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 an autocalibration algorithm for upgrading a projective reconstruction to a metric reconstruction by estimating the absolute dual quadric. The algorithm enforces the rank degeneracy and the positive semidefiniteness of the dual quadric as part of the estimation procedure, rather than as a post-processing step. Furthermore, the method allows the user, if he or she so desires, to enforce conditions on the plane at infinity so that the reconstruction satisfies the chirality constraints. The algorithm works by constructing low degree polynomial optimization problems, which are solved to their global optimum using a series of convex linear matrix inequality relaxations. The algorithm is fast, stable, robust and has time complexity independent of the number of views. We show extensive results on synthetic as well as real datasets to validate our algorithm. We address the problem of autocalibration of a moving camera with unknown constant intrinsic parameters. Existing autocalibration techniques use numerical optimization algorithms whose convergence to the correct result cannot be guaranteed, in general. To address this problem, we have developed a method where an interval branch-and-bound method is employed for numerical minimization. Thanks to the properties of interval analysis this method converges to the global solution with mathematical certainty and arbitrary accuracy and the only input information it requires from the user are a set of point correspondences and a search interval. The cost function is based on the Huang-Faugeras constraint of the essential matrix. A recently proposed interval extension based on Bernstein polynomial forms has been investigated to speed up the search for the solution. Finally, experimental results are presented. In this paper we address the problem of uncalibrated structure and motion recovery from image sequences that contain dominant planes in some of the views. Traditional approaches fail when the features common to three consecutive views are all located on a plane. This happens because in the uncalibrated case there is a fundamental ambiguity in relating the structure before and after the plane. This is, however, a situation that is often hard to avoid in man-made environments. We propose a complete approach that detects the problem and defers the computation of parameters that are ambiguous in projective space (i.e. the registration between partial reconstructions only sharing a common plane and poses of cameras only seeing planar features) till after self-calibration. Also a new linear self-calibration algorithm is proposed that couples the intrinsics between multiple subsequences. The final result is a complete metric 3D reconstruction of both structure and motion for the whole sequence. Experimental results on real image sequences show that the approach yields very good results. 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. In this paper, an iterative algorithm for auto-calibration is presented. The proposed algorithm switches between linearly estimating the dual of the absolute conic and the intrinsic parameters, while also incorporating the rank-3 constraint on the intrinsic parameters. The most important property of the algorithm is that it is completely general in the sense that any type of constraint on the intrinsic parameters might be used. The proposed algorithm locates in-between of a non-linear optimization and initial linear computation, and provides robust and sufficiently accurate initial values for a bundle adjustment routine. The performance of the algorithm is shown for both simulated and real data, especially in the important case of natural (zero skew and unit aspect ratio) cameras. 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. 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. In this paper the feasibility of self-calibration in the presence of varying internal camera parameters is under investigation. A self-calibration method is presented which efficiently deals with all kinds of constraints on the internal camera parameters. Within this framework a practical method is proposed which can retrieve metric reconstruction from image sequences obtained with uncalibrated zooming focusing cameras. The feasibility of the approach is illustrated on real and synthetic examples.