In this paper, a globally optimal algorithm based on a maximum feasible subsystem framework is proposed for robust pairwise registration of point cloud data. Registration is formulated as a branch-and-bound problem with mixed-integer linear programming. Among the putative matches of three-dimensional (3D) features between two sets of range data, the proposed algorithm finds the maximum number of geometrically correct correspondences in the presence of incorrect matches, and it estimates the transformation parameters in a globally optimal manner. The optimization requires no initialization of transformation parameters. Experimental results demonstrated that the presented algorithm was more accurate and reliable than state-of-the-art registration methods and showed robustness against severe outliers/mismatches. This global optimization technique was highly effective, even when the geometric overlap between the datasets was very small.

We present photometric stereo algorithms robust to non-Lambertian reflection, which are based on a convolutional neural network in which surface normals of objects with complex geometry and surface reflectance are estimated from a given set of an arbitrary number of images. These images are taken from the same viewpoint under different directional illumination conditions. The proposed method focuses on surface normal estimation, where multi-scale feature aggregation is proposed to obtain a more accurate surface normal, and max pooling is adopted to obtain an intermediate order-agnostic representation in the photometric stereo scenario. The proposed multi-scale feature aggregation scheme using feature concatenation is easily incorporated into existing photometric stereo network architectures. Our experiments were performed with a DiLiGent photometric stereo benchmark dataset consisting of ten real objects, and they demonstrated that the accuracies of our calibrated and uncalibrated photometric stereo approaches were improved over those of baseline methods. In particular, our experiments also demonstrated that our uncalibrated photometric stereo outperformed the state-of-the-art method. Our work is the first to consider the multi-scale feature aggregation in photometric stereo, and we showed that our proposed multi-scale fusion scheme estimated the surface normal accurately and was beneficial to improving performance.