While the common environment representation in structure from motion is given by a sparse point cloud, the community has also investigated the use of lines to better enforce the inherent regularities in man-made surroundings. Following the potential of this idea, the present paper introduces a more flexible higher-order extension of points that provides a general model for structural edges in the environment, no matter if straight or curved. Our model relies on linked Bezier curves, the geometric intuition of which proves great benefits during parameter initialization and regularization. We present the first fully automatic pipeline that is able to generate spline-based representations without any human supervision. Besides a full graphical formulation of the problem, we introduce both geometric and photometric cues as well as higher-level concepts such overall curve visibility and viewing angle restrictions to automatically manage the correspondences in the graph. Results prove that curve-based structure from motion with splines is able to outperform state-of-the-art sparse feature-based methods, as well as to model curved edges in the environment.
Full bundle adjustment over general curve models and camera poses has first been shown in @cite_10 . The approach however suffers from a bias that occurs when the model is only partially observed. @cite_21 discusses this problem in detail, and presents a lifting approach that transparently handles missing data. @cite_16 solves the problem by modeling curves as a set of shorter line segments, and @cite_32 models the occlusions explicitly. While @cite_21 is the most related to our approach, the lifted formulation is computationally demanding, the work does not discuss the fully automatic establishmentment of a correspondence graph that would enable fully automatic incremental structure-from-motion. Our main contribution is an efficient, fully automatic solution to this problem, thus enabling automatic curve-based structure from motion in larger scale environments.
@cite_21 @cite_10 @cite_32 @cite_16
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Recent work in structure from motion (SfM) has successfully built 3D models from large unstructured collections of images downloaded from the Internet. Most approaches use incremental algorithms that solve progressively larger bundle adjustment problems. These incremental techniques scale poorly as the number of images grows, and can drift or fall into bad local minima. We present an alternative formulation for SfM based on finding a coarse initial solution using a hybrid discrete-continuous optimization, and then improving that solution using bundle adjustment. The initial optimization step uses a discrete Markov random field (MRF) formulation, coupled with a continuous Levenberg-Marquardt refinement. The formulation naturally incorporates various sources of information about both the cameras and the points, including noisy geotags and vanishing point estimates. We test our method on several large-scale photo collections, including one with measured camera positions, and show that it can produce models that are similar to or better than those produced with incremental bundle adjustment, but more robustly and in a fraction of the time. Bundle adjustment jointly optimizes camera intrinsics and extrinsics and 3D point triangulation to reconstruct a static scene. The triangulation constraint however is invalid for moving points captured in multiple unsynchronized videos and bundle adjustment is not purposed to estimate the temporal alignment between cameras. In this paper, we present a spatiotemporal bundle adjustment approach that jointly optimizes four coupled sub-problems: estimating camera intrinsics and extrinsics, triangulating 3D static points, as well as subframe temporal alignment between cameras and estimating 3D trajectories of dynamic points. Key to our joint optimization is the careful integration of physics-based motion priors within the reconstruction pipeline, validated on a large motion capture corpus. We present an end-to-end pipeline that takes multiple uncalibrated and unsynchronized video streams and produces a dynamic reconstruction of the event. Because the videos are aligned with sub-frame precision, we reconstruct 3D trajectories of unconstrained outdoor activities at much higher temporal resolution than the input videos. This paper considers the problem of sustained multicamera tracking in the presence of occlusion and changes in the target motion model. The key insight of the proposed method is the fact that, under mild conditions, the 2D trajectories of the target in the image planes of each of the cameras are constrained to evolve in the same subspace. This observation allows for identifying, at each time instant, a single (piecewise) linear model that explains all the available 2D measurements. In turn, this model can be used in the context of a modified particle filter to predict future target locations. In the case where the target is occluded to some of the cameras, the missing measurements can be estimated using the facts that they must lie both in the subspace spanned by previous measurements and satisfy epipolar constraints. Hence, by exploiting both dynamical and geometrical constraints the proposed method can robustly handle substantial occlusion, without the need for performing 3D reconstruction, calibrated cameras or constraints on sensor separation. The performance of the proposed tracker is illustrated with several challenging examples involving targets that substantially change appearance and motion models while occluded to some of the cameras. If a physical object has a smooth or piecewise smooth boundary, its images obtained by cameras in varying positions undergo smooth apparent deformations. These deformations are locally well approximated by affine transforms of the image plane. In consequence the solid object recognition problem has often been led back to the computation of affine invariant image local features. Such invariant features could be obtained by normalization methods, but no fully affine normalization method exists for the time being. Even scale invariance is dealt with rigorously only by the scale-invariant feature transform (SIFT) method. By simulating zooms out and normalizing translation and rotation, SIFT is invariant to four out of the six parameters of an affine transform. The method proposed in this paper, affine-SIFT (ASIFT), simulates all image views obtainable by varying the two camera axis orientation parameters, namely, the latitude and the longitude angles, left over by the SIFT method. Then it covers the other four parameters by using the SIFT method itself. The resulting method will be mathematically proved to be fully affine invariant. Against any prognosis, simulating all views depending on the two camera orientation parameters is feasible with no dramatic computational load. A two-resolution scheme further reduces the ASIFT complexity to about twice that of SIFT. A new notion, the transition tilt, measuring the amount of distortion from one view to another, is introduced. While an absolute tilt from a frontal to a slanted view exceeding 6 is rare, much higher transition tilts are common when two slanted views of an object are compared (see Figure hightransitiontiltsillustration). The attainable transition tilt is measured for each affine image comparison method. The new method permits one to reliably identify features that have undergone transition tilts of large magnitude, up to 36 and higher. This fact is substantiated by many experiments which show that ASIFT significantly outperforms the state-of-the-art methods SIFT, maximally stable extremal region (MSER), Harris-affine, and Hessian-affine.