| 1. |
- Miraldo, Pedro, et al.
(författare)
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A Unified Model for Line Projections in Catadioptric Cameras With Rotationally Symmetric Mirrors
- 2022
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Ingår i: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. - 1063-6919. ; 2022-June, s. 15776-15785
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Konferensbidrag (refereegranskat)abstract
- Lines are among the most used computer vision features, in applications such as camera calibration to object detection. Catadioptric cameras with rotationally symmetric mirrors are omnidirectional imaging devices, capturing up to a 360 degrees field of view. These are used in many applications ranging from robotics to panoramic vision. Although known for some specific configurations, the modeling of line projection was never fully solved for general central and non-central catadioptric cameras. We start by taking some general point reflection assumptions and derive a line reflection constraint. This constraint is then used to define a line projection into the image. Next, we compare our model with previous methods, showing that our general approach outputs the same polynomial degrees as previous configuration-specific systems. We run several experiments using synthetic and real-world data, validating our line projection model. Lastly, we show an application of our methods to an absolute camera pose problem.
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| 2. |
- Brynte, Lucas, 1990, et al.
(författare)
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On the Tightness of Semidefinite Relaxations for Rotation Estimation
- 2022
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 1573-7683 .- 0924-9907. ; 64:1, s. 57-67
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Tidskriftsartikel (refereegranskat)abstract
- Why is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance, we note that there are few failure cases reported in the literature, in particular for estimation problems with a single rotation, motivating us to gain further theoretical understanding. A general framework based on tools from algebraic geometry is introduced for analyzing the power of semidefinite relaxations of problems with quadratic objective functions and rotational constraints. Applications include registration, hand–eye calibration, and rotation averaging. We characterize the extreme points and show that there exist failure cases for which the relaxation is not tight, even in the case of a single rotation. We also show that some problem classes are always tight given an appropriate parametrization. Our theoretical findings are accompanied with numerical simulations, providing further evidence and understanding of the results.
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| 3. |
- Iglesias, José Pedro Lopes, 1994, et al.
(författare)
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Accurate Optimization of Weighted Nuclear Norm for Non-Rigid Structure from Motion
- 2020
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Ingår i: Computer Vision – ECCV 2020 - 16th European Conference, 2020, Proceedings. - Cham : Springer International Publishing. - 0302-9743 .- 1611-3349. - 9783030585822 ; 12372 LNCS, s. 21-37
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Konferensbidrag (refereegranskat)abstract
- Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when applying more general singular value penalties, such as weighted nuclear norm priors, direct optimization over the elements of the matrix is typically used. Due to non-differentiability of the resulting objective function, first order sub-gradient or splitting methods are predominantly used. While these offer rapid iterations it is well known that they become inefficient near the minimum due to zig-zagging and in practice one is therefore often forced to settle for an approximate solution. In this paper we show that more accurate results can in many cases be achieved with 2nd order methods. Our main result shows how to construct bilinear formulations, for a general class of regularizers including weighted nuclear norm penalties, that are provably equivalent to the original problems. With these formulations the regularizing function becomes twice differentiable and 2nd order methods can be applied. We show experimentally, on a number of structure from motion problems, that our approach outperforms state-of-the-art methods.
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| 4. |
- Iglesias, José Pedro Lopes, 1994, et al.
(författare)
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expOSE: Accurate Initialization-Free Projective Factorization using Exponential Regularization
- 2023
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Ingår i: 2023 IEEE/CVF CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR). - 1063-6919. - 9798350301298 ; , s. 8959-8968
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Konferensbidrag (refereegranskat)abstract
- Bundle adjustment is a key component in practically all available Structure from Motion systems. While it is crucial for achieving accurate reconstruction, convergence to the right solution hinges on good initialization. The recently introduced factorization-based pOSE methods formulate a surrogate for the bundle adjustment error without reliance on good initialization. In this paper, we show that pOSE has an undesirable penalization of large depths. To address this we propose expOSE which has an exponential regularization that is negligible for positive depths. To achieve efficient inference we use a quadratic approximation that allows an iterative solution with VarPro. Furthermore, we extend the method with radial distortion robustness by decomposing the Object Space Error into radial and tangential components. Experimental results confirm that the proposed method is robust to initialization and improves reconstruction quality compared to state-of-the-art methods even without bundle adjustment refinement.
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| 5. |
- Iglesias, José Pedro Lopes, 1994, et al.
(författare)
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Global Optimality for Point Set Registration Using Semidefinite Programming
- 2020
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Ingår i: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. - 1063-6919. ; 2020, s. 8284-8292, s. 8284-8292
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Konferensbidrag (refereegranskat)abstract
- In this paper we present a study of global optimality conditions for Point Set Registration (PSR) with missing data. PSR is the problem of aligning multiple point clouds with an unknown target point cloud. Since non-linear rotation constraints are present the problem is inherently non-convex and typically relaxed by computing the Lagrange dual, which is a Semidefinite Program (SDP). In this work we show that given a local minimizer the dual variables of the SDP can be computed in closed form. This opens up the possibility of verifying the optimally, using the SDP formulation without explicitly solving it. In addition it allows us to study under what conditions the relaxation is tight, through spectral analysis. We show that if the errors in the (unknown) optimal solution are bounded the SDP formulation will be able to recover it.
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| 6. |
- Iglesias, José Pedro Lopes, 1994, et al.
(författare)
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Radial Distortion Invariant Factorization for Structure from Motion
- 2021
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Ingår i: Proceedings of the IEEE International Conference on Computer Vision. - 1550-5499. ; , s. 5886-5895
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Konferensbidrag (refereegranskat)abstract
- Factorization methods are frequently used for structure from motion problems (SfM). In the presence of noise they are able to jointly estimate camera matrices and scene points in overdetermined settings, without the need for accurate initial solutions. While the early formulations were restricted to affine models, recent approaches have been show to work with pinhole cameras by minimizing object space errors. In this paper we propose a factorization approach using the so called radial camera, which is invariant to radial distortion and changes in focal length. Assuming a known principal point our approach can reconstruct the 3D scene in settings with unknown and varying radial distortion and focal length. We show on both real and synthetic data that our approach outperforms state-of-the-art factorization methods under these conditions.
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| 7. |
- Iglesias, José Pedro Lopes, 1994
(författare)
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Towards Reliable and Accurate Global Structure-from-Motion
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Reconstruction of objects or scenes from sparse point detections across multiple views is one of the most tackled problems in computer vision. Given the coordinates of 2D points tracked in multiple images, the problem consists of estimating the corresponding 3D points and cameras' calibrations (intrinsic and pose), and can be solved by minimizing reprojection errors using bundle adjustment. However, given bundle adjustment's nonlinear objective function and iterative nature, a good starting guess is required to converge to global minima. Global and Incremental Structure-from-Motion methods appear as ways to provide good initializations to bundle adjustment, each with different properties. While Global Structure-from-Motion has been shown to result in more accurate reconstructions compared to Incremental Structure-from-Motion, the latter has better scalability by starting with a small subset of images and sequentially adding new views, allowing reconstruction of sequences with millions of images. Additionally, both Global and Incremental Structure-from-Motion methods rely on accurate models of the scene or object, and under noisy conditions or high model uncertainty might result in poor initializations for bundle adjustment. Recently pOSE, a class of matrix factorization methods, has been proposed as an alternative to conventional Global SfM methods. These methods use VarPro - a second-order optimization method - to minimize a linear combination of an approximation of reprojection errors and a regularization term based on an affine camera model, and have been shown to converge to global minima with a high rate even when starting from random camera calibration estimations. This thesis aims at improving the reliability and accuracy of global SfM through different approaches. First, by studying conditions for global optimality of point set registration, a point cloud averaging method that can be used when (incomplete) 3D point clouds of the same scene in different coordinate systems are available. Second, by extending pOSE methods to different Structure-from-Motion problem instances, such as Non-Rigid SfM or radial distortion invariant SfM. Third and finally, by replacing the regularization term of pOSE methods with an exponential regularization on the projective depth of the 3D point estimations, resulting in a loss that achieves reconstructions with accuracy close to bundle adjustment.
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| 8. |
- Örnhag, Marcus Valtonen, et al.
(författare)
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Bilinear Parameterization for Non-Separable Singular Value Penalties
- 2021
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Ingår i: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. - 1063-6919. ; , s. 3896-3905
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Konferensbidrag (refereegranskat)abstract
- Low rank inducing penalties have been proven to successfully uncover fundamental structures considered in computer vision and machine learning; however, such methods generally lead to non-convex optimization problems. Since the resulting objective is non-convex one often resorts to using standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), or other subgradient methods, which exhibit slow convergence in the neighbourhood of a local minimum. We propose a method using second order methods, in particular the variable projection method (VarPro), by replacing the nonconvex penalties with a surrogate capable of converting the original objectives to differentiable equivalents. In this way we benefit from faster convergence.The bilinear framework is compatible with a large family of regularizers, and we demonstrate the benefits of our approach on real datasets for rigid and non-rigid structure from motion. The qualitative difference in reconstructions show that many popular non-convex objectives enjoy an advantage in transitioning to the proposed framework.
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