text: Geometric model fitting is a fundamental research topic in computer vision and it aims to fit and segment multiple-structure data. In this paper, we propose a novel superpixel-guided two-view geometric model fitting method (called SDF), which can obtain reliable and consistent results for real images. Specifically, SDF includes three main parts: a deterministic sampling algorithm, a model hypothesis updating strategy and a novel model selection algorithm. The proposed deterministic sampling algorithm generates a set of initial model hypotheses according to the prior information of superpixels. Then the proposed updating strategy further improves the quality of model hypotheses. After that, by analyzing the properties of the updated model hypotheses, the proposed model selection algorithm extends the conventional "fit-and-remove" framework to estimate model instances in multiple-structure data. The three parts are tightly coupled to boost the performance of SDF in both speed and accuracy, and SDF has the deterministic nature. Experimental results show that the proposed SDF has significant advantages over several state-of-the-art fitting methods when it is applied to real images with single-structure and multiple-structure data.
  @cite_35: Finding the largest consensus set is one of the key ideas used by the original RANSAC for removing outliers in robust-estimation. However, because of its random and non-deterministic nature, RANSAC does not fulfill the goal of consensus set maximization exactly and optimally. Based on global optimization, this paper presents a new algorithm that solves the problem exactly. We reformulate the problem as a mixed integer programming (MIP), and solve it via a tailored branch-and-bound method, where the bounds are computed from the MIP's convex under-estimators. By exploiting the special structure of linear robust-estimation, the new algorithm is also made efficient from a computational point of view.
  @cite_26: 
  @cite_4: Outliers pose a problem in all real structure from motion systems. Due to the use of automatic matching methods one has to expect that a (sometimes very large) portion of the detected correspondences can be incorrect. In this paper we propose a method that estimates the relative translation between two cameras and simultaneously maximizes the number of inlier correspondences. Traditionally, outlier removal tasks have been addressed using RANSAC approaches. However, these are random in nature and offer no guarantees of finding a good solution. If the amount of mismatches is large, the approach becomes costly because of the need to evaluate a large number of random samples. In contrast, our approach is based on the branch and bound methodology which guarantees that an optimal solution will be found. While most optimal methods trade speed for optimality, the proposed algorithm has competitive running times on problem sizes well beyond what is common in practice. Experiments on both real and synthetic data show that the method outperforms state-of-the-art alternatives, including RANSAC, in terms of solution quality. In addition, the approach is shown to be faster than RANSAC in settings with a large amount of outliers.
  @cite_16: Maximum consensus is one of the most popular criteria for robust estimation in computer vision. Despite its widespread use, optimising the criterion is still customarily done by randomised sample-and-test techniques, which do not guarantee optimality of the result. Several globally optimal algorithms exist, but they are too slow to challenge the dominance of randomised methods. We aim to change this state of affairs by proposing a very efficient algorithm for global maximisation of consensus. Under the framework of LP-type methods, we show how consensus maximisation for a wide variety of vision tasks can be posed as a tree search problem. This insight leads to a novel algorithm based on A* search. We propose efficient heuristic and support set updating routines that enable A* search to rapidly find globally optimal results. On common estimation problems, our algorithm is several orders of magnitude faster than previous exact methods. Our work identifies a promising solution for globally optimal consensus maximisation.
  @cite_24: Although the problem of determining the minimum cost path through a graph arises naturally in a number of interesting applications, there has been no underlying theory to guide the development of efficient search procedures. Moreover, there is no adequate conceptual framework within which the various ad hoc search strategies proposed to date can be compared. This paper describes how heuristic information from the problem domain can be incorporated into a formal mathematical theory of graph searching and demonstrates an optimality property of a class of search strategies.
  @cite_34: This work presents a novel approach for detecting inliers in a given set of correspondences (matches). It does so without explicitly identifying any consensus set, based on a method for inlier rate estimation (IRE). Given such an estimator for the inlier rate, we also present an algorithm that detects a globally optimal transformation. We provide a theoretical analysis of the IRE method using a stochastic generative model on the continuous spaces of matches and transformations. This model allows rigorous investigation of the limits of our IRE method for the case of 2D-translation, further giving bounds and insights for the more general case. Our theoretical analysis is validated empirically and is shown to hold in practice for the more general case of 2D-affinities. In addition, we show that the combined framework works on challenging cases of 2D-homography estimation, with very few and possibly noisy inliers, where RANSAC generally fails.
  @cite_17: What is the computational complexity of geometric model estimation in the presence of noise and outliers? We show that the number of outliers can be minimized in polynomial time with respect to the number of measurements, although exponential in the model dimension. Moreover, for a large class of problems, we prove that the statistically more desirable truncated @math L2-norm can be optimized with the same complexity. In a similar vein, it is also shown how to transform a multi-model estimation problem into a purely combinatorial one--with worst-case complexity that is polynomial in the number of measurements but exponential in the number of models. We apply our framework to a series of hard fitting problems. It gives a practical method for simultaneously dealing with measurement noise and large amounts of outliers in the estimation of low-dimensional models. Experimental results and a comparison to random sampling techniques are presented for the applications rigid registration, triangulation and stitching.
summary: Deterministic sampling based fitting methods (e.g., @cite_26 @cite_35 @cite_34 @cite_4 @cite_17 @cite_16 ) are able to provide consistent and reliable fitting results. For example, Li @cite_35 used a tailored branch-and-bound scheme to deterministically solve the global optimization problem for model fitting. @cite_26 deterministically generated model hypotheses based on the maximum feasible subsystem framework for model fitting. @cite_34 employed a method for inlier rate estimation to compute a globally optimal transformation for model fitting. @cite_4 extended a branch-and-bound scheme to solve the two-view translation estimation problem. @cite_17 proposed to use loss functions to perform model estimation. @cite_16 used the Astar search algorithm @cite_24 to provide a globally optimal solution for the model fitting problem.