Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration

Abstract

Abstract-The Iterative Closest Point (ICP) algorithm is one of the most widely used methods for point-set registration. However, being based on local iterative optimization, ICP is known to be susceptible to local minima. Its performance critically relies on the quality of the initialization and only local optimality is guaranteed. This paper presents the first globally optimal algorithm, named Go-ICP, for Euclidean (rigid) registration of two 3D point-sets under the L 2 error metric defined in ICP. The Go-ICP method is based on a branch-and-bound (BnB) scheme that searches the entire 3D motion space SE(3). By exploiting the special structure of SE(3) geometry, we derive novel upper and lower bounds for the registration error function. Local ICP is integrated into the BnB scheme, which speeds up the new method while guaranteeing global optimality. We also discuss extensions, addressing the issue of outlier robustness. The evaluation demonstrates that the proposed method is able to produce reliable registration results regardless of the initialization. Go-ICP can be applied in scenarios where an optimal solution is desirable or where a good initialization is not always available.Index Terms-3D point-set registration, global optimization, branch-and-bound, SE(3) space search, iterative closest point !

Calculation of Talocrural Joint Axis Motion by Approximating Trochlea Tali with Conical Side Surface

“…The four coordinate systems of the tibia in the four combined postures must be matched to the initial posture. In this study, the globally optimal iterative closest point (Go-ICP) algorithm was used for an objective and highly accurate matching of each coordinate system [12,13]. The Go-ICP algorithm is one of the automated 3D registration methods, which is composed of the branch and bound and voxel ICP and can efficiently derive an optimal solution.…”

A Review of Point Feature Based Medical Image Registration

“…Nevertheless, the ICP algorithm suffers from its accurate demands of an initial estimation and limited application for only rigid transformations considerably. Another drawback that confines the application of the ICP approach is that the local minimum is obtained ultimately instead of a global minimum, even though Yang et al [46] introduced a globally optimal solution Go-ICP based on the branch-and-bound algorithm under the L2-norm closest-point error metric. Another application is to combine the ICP algorithm with some global algorithms to obtain a global minimum [19,29].…”

“…Consequently, the first step of the segmentation and 3D reconstruction, which is based on the slices, is to register the upper and lower adjacent slice images. Although the active contour and active shape methods [46,88,89] have been proposed for the registration of slice images, the two main drawbacks of slice registration have not been conquered fundamentally. One drawback is that the quality of the initial position directly affects the registration result and speed, and the other is that the robustness and precision is rapidly reduced when there are inter-subject anatomical variabilities.…”

Registration with Adjacent Anatomical Structures for Cardiac Resynchronization Therapy Guidance

“…for the initial cube, where (r 0 , t 0 ) represents the center of the 3D motion domain C r × C t and γ is the uncertainty radius [10]. If the current error estimate E * is close to E, the solution is found.…”

“…It is additionally much more efficient than the standard BnB algorithm, since even if it explores the whole possible solution space, it refines the intermediate results with the ICP method, thus benefitting from the good attributes of both algorithms. It has been shown that the algorithm is well suited to registering partial surfaces, has high noise tolerance and is robust to outliers [10] .…”