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Robust point set registration is a challenging problem, especially in the cases of noise, outliers, and partial overlapping. Previous methods generally formulate their objective functions based on the mean-square error (MSE) loss and, hence, are only able to register point sets under predefined constraints (e.g., with Gaussian noise). This article proposes a novel objective function based on a bidirectional kernel mean ${p}$ -power error (KMPE) loss, to jointly deal with the above nonideal situations. KMPE is a nonsecond-order similarity measure in kernel space and shows a strong robustness against various noise and outliers. Moreover, a bidirectional measure is applied to judge the registration, which can avoid the ill-posed problem when a lot of points converges to the same point. In particular, we develop two effective optimization methods to deal with the point set registrations with the similarity and the affine transformations, respectively. The experimental results demonstrate the effectiveness of our methods.

Taking “divide-and-conquer” as a basic idea, cooperative coevolution (CC) has shown a promising prospect in large scale global optimization. However, its high requirement on the decomposition accuracy can hardly be satisfied in practice. Directing against this issue, this study proposes a bi-hierarchical cooperative coevolution (BHCC), which can tolerate a certain degree of decomposition error. Besides the cooperation among sub-problems as in the conventional CC, BHCC introduces a kind of cooperation between sub-problems and the overall problem. By systematically exploiting the excellent sub-solutions obtained during the sub-space optimization process, it initializes the population for the optimization process on the overall problem and thus can conduct search in promising regions of the whole solution space. The newly acquired complete solutions are in turn employed to update the context vector and the population of each sub-problem, where the context vector is used for sub-solution evaluation. Consequently, the search direction misdirected by an improper decomposition can be corrected to a great extent. To keep the balance between the two types of optimization processes, an adaptive triggering mechanism for the overall optimization process is specially designed for BHCC. Experimental results on two widely-used benchmark suites verify the effectiveness of the new strategies in BHCC and also indicate that BHCC is more robust than existing CCs and can achieve competitive performance compared with several state-of-the-art algorithms.

With the development of RGBD sensors, the high-quality color point cloud can be obtained expediently. In this paper, we propose a novel registration method for 3D color point clouds from different views, which is a critical issue in many applications. Different from traditional feature-based methods, we design a hybrid feature representation with color moments of the point, which could be applied naturally for any color point cloud. And these features are extracted from point clouds based on the supervoxel segmentation. By jointly conducting these features for similarity measure, a weight parameter is dynamically adapted between the color and the spatial information. The registration algorithm is under a classic iterative framework for building the correspondence and estimating transformation parameters. In addition, we provide a mutual correspondence matching condition with hybrid features to build some more robust relationships for estimating transformation parameters. Experimental results demonstrate that our method can effectively reduce the number of point data for registration and achieve good matching results even in a poor initial condition.

It has been shown that cooperative coevolution (CC) can effectively deal with large scale optimization problems (LSOPs) through a ‘divide-and-conquer’ strategy. However, its performance is severely restricted by the current context-vector-based sub-solution evaluation method, since this method needs to invoke the original high dimensional simulation model when evaluating each sub-solution, thus requiring many computation resources. To alleviate this issue, this study proposes a novel surrogate model assisted cooperative coevolution (SACC) framework. SACC constructs a surrogate model for each sub-problem and employs it to evaluate corresponding sub-solutions. The original simulation model is only adopted to reevaluate a small number of promising sub-solutions selected by surrogate models, and these really evaluated sub-solutions will in turn be employed to update surrogate models. By this means, the computation cost could be greatly reduced without significantly sacrificing evaluation quality. By taking the radial basis function (RBF) and the success-history based adaptive differential evolution (SHADE) as surrogate model and optimizer, respectively, this study further designs a concrete SACC algorithm named RBF-SHADE-SACC. RBF and SHADE have only been proved to be effective on small and medium scale problems. This study scales them up to LSOPs under the SACC framework, where they are tailored to a certain extent for adapting to the characteristics of LSOPs and SACC. Empirical studies on IEEE CEC 2010 benchmark functions demonstrate that SACC can significantly enhance the sub-solution evaluation efficiency, and even with much fewer computation resources, RBF-SHADE-SACC can find much better solutions than traditional CC algorithms.

Divide-and-conquer-based (DC-based) evolutionary algorithms (EAs) have achieved notable success in dealing with large-scale optimization problems (LSOPs). However, the appealing performance of this type of algorithms generally requires a high-precision decomposition of the optimization problem, which is still a challenging task for existing decomposition methods. This study attempts to address the above issue from a different perspective and proposes an eigenspace divide-and-conquer (EDC) approach. Different from existing DC-based algorithms that perform decomposition and optimization in the original solution space, EDC first establishes an eigenspace by conducting singular value decomposition on a set of high-quality solutions selected from recent generations. Then it transforms the optimization problem into the eigenspace, and thus significantly weakens the dependencies among the corresponding eigenvariables. Accordingly, these eigenvariables can be efficiently grouped by a simple random decomposition strategy and each of the resulting subproblems can be addressed more easily by a traditional EA. To verify the efficiency of EDC, comprehensive experimental studies were conducted on two sets of benchmark functions. Experimental results indicate that EDC is robust to its parameters and has good scalability to the problem dimension. The comparison with several state-of-the-art algorithms further confirms that EDC is pretty competitive and performs better on complicated LSOPs.