Fully Differentiable RANSAC

We propose the fully differentiable $\nabla$-RANSAC.It predicts the inlier probabilities of the input data points, exploits the predictions in a guided sampler, and estimates the model parameters (e.g., fundamental matrix) and its quality while propagating the gradients through the entire procedure. The random sampler in $\nabla$-RANSAC is based on a clever re-parametrization strategy, i.e.\ the Gumbel Softmax sampler, that allows propagating the gradients directly into the subsequent differentiable minimal solver. The model quality function marginalizes over the scores from all models estimated within $\nabla$-RANSAC to guide the network learning accurate and useful probabilities.$\nabla$-RANSAC is the first to unlock the end-to-end training of geometric estimation pipelines, containing feature detection, matching and RANSAC-like randomized robust estimation. As a proof of its potential, we train $\nabla$-RANSAC together with LoFTR, i.e. a recent detector-free feature matcher, to find reliable correspondences in an end-to-end manner. We test $\nabla$-RANSAC on a number of real-world datasets on fundamental and essential matrix estimation. It is superior to the state-of-the-art in terms of accuracy while being among the fastest methods. The code and trained models will be made public

RES-Q: Robust Outlier Detection Algorithm for Fundamental Matrix Estimation

Detection of outliers present in noisy images for an accurate fundamental matrix estimation is an important research topic in the field of 3-D computer vision. Although a lot of research is conducted in this domain, not much study has been done in utilizing the robust statistics for successful outlier detection algorithms. This paper proposes to utilize a reprojection residual error-based technique for outlier detection. Given a noisy stereo image pair obtained from a pair of stereo cameras and a set of initial point correspondences between them, reprojection residual error and 3-sigma principle together with robust statistic-based Qn estimator (RES-Q) is proposed to efficiently detect the outliers and estimate the fundamental matrix with superior accuracy. The proposed RES-Q algorithm demonstrates greater precision and lower reprojection residual error than the state-of-the-art techniques. Moreover, in contrast to the assumption of Gaussian noise or symmetric noise model adopted by most previous approaches, the RES-Q is found to be robust for both symmetric and asymmetric random noise assumptions. The proposed algorithm is experimentally tested on both synthetic and real image data sets, and the experiments show that RES-Q is more effective and efficient than the classical outlier detection algorithms

Five-Point Fundamental Matrix Estimation for Uncalibrated Cameras

We aim at estimating the fundamental matrix in two views from five correspondences of rotation invariant features obtained by e.g.\ the SIFT detector. The proposed minimal solver first estimates a homography from three correspondences assuming that they are co-planar and exploiting their rotational components. Then the fundamental matrix is obtained from the homography and two additional point pairs in general position. The proposed approach, combined with robust estimators like Graph-Cut RANSAC, is superior to other state-of-the-art algorithms both in terms of accuracy and number of iterations required. This is validated on synthesized data and $561$ real image pairs. Moreover, the tests show that requiring three points on a plane is not too restrictive in urban environment and locally optimized robust estimators lead to accurate estimates even if the points are not entirely co-planar. As a potential application, we show that using the proposed method makes two-view multi-motion estimation more accurate

Graph-Cut RANSAC

A novel method for robust estimation, called Graph-Cut RANSAC, GC-RANSAC in short, is introduced. To separate inliers and outliers, it runs the graph-cut algorithm in the local optimization (LO) step which is applied when a so-far-the-best model is found. The proposed LO step is conceptually simple, easy to implement, globally optimal and efficient. GC-RANSAC is shown experimentally, both on synthesized tests and real image pairs, to be more geometrically accurate than state-of-the-art methods on a range of problems, e.g. line fitting, homography, affine transformation, fundamental and essential matrix estimation. It runs in real-time for many problems at a speed approximately equal to that of the less accurate alternatives (in milliseconds on standard CPU)

Formalization of the General Video Temporal Synchronization Problem

In this work, we present a theoretical formalization of the temporal synchronization problem and a method to temporally synchronize multiple stationary video cameras with overlapping views of the same scene. The method uses a two stage approach that first approximates the synchronization by tracking moving objects and identifying curvature points. The method then proceeds to refine the estimate using a consensus based matching heuristic to find frames that best agree with the pre-computed camera geometries from stationary background image features. By using the fundamental matrix and the trifocal tensor in the second refinement step, we improve the estimation of the first step and handle a broader more generic range of input scenarios and camera conditions. The method is relatively simple compared to current techniques and is no harder than feature tracking in stage one and computing accurate geometries in stage two. We also provide a robust method to assist synchronization in the presence of inaccurate geometry computation, and a theoretical limit on the accuracy that can be expected from any synchronization syste

Robust Inference Under Heteroskedasticity via the Hadamard Estimator

Drawing statistical inferences from large datasets in a model-robust way is an important problem in statistics and data science. In this paper, we propose methods that are robust to large and unequal noise in different observational units (i.e., heteroskedasticity) for statistical inference in linear regression. We leverage the Hadamard estimator, which is unbiased for the variances of ordinary least-squares regression. This is in contrast to the popular White's sandwich estimator, which can be substantially biased in high dimensions. We propose to estimate the signal strength, noise level, signal-to-noise ratio, and mean squared error via the Hadamard estimator. We develop a new degrees of freedom adjustment that gives more accurate confidence intervals than variants of White's sandwich estimator. Moreover, we provide conditions ensuring the estimator is well-defined, by studying a new random matrix ensemble in which the entries of a random orthogonal projection matrix are squared. We also show approximate normality, using the second-order Poincare inequality. Our work provides improved statistical theory and methods for linear regression in high dimensions