Optimal Randomized RANSAC

A randomized model verification strategy for RANSAC is presented. The proposed method finds, like RANSAC, a solution that is optimal with user-specified probability. The solution is found in time that is close to the shortest possible and superior to any deterministic verification strategy. A provably fastest model verification strategy is designed for the (theoretical) situation when the contamination of data by outliers is known. In this case, the algorithm is the fastest possible (on the average) of all randomized RANSAC algorithms guaranteeing a confidence in the solution. The derivation of the optimality property is based on Wald's theory of sequential decision making, in particular, a modified sequential probability ratio test (SPRT). Next, the R-RANSAC with SPRT algorithm is introduced. The algorithm removes the requirement for a priori knowledge of the fraction of outliers and estimates the quantity online. We show experimentally that on standard test data, the method has performance close to the theoretically optimal and is 2 to 10 times faster than standard RANSAC and is up to four times faster than previously published methods

Superpixel-based Two-view Deterministic Fitting for Multiple-structure Data

This paper proposes a two-view deterministic geometric model fitting method, termed Superpixel-based Deterministic Fitting (SDF), for multiple-structure data. SDF starts from superpixel segmentation, which effectively captures prior information of feature appearances. The feature appearances are beneficial to reduce the computational complexity for deterministic fitting methods. SDF also includes two original elements, i.e., a deterministic sampling algorithm and a novel model selection algorithm. The two algorithms are tightly coupled to boost the performance of SDF in both speed and accuracy. Specifically, the proposed sampling algorithm leverages the grouping cues of superpixels to generate reliable and consistent hypotheses. The proposed model selection algorithm further makes use of desirable properties of the generated hypotheses, to improve the conventional fit-and-remove framework for more efficient and effective performance. The key characteristic of SDF is that it can efficiently and deterministically estimate the parameters of model instances in multi-structure data. Experimental results demonstrate that the proposed SDF shows superiority over several state-of-the-art fitting methods for real images with single-structure and multiple-structure data.Comment: Accepted by European Conference on Computer Vision (ECCV

Randomized hybrid linear modeling by local best-fit flats

The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in a D-dimensional Euclidean space. It arises, for example, in object tracking and structure from motion. The hybrid linear model can be considered as the second simplest (behind linear) manifold model of data. In this paper we will present a very simple geometric method for hybrid linear modeling based on selecting a set of local best fit flats that minimize a global l1 error measure. The size of the local neighborhoods is determined automatically by the Jones' l2 beta numbers; it is proven under certain geometric conditions that good local neighborhoods exist and are found by our method. We also demonstrate how to use this algorithm for fast determination of the number of affine subspaces. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the algorithm on synthetic and real hybrid linear data.Comment: To appear in the proceedings of CVPR 201

Learning how to be robust: Deep polynomial regression

Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased results when the input data is heavily contaminated by outliers. Moreover, the problem is even harder when outliers have strong structure. Departing from problem-tailored heuristics for robust estimation of parametric models, we explore deep convolutional neural networks. Our work aims to find a generic approach for training deep regression models without the explicit need of supervised annotation. We bypass the need for a tailored loss function on the regression parameters by attaching to our model a differentiable hard-wired decoder corresponding to the polynomial operation at hand. We demonstrate the value of our findings by comparing with standard robust regression methods. Furthermore, we demonstrate how to use such models for a real computer vision problem, i.e., video stabilization. The qualitative and quantitative experiments show that neural networks are able to learn robustness for general polynomial regression, with results that well overpass scores of traditional robust estimation methods.Comment: 18 pages, conferenc