On Computing the Translations Norm in the Epipolar Graph

This paper deals with the problem of recovering the unknown norm of relative translations between cameras based on the knowledge of relative rotations and translation directions. We provide theoretical conditions for the solvability of such a problem, and we propose a two-stage method to solve it. First, a cycle basis for the epipolar graph is computed, then all the scaling factors are recovered simultaneously by solving a homogeneous linear system. We demonstrate the accuracy of our solution by means of synthetic and real experiments.Comment: Accepted at 3DV 201

Spectral Motion Synchronization in SE(3)

This paper addresses the problem of motion synchronization (or averaging) and describes a simple, closed-form solution based on a spectral decomposition, which does not consider rotation and translation separately but works straight in SE(3), the manifold of rigid motions. Besides its theoretical interest, being the first closed form solution in SE(3), experimental results show that it compares favourably with the state of the art both in terms of precision and speed

Multiple structure recovery with maximum coverage

We present a general framework for geometric model fitting based on a set coverage formulation that caters for intersecting structures and outliers in a simple and principled manner. The multi-model fitting problem is formulated in terms of the optimization of a consensus-based global cost function, which allows to sidestep the pitfalls of preference approaches based on clustering and to avoid the difficult trade-off between data fidelity and complexity of other optimization formulations. Two especially appealing characteristics of this method are the ease with which it can be implemented and its modularity with respect to the solver and to the sampling strategy. Few intelligible parameters need to be set and tuned, namely the inlier threshold and the number of desired models. The summary of the experiments is that our method compares favourably with its competitors overall, and it is always either the best performer or almost on par with the best performer in specific scenarios

Multiple structure recovery via robust preference analysis

2noThis paper address the extraction of multiple models from outlier-contaminated data by exploiting preference analysis and low rank approximation. First points are represented in the preference space, then Robust PCA (Principal Component Analysis) and Symmetric NMF (Non negative Matrix Factorization) are used to break the multi-model fitting problem into many single-model problems, which in turn are tackled with an approach inspired to MSAC (M-estimator SAmple Consensus) coupled with a model-specific scale estimate. Experimental validation on public, real data-sets demonstrates that our method compares favorably with the state of the art.openopenMagri, Luca; Fusiello, AndreaMagri, Luca; Fusiello, Andre

Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition

This paper deals with the rotation synchronization problem, which arises in global registration of 3D point-sets and in structure from motion. The problem is formulated in an unprecedented way as a "low-rank and sparse" matrix decomposition that handles both outliers and missing data. A minimization strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against state-of-the-art algorithms on simulated and real data. The results show that R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript submitted to CVI

Hierarchical structure-and-motion recovery from uncalibrated images

This paper addresses the structure-and-motion problem, that requires to find camera motion and 3D struc- ture 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.Comment: Accepted for publication in CVI

Bearing-based Network Localizability: A Unifying View

This paper provides a unifying view and offers new insights on bearing-based network localizability, that is the problem of establishing whether a set of directions between pairs of nodes uniquely determines (up to translation and scale) the position of the nodes in d-space. If nodes represent cameras then we are in the context of global structure from motion. The contribution of the paper is theoretical: first, we rewrite and link in a coherent structure several results that have been presented in different communities using disparate formalisms; second, we derive some new localizability results within the edge-based formulation

Multiple structure recovery with T-linkage

reserved2noThis work addresses the problem of robust fitting of geometric structures to noisy data corrupted by outliers. An extension of J-linkage (called T-linkage) is presented and elaborated. T-linkage improves the preference analysis implemented by J-linkage in term of performances and robustness, considering both the representation and the segmentation steps. A strategy to reject outliers and to estimate the inlier threshold is proposed, resulting in a versatile tool, suitable for multi-model fitting “in the wild”. Experiments demonstrate that our methods perform better than J-linkage on simulated data, and compare favorably with state-of-the-art methods on public domain real datasets.mixedMagri L.; Fusiello A.Magri, L.; Fusiello, A

Solving bundle block adjustment by generalized anisotropic Procrustes analysis

The paper presents a new analytical tool to solve the classical photogrammetric bundle block adjustment. The analytical model is based on the generalized extension of the anisotropic row-scaling Procrustes analysis, that has been recently proposed by the same authors to solve the image exterior orientation problem. The main advantage of the method is given by the fact that the problem solution does not require any approximate value of the unknown parameters, nor any linearization procedure. Moreover, the algorithm is exceedingly simple to describe and easy to implement. Empirical results indicate that a zero-information initialization of the iterative relaxation procedure leads almost always to the correct final least squares solution. Experiments confirm the accuracy of the proposed method, when compared to the results obtained by applying a classical photogrammetric bundle block adjustment

FAST AND RESISTANT PROCRUSTEAN BUNDLE ADJUSTMENT

In a recent paper (Fusiello and Crosilla, 2015) a Procrustean formulation of the bundle block adjustment has been presented, with a solution based on alternating least squares. This paper improves on it in two respects: it introduces a faster iterative scheme that minimizes the same cost function, thereby achieving the same accuracy, and makes the method resistant to rogue measures through iteratively reweighted least-squares. Empirical results confirm the effectiveness of these enhancements