ノンパラメトリック連続センサ位置合わせ
Nonparametric Continuous Sensor Registration
再生核ヒルベルト空間とリー群を用いて連続関数の意味的・幾何学的同時表現を可能にし、解像度に依存しない位置合わせを実現した論文。RGB-Dカメラへの実装でロバストな視覚オドメトリ性能を示す。
著者: William Clark, Maani Ghaffari, Anthony Bloch
分類: math.OC, cs.CV, cs.LG, cs.RO
原文アブストラクト
This paper develops a new mathematical framework that enables nonparametric joint semantic and geometric representation of continuous functions using data. The joint embedding is modeled by representing the processes in a reproducing kernel Hilbert space. The functions can be defined on arbitrary smooth manifolds where the action of a Lie group aligns them. The continuous functions allow the registration to be independent of a specific signal resolution. The framework is fully analytical with a closed-form derivation of the Riemannian gradient and Hessian. We study a more specialized but widely used case where the Lie group acts on functions isometrically. We solve the problem by maximizing the inner product between two functions defined over data, while the continuous action of the rigid body motion Lie group is captured through the integration of the flow in the corresponding Lie algebra. Low-dimensional cases are derived with numerical examples to show the generality of the proposed framework. The high-dimensional derivation for the special Euclidean group acting on the Euclidean space showcases the point cloud registration and bird's-eye view map registration abilities. An implementation of this framework for RGB-D cameras outperforms the state-of-the-art robust visual odometry and performs well in texture and structure-scarce environments.
