Translation averaging solves for 3D camera translations given many pairwise relative translation directions. The mismatch between inputs (directions) and output estimates (absolute translations) makes translation averaging a challenging problem, which is often addressed by comparing either directions or displacements using relaxed cost functions that are relatively easy to optimize. However, the distinctly different nature of the cost functions leads to varied behaviour under different baselines and noise conditions. In this paper, we argue that translation averaging can benefit from a fusion of the two approaches. Specifically, we recursively fuse the individual updates suggested by direction and displacement-based methods using their uncertainties. The uncertainty of each estimate is modelled by the inverse of the Hessian of the corresponding optimization problem. As a result, our method utilizes the advantages of both methods in a principled manner. The superiority of our translation averaging scheme is demonstrated via the improved accuracies of camera translations on benchmark datasets compared to the state-of-the-art methods.

In Structure-from-Motion (SfM), the underlying view-graphs of unordered image collections generally have a highly redundant set of edges that can be sparsified for efficiency without significant loss of reconstruction quality. Often, there are also false edges due to incorrect image retrieval and repeated structures (symmetries) that give rise to ghosting and superimposed reconstruction artifacts. We present a unified method to simultaneously sparsify the viewgraph and remove false edges. We propose a scoring mechanism based on camera triplets that identifies edge redundancy as well as false edges. Our edge selection is formulated as an optimization problem which can be provably solved using a simple thresholding scheme. This results in a highly efficient algorithm which can be incorporated as a pre-processing step into any SfM pipeline, making it practically usable. We demonstrate the utility of our method on generic and ambiguous datasets that cover the range of small, medium and large-scale datasets, all with different statistical properties. Sparsification of generic datasets using our method significantly reduces reconstruction time while maintaining the accuracy of the reconstructions as well as removing ghosting artifacts. For ambiguous datasets, our method removes false edges, thereby avoiding incorrect superimposed reconstructions.

Geometric estimation problems in vision are often solved via minimization of statistical loss functions which account for the presence of outliers in the observations. The corresponding energy landscape often has many local minima. Many approaches attempt to avoid local minima by an-nealing the scale parameter of loss functions using methods such as graduated non-convexity (GNC). However, little attention has been paid to the annealing schedule, which is often carried out in a fixed manner, resulting in a poor speed-accuracy trade-off and unreliable convergence to the global minimum. In this paper, we propose a principled approach for adaptively annealing the scale for GNC by tracking the positive-definiteness (i.e. local convexity) of the Hessian of the cost function. We illustrate our approach using the classic problem of registering 3D correspondences in the presence of noise and outliers. We also develop approximations to the Hessian that significantly speeds up our method. The effectiveness of our approach is validated by comparing its performance with state-of-the-art 3D registration approaches on a number of synthetic and real datasets. Our approach is accurate and efficient and converges to the global solution more reliably than the state-of-the-art methods.

In 3D computer vision, translation averaging solves for absolute translations given a set of pairwise relative translation directions. While there has been much work on robustness to outliers and studies on the uniqueness of the solution, this paper deals with a distinctly different problem of sensitivity in translation averaging under uncertainty. We first analyze sensitivity in estimating scales corresponding to relative directions under small perturbations of the relative directions. Then, we formally define the conditioning of the translation averaging problem, which assesses the reliability of estimated translations based solely on the input directions. We give a sufficient criterion to ensure that the problem is well-conditioned. Subsequently, we provide an efficient algorithm to identify and remove combinations of directions which make the problem ill-conditioned while ensuring uniqueness of the solution. We demonstrate the utility of such analysis in global structure-from-motion pipelines for obtaining 3D reconstructions, which reveals the benefits of filtering the ill-conditioned set of directions in translation averaging in terms of reduced translation errors, a higher number of 3D points triangulated and faster convergence of bundle adjustment.

In this study, a combination of adaptive vector median filter (VMF) and weighted mean filter is proposed for removal of high‐density impulse noise from colour images. In the proposed filtering scheme, the noisy and non‐noisy pixels are classified based on the non‐causal linear prediction error. For a noisy pixel, the adaptive VMF is processed over the pixel where the window size is adapted based on the availability of good pixels. Whereas, a non‐noisy pixel is substituted with the weighted mean of the good pixels of the processing window. The experiments have been carried out on a large database for different classes of images, and the performance is measured in terms of peak signal‐to‐noise ratio, mean squared error, structural similarity and feature similarity index. It is observed from the experiments that the proposed filter outperforms (∼1.5 to 6 dB improvement) some of the existing noise removal techniques not only at low density impulse noise but also at high‐density impulse noise.