Regression of 3D Rigid Transformations on Real-Valued Vectors in Closed Form

Takuya Funatomi, Masaaki Iiyama, Koh Kakusho, Michihiko Minoh

Abstract: In this paper, we present a regression for predict-ing 3D rigid transformations from real-valued vectors. We usea unit dual quaternion to represent the transformation. Theregression is formulated as blending unit dual quaternions. Toformulate it in a closed form, we introduce an approximationbased on error metrics according to geometric algebra. Finally,we take an articulated motion and an elastic deformation asexamples to present the descriptive power of our method inmodeling the motion and the deformation.