The present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of symmetry. By reflecting the points of each set with respect to the plane of symmetry, we can largely increase the overlap between the sets and therefore boost the registration process. However, prior knowledge about the plane of symmetry is generally unavailable or at least very hard to find, especially with limited partial views. Finding this plane could strongly benefit from a prior alignment of the partial point sets. We solve this chicken-and-egg problem by jointly optimizing the relative pose and symmetry plane parameters. We present a globally optimal solver by employing the branch-and-bound paradigm and thereby demonstrate that joint symmetry plane fitting leads to a great improvement over the current state of the art in globally optimal point set registration for common objects. We conclude with an interesting application of our method to dense 3D reconstruction of scenes with repetitive objects.
Missing data is a common problem in credit evaluation practice and can obstruct the development and application of an evaluation model. Block-wise missing data is a particularly troublesome issue. Based on multi-task feature selection approach, this paper proposes a method called MMPFS to build a model for credit evaluation that primarily includes two steps: (1) dividing the dataset into several nonoverlapping subsets based on missing patterns, and (2) integrating the multi-task feature selection approach using logistic regression to perform joint feature learning on all subsets. The proposed method has the following advantages: (1) missing data do not need to be managed in advance, (2) available data can be fully used for model learning, (3) information loss or bias caused by general missing data processing methods can be avoided, and (4) overfitting risk caused by redundant features can be reduced. The implementation framework and algorithm principle of the proposed method are described, and three credit datasets from UCI are investigated to compare the proposed method with other commonly used missing data treatments. The results show that MMPFS can produce a better credit evaluation model than data preprocessing methods, such as sample deletion and data imputation.
