real data. In this paper we provide new simple closed-form solutions to two minimal absolute pose problems for the case of known vertical direction. In the first problem we estimate absolute pose of a calibrated camera from two 2D-3D correspondences and a given vertical direction. In the second problem we assume camera with unknown focal length and radial distortion and estimate its pose together with the focal length and the radial distortion from three 2D-3D correspondences and a given vertical direction. The vertical direction can be obtained either by direct physical measurement by, e.g., gyroscopes and inertial measurement units or from vanishing points constructed in images. Both our problems result in solving one polynomial equation of degree two in one variable and one, respectively two, systems of linear equations and can be efficiently solved in a closed-form. By evaluating our algorithms on synthetic and real data we demonstrate that both our solutions are fast, efficient and numerically stabled.