A Branch-and-Bound Approach to Correspondence and Grouping Problems

Abstract

Abstract-Data correspondence/grouping under an unknown parametric model is a fundamental topic in computer vision. Finding feature correspondences between two images is probably the most popular application of this research field, and is the main motivation of our work. It is a key ingredient for a wide range of vision tasks, including three-dimensional reconstruction and object recognition. Existing feature correspondence methods are based on either local appearance similarity or global geometric consistency or a combination of both in some heuristic manner. None of these methods is fully satisfactory, especially in the presence of repetitive image textures or mismatches. In this paper, we present a new algorithm that combines the benefits of both appearance-based and geometry-based methods and mathematically guarantees a global optimization. Our algorithm accepts the two sets of features extracted from two images as input, and outputs the feature correspondences with the largest number of inliers, which verify both the appearance similarity and geometric constraints. Specifically, we formulate the problem as a mixed integer program and solve it efficiently by a series of linear programs via a branch-and-bound procedure. We subsequently generalize our framework in the context of data correspondence/grouping under an unknown parametric model and show it can be applied to certain classes of computer vision problems. Our algorithm has been validated successfully on synthesized data and challenging real images.

Globally Optimal 2D-3D Registration from Points or Lines without Correspondences

“…[2]. In a naive form they may only be applied to linear transformations, so to be more widely applicable nonlinear constraints are relaxed into linear convex and concave envelopes (e.g.…”

“…In a naive form they may only be applied to linear transformations, so to be more widely applicable nonlinear constraints are relaxed into linear convex and concave envelopes (e.g. [27,2]). Alternatively, Jurie [18] approximates perspective pose by orthographic pose to create a linear 2D-3D registration problem that is solved by similar techniques, however its use of the Gaussian error model results in an approach that is not robust to outliers.…”

Point Matching in the Presence of Outliers in Both Point Sets: A Concave Optimization Approach

“…In contrast, our method can handle outliers in both point sets. In [1], BnB was used to find the maximum set of consistent point correspondences. But the method is very slow because a generic linear program needs to be solved to obtain the upper bound.…”

“…Let is a large but sparse matrix and can be implemented using the function speye in Matlab. 1 We omit the constant θ T 0 Hθ 0 since it doesn't affect the optimization. 2 This is different from the conventional definition.…”

Data association using relative compatibility of multiple observations for EKF-SLAM

“…The matching problem was represented in interpretation tree and searching space was bound by branch and bound scheme [11]. Similar concepts have been used by several researchers [12][13][14]. Bailey et al proposed a data association scheme which considers relative geometry in two laser scans [15].…”