This paper first presents robust algorithms to extract invariants of the linear Lie algebra model from 3D objects. In particular, an extended 3D Hough transform is presented to extract accurate estimates of the normal vectors. The Least square fitting is used to find normal vectors and representation matrices. Then an algorithm of segmentation for 3D objects is shown using the invariants of the linear Lie algebra. Distributions of invariants, both in the invariant space and on the object surface, are used for clustering and edge detection.

Recently, there has been a surge of interest in Artificial Intelligence (AI) and its applications have been considered in various fields. Mobile networks are becoming an indispensable part of our society, and are considered as one of the promising applications of AI. In the Beyond 5G/6G era, AI will continue to penetrate networks and AI will become an integral part of mobile networks. This paper provides an overview of the collaborations between networks and AI from two categories, “AI for Network” and “Network for AI,” and predicts mobile networks in the B5G/6G era. It is expected that the future mobile network will be an integrated infrastructure, which will not only be a mere application of AI, but also provide as the process infrastructure for AI applications. This integration requires a driving application, and the network operation is one of the leading candidates. Furthermore, the paper describes the latest research and standardization trends in the autonomous networks, which aims to fully automate network operation, as a future network operation concept with AI, and discusses research issues in the future mobile networks.

Uniform color spaces are very important in color engineering, image source coding and multimedia information processing. In spite of many efforts have been paid on the subject, however, construction of an exact uniform color space seems difficult until now. Existing approaches mainly used local and heuristic approximations. Moreover, there seemed also certain confusion in definitions of the uniform spaces. In this paper we discuss the issue from a point of view of global Riemannian geometry. The equivalence between global and local definitions of uniform space are shown. Then both an exact and a simplified algorithm are presented to uniformize either a part or the totality of a color space. These algorithms can be expected to find applications in optimal quantization of color information.